Consider the system of inequalities,

3x+2y≥-19

x+3y<-11

​​Enter three different points, separated by commas, that are solutions to the system of inequalities.


Enter three different points, separated by commas, that are not solutions to the system of inequalities.

Answers

Answer 1

The system of inequalities is solved and the solutions are ( -5, - 2 )

Given data ,

Let the first inequality be A , 3x+2y≥-19

Let the second inequality be B , x+3y<-11

On simplifying , we get

The solution to the inequality is the point of intersection of the graph

Now , on plotting the graph , we get

The point of intersection is P ( -5 , -2 ) and the solution is point P

And , the points which are not a solution is Q ( 1 , -5 ) , ( 0 , 0 )

Hence , the system of inequalities are solved

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ1

Consider The System Of Inequalities,3x+2y-19x+3y&lt;-11Enter Three Different Points, Separated By Commas,

Related Questions

An item is regularly priced at $55 . It is on sale for $40 off the regular price. What is the sale price?

Answers

Answer:22

Step-by-step explanation:

First you put

40/100

and that makes

11/22

how many partitions of 2 parts can be amde of {1,2,...100}

Answers

There are [tex](1/2) * (2^{100} - 2)[/tex] partitions of {1, 2, ..., 100} into two parts.

How to find the number of partitions of {1, 2, ..., 100} into two parts?

We can use the following formula:

Number of partitions = (n choose k)/2, where n is the total number of elements, and k is the number of elements in one of the two parts.

In this case, we want to divide the set {1, 2, ..., 100} into two parts, each with k elements.

Since we are not distinguishing between the two parts, we divide the total number of partitions by 2.

The number of ways to choose k elements from a set of n elements is given by the binomial coefficient (n choose k).

So the number of partitions of {1, 2, ..., 100} into two parts is:

(100 choose k)/2

where k is any integer between 1 and 99 (inclusive).

To find the total number of partitions, we need to sum this expression for all values of k between 1 and 99:

Number of partitions = (100 choose 1)/2 + (100 choose 2)/2 + ... + (100 choose 99)/2

This is equivalent to:

Number of partitions = (1/2) * ([tex]2^{100}[/tex] - 2)

Therefore, there are (1/2) * ([tex]2^{100][/tex] - 2) partitions of {1, 2, ..., 100} into two parts.

Learn more about partitions of a set into two parts

brainly.com/question/18651359

#SPJ11

Sam is competing in a diving event at a swim meet. When it's his turn, he jumps upward off
the diving board at a height of 10 meters above the water with a velocity of 4 meters per
second.
Which equation can you use to find how many seconds Sam is in the air before entering the
water?
If an object travels upward at a velocity of v meters per second from s meters above the
ground, the object's height in meters, h, after t seconds can be modeled by the formula
h = -4.9t² vt + s.
0 -4.9t² + 4t + 10
10 = -4.9t² + 4t
To the nearest tenth of a second, how long is Sam in the air before entering the water?

Answers

The time is 4.6 seconds when Sam enters the water again

How to solve the equation

So, we have the equation:

0 = -4.9t² + 4t + 10

Now, we can solve this quadratic equation for t using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

In our equation, a = -4.9, b = 4, and c = 10.

t = (-4 ± √(4² - 4(-4.9)(10))) / 2(-4.9)

t = (-4 ± √(16 + 196)) / (-9.8)

t = (-4 ± √212) / (-9.8)

The two possible values for t are:

t ≈ 0.444 (when Sam is at the surface of the water, just after jumping)

t ≈ 4.597 (when Sam enters the water again)

Read more on quadratic equation here:https://brainly.com/question/1214333

#SPJ1

Answer: The time is 4.6 seconds when Sam enters the water again

How to solve the equation

So, we have the equation:

0 = -4.9t² + 4t + 10

Now, we can solve this quadratic equation for t using the quadratic  formula:

t = (-b ± √(b² - 4ac)) / 2a

In our equation, a = -4.9, b = 4, and c = 10.

t = (-4 ± √(4² - 4(-4.9)(10))) / 2(-4.9)t = (-4 ± √(16 + 196)) / (-9.8)t = (-4 ± √212) / (-9.8)

The two possible values for t are:

t ≈ 0.444 (when Sam is at the surface of the water, just after jumping)

t ≈ 4.597 (when Sam enters the water again)


Read more on quadratic equation here:

brainly.com/question/1214333#SPJ1

find the limit. use l'hospital's rule where appropriate. if there is a more elementary method, consider using it. lim x→7 x − 7 x2 − 49

Answers

The limit of the given expression as x approaches 7 is 1/14.

How to find the limit?

To evaluate the limit:

lim x → 7 (x - 7) / ([tex]x^2[/tex] - 49)

We can see that this is an indeterminate form of type 0/0, since both the numerator and denominator approach 0 as x approaches 7. We can use L'Hospital's rule to evaluate this limit:

lim x → 7 (x - 7) / ([tex]x^2[/tex] - 49)

= lim x → 7 1 / (2x) [by applying L'Hospital's rule once]

= 1 / 14 [substituting x = 7]

Therefore, the limit of the given expression as x approaches 7 is 1/14.

Learn more about l'hospital's rule

brainly.com/question/14105620

#SPJ11

Use the Chain Rule to find the indicated partial derivatives.
u =
r2 + s2
, r = y + x cos t, s = x + y sin t
∂u
∂x
∂u
∂y
∂u
∂t
when x = 4, y = 5, t = 0
∂u
∂x
= ∂u
∂y
= ∂u
∂t
=

Answers

The partial derivatives of u with respect to x, y, and t are, [tex]\dfrac{\partial u}{\partial x}[/tex] = 22, [tex]\dfrac{\partial u}{\partial y}[/tex] = 18 and [tex]\dfrac{\partial u}{\partial t}[/tex] = 40.

We can use the chain rule to find the partial derivatives of u with respect to x, y, and t.

First, we will find the partial derivative of u with respect to r and s:

u = r² + s²

[tex]\dfrac{\partial u}{\partial r}[/tex] = 2r

[tex]\dfrac{\partial u}{\partial s}[/tex] = 2s

Next, we will find the partial derivatives of r with respect to x, y, and t:

r = y + xcos(t)

[tex]\dfrac{\partial r}{\partial x}[/tex] = cos(t)

[tex]\dfrac{\partial r}{\partial y}[/tex] = 1

[tex]\dfrac{\partial r}{\partial t}[/tex] = -xsin(t)

Similarly, we will find the partial derivatives of s with respect to x, y, and t:

s = x + ysin(t)

[tex]\dfrac{\partial s}{\partial x}[/tex] = 1

[tex]\dfrac{\partial s}{\partial y}[/tex] = sin(t)

[tex]\dfrac{\partial s}{\partial t}[/tex] = ycos(t)

Now, we can use the chain rule to find the partial derivatives of u with respect to x, y, and t:

[tex]\dfrac{\partial u}{\partial x} = \dfrac{\partial u}{\partial r} \times \dfrac{\partial r}{\partial x} + \dfrac{\partial u}{\partial s} \times \dfrac{\partial s}{\partial x}[/tex]

[tex]\dfrac{\partial u}{\partial x}[/tex] = 2r * cos(t) + 2s * 1

At x = 4, y = 5, t = 0, we have:

r = 5 + 4cos(0) = 9

s = 4 + 5sin(0) = 4

Substituting these values into the partial derivative formula, we get:

[tex]\dfrac{\partial u}{\partial x}[/tex] = 2(9)(1) + 2(4)(1) = 22

Similarly, we can find the partial derivatives with respect to y and t:

[tex]\dfrac{\partial u}{\partial y} = \dfrac{\partial u}{\partial r} \times \dfrac{\partial r}{\partial y} + \dfrac{\partial u}{\partial s} \times \dfrac{\partial s}{\partial y}[/tex]

[tex]\dfrac{\partial u}{\partial y}[/tex] = 2r * 1 + 2s * sin(t)

[tex]\dfrac{\partial u}{\partial t}[/tex] = 2(9)(1) + 2(4)(0) = 18

[tex]\dfrac{\partial u}{\partial t} = \dfrac{\partial u}{\partial r} \times \dfrac{\partial r}{\partial t} + \dfrac{\partial u}{\partial s} \times \dfrac{\partial s}{\partial t}[/tex]

[tex]\dfrac{\partial u}{\partial t}[/tex] = 2r * (-xsin(t)) + 2s * (ycos(t))

[tex]\dfrac{\partial u}{\partial t}[/tex] = 2(9)(-4sin(0)) + 2(4)(5cos(0)) = 40

Therefore, the partial derivatives of u with respect to x, y, and t are:

[tex]\dfrac{\partial u}{\partial x}[/tex] = 22

[tex]\dfrac{\partial u}{\partial y}[/tex] = 18

[tex]\dfrac{\partial u}{\partial t}[/tex] = 40

To know more about partial derivatives, here

https://brainly.com/question/31397807

#SPJ4

find the running time equation of this program: def prob6(l): if len(l)<2: return 1 left = l[len(0) : len(l)//2] s = 0 for x in left: s = x return s prob6(left)

Answers

To get the running time equation of the given program, let's analyse it step by step.


The program consists of the following operations:
Step:1. Check if the length of the list is less than 2.
Step:2. Divide the list into two parts (left and right).
Step:3. Iterate through the left part and calculate the sum.
Step:4. Call the function recursively on the left part.
The running time equation can be represented as T(n), where n is the length of the list. The steps can be analyzed as follows:
1. The comparison takes constant time, so O(1).
2. Dividing the list also takes constant time, O(1).
3. Iterating through the left part takes O(n/2) as it processes half of the list.
4. Recursively calling the function with half of the list will have a running time of T(n/2).
Putting everything together, we get the following equation: T(n) = T(n/2) + O(n/2) + O(1)
This represents the running time equation of the given program.

Learn more about running time equation here, https://brainly.com/question/18075422

#SPJ11

Bus stops A, B, C, and D are on a straight road. The distance from A to D is exactly 1 km. The distance from B to C is 2 km. The distance from B to D is 3 km, the distance from A to B is 4 km, and the distance from C to D is 5 km. What is the distance between stops A and C?

Answers

Okay, let's think this through step-by-step:

* A to D is 1 km

* B to C is 2 km

* B to D is 3 km

* A to B is 4 km

* C to D is 5 km

So we have:

A -> B = 4 km

B -> C = 2 km

C -> D = 5 km

We want to find A -> C.

A -> B is 4 km

B -> C is 2 km

So A -> C = 4 + 2 = 6 km

Therefore, the distance between stops A and C is 6 km.

Suppose that {an}n-1 is a sequence of positive terms and set sn= m_, ak. Suppose it is known that: 1 lim an+1 11-00 Select all of the following that must be true. 1 ak must converge. 1 ak must converge to 1 must converge. {sn} must be bounded. {sn) is monotonic. lim, + 8. does not exist. ? Check work Exercise.

Answers

From the given information, we know that {an} is a sequence of positive terms, so all of its terms are greater than 0. We also know that sn = m∑ ak, which means that sn is a sum of a finite number of positive terms.

Now, let's look at the given limit: lim an+1 = 0 as n approaches infinity. This tells us that the terms of {an} must approach 0 as n approaches infinity since the limit of an+1 is dependent on the limit of an. Therefore, we can conclude that {an} is a decreasing sequence of positive terms. Using this information, we can determine the following:- ak must converge: Since {an} is decreasing and positive, we know that the terms of {ak} are also decreasing and positive. Therefore, {ak} must converge by the Monotone Convergence Theorem. - ak must converge to 0: Since {an} approaches 0 as n approaches infinity, we know that the terms of {ak} must also approach 0. Therefore, {ak} must converge to 0.
- {sn} must be bounded: Since {ak} converges to 0, we know that there exists some N such that ak < 1 for all n > N. Therefore, sn < m(N-1) + m for all n > N. This shows that {sn} is bounded above by some constant.
- {sn} is monotonic: Since {an} is decreasing and positive, we know that {ak} is also decreasing and positive. Therefore, sn+1 = sn + ak+1 < sn, which shows that {sn} is a decreasing sequence. - limn→∞ sn does not exist: Since {an} approaches 0 as n approaches infinity, we know that {sn} approaches a finite limit if and only if {ak} approaches a nonzero limit. However, we know that {ak} approaches 0, so {sn} does not approach a finite
Therefore, the correct answers
- ak must converge
- ak must converge to 0
- {sn} must be bounded
- {sn} is monotonic
- limn→∞ sn does not exist

Learn more about finite number here:brainly.com/question/1622435

#sPJ11

Julie is using the set {7,8,9,10,11} to solve the inequality shown. 2h-3>15 Select all of the solutions to the inequality.

Answers

Answer:

10,11

Step-by-step explanation:

Solving inequality:

Givne set: {7, 8 , 9 , 10 , 11}

To solve the inequality, isolate 'h'.

        2h - 3 > 15

Add 3 to both sides,

     2h - 3 + 3 > 15 + 3

               2h  > 18

Divide both sides by 2,

                [tex]\sf \dfrac{2h}{2} > \dfrac{18}{2}[/tex]

                 h > 9

h = {10 , 11}

in each of the problems 7 through 9 find the inverse laplace transform of the given function by using the convolution theoremf(s)=1/(s +1)^2 (s^2+ 4)

Answers

The inverse Laplace transform of f(s) is: f(t) = -2t*u(t)[tex]e^{-t}[/tex] - 4u(t)[tex]e^{-t}[/tex]+ 4u(t)

What is convolution theorem?

The convolution theorem is a fundamental result in mathematics and signal processing that relates the convolution operation in the time domain to multiplication in the frequency domain.

To find the inverse Laplace transform of the given function, we will use the convolution theorem, which states that the inverse Laplace transform of the product of two functions is the convolution of their inverse Laplace transforms.

We can rewrite the given function as:

f(s) = 1/(s+1)² * (s² + 4)

Taking the inverse Laplace transform of both sides, we get:

[tex]L^{-1}[/tex]{f(s)} = [tex]L^{-1}[/tex]{1/(s+1)²} *[tex]L^{-1}[/tex]{s² + 4}

We can use partial fraction decomposition to find the inverse Laplace transform of 1/(s+1)²:[tex]e^{-t}[/tex]

1/(s+1)² = d/ds(-1/(s+1))

Thus, [tex]L^{-1}[/tex]{1/(s+1)²} = -t*[tex]e^{-t}[/tex]

To find the inverse Laplace transform of s²+4, we can use the table of Laplace transforms and the property of linearity of the Laplace transform:

L{[tex]t^{n}[/tex]} = n!/[tex]s^{(n+1)}[/tex]

L{4} = 4/[tex]s^{0}[/tex]

[tex]L^{-1}[/tex]{s² + 4} = L^-1{s²} + [tex]L^{-1}[/tex]{4} = 2*d²/dt²δ(t) + 4δ(t)

Now, we can use the convolution theorem to find the inverse Laplace transform of f(s):

[tex]L^{-1}[/tex]{f(s)} = [tex]L^{-1}[/tex]{1/(s+1)²} * [tex]L^{-1}[/tex]{s² + 4} = (-te^(-t)) * (2d²/dt²δ(t) + 4δ(t))

Simplifying this expression, we get:

[tex]L^{-1}[/tex]{f(s)} = -2[tex]te^{-t}[/tex]δ''(t) - 4[tex]te^{-t}[/tex]δ'(t) + 4[tex]e^{-t}[/tex]δ(t)

Therefore, the inverse Laplace transform of f(s) is:

f(t) = -2t*u(t)[tex]e^{-t}[/tex] - 4u(t)[tex]e^{-t}[/tex]+ 4u(t).

To learn more about convolution theorem  from the given link:

https://brainly.com/question/29673703

#SPJ1

Gary deposited $9,000 in a savings account with simple interest. Four months later, he had earned $180 in interest. What was the interest rat

Answers

Using the simple interest system, the interest rate for which Gary deposited $9,000 and earned $180 in interest after four months is 6%.

What is the simple interest system?

The simple interest system is based on the process of computing interest on the principal only for each period.

This contrasts with the compound interest system that charges interest on both accumulated interest and the principal.

The simple interest formula is given as SI = (P × R × T)/100, where SI = simple interest, P = Principal, R = Rate of Interest in % per annum, and T = Time.

The principal amount invested by Gary = $9,000

Time = 4 months = 4/12 years

Interest = $180

Therefore, 180 = ($9,000 x R x 4/12)/100

R = 180/($9,000 x 4/12)/100

R = 6%

Thus, the interest rate is 6%.

Learn more about the simple interest system at https://brainly.com/question/25793394.

#SPJ1

Suppose a binary tree has leaves l1, l2, . . . , lMat depths d1, d2, . . . , dM, respectively.
Prove that Σ 2^-di <= 1.

Answers

In a binary tree with leaves l1, l2, ..., lM at depths d1, d2, ..., dM respectively, the sum of [tex]2^-^d^_i[/tex] for all leaves is always less than or equal to 1: Σ  [tex]2^-^d^_i[/tex] <= 1.

In a binary tree, each leaf node is reached by following a unique path from the root. Since it is a binary tree, each internal node has two child nodes.

Consider a full binary tree, where all leaves have the maximum number of nodes at each depth. For a full binary tree, the total number of leaves is  [tex]2^d[/tex] , where d is the depth.

Each leaf node contributes [tex]2^-^d[/tex] to the sum. Thus, the sum for a full binary tree is Σ  [tex]2^-^d[/tex] = (2⁰ + 2⁰ + ... + 2⁰) = [tex]2^d[/tex] * [tex]2^-^d[/tex]  = 1. Now, if we remove any node from the full binary tree, the sum can only decrease, as we are reducing the number of terms in the sum. Hence, for any binary tree, the sum Σ [tex]2^-^d^_i[/tex]  will always be less than or equal to 1.

To know more about binary tree click on below link:

https://brainly.com/question/13152677#

#SPJ11

let x have the following cumulative distribution function (cdf): f(x)={0,x<0,18x 316x2,0≤x<2,1,2≤x. p(1

Answers

For the cumulative distribution function, p(1 < X ≤ 2) ≈ 0.2222.

What is the probability of 1 < X ≤ 2?

The probability p(1 < X ≤ 2) can be computed by finding the area under the curve of the probability density function (pdf) between x = 1 and x = 2.

Since the cumulative distribution function (cdf) is given, we can differentiate it to obtain the pdf. Thus, the pdf is:

f(x) = { 0, x < 0

18x, 0 ≤ x < 1/4

31/6 - 79x/12, 1/4 ≤ x < 2/3

0, x ≥ 2/3

The probability that 1 < X ≤ 2 can then be computed as follows:

p(1 < X ≤ 2) = ∫₁² f(x) dx

Using the pdf defined above, we can evaluate the integral as follows:

p(1 < X ≤ 2) = ∫₁^(2/3) (31/6 - 79x/12) dx

= [(31/6)x - (79/24)x^2]₁^(2/3)

= (31/6)(2/3) - (79/24)(4/9) - (0) (substituting x = 2/3 and x = 1)

= 0.2222

Therefore, p(1 < X ≤ 2) ≈ 0.2222.

Learn more about cumulative distribution

https://brainly.com/question/19884447?referrer=searchResults

#SPJ11

For the cumulative distribution function, p(1 < X ≤ 2) ≈ 0.2222.

What is the probability of 1 < X ≤ 2?

The probability p(1 < X ≤ 2) can be computed by finding the area under the curve of the probability density function (pdf) between x = 1 and x = 2.

Since the cumulative distribution function (cdf) is given, we can differentiate it to obtain the pdf. Thus, the pdf is:

f(x) = { 0, x < 0

18x, 0 ≤ x < 1/4

31/6 - 79x/12, 1/4 ≤ x < 2/3

0, x ≥ 2/3

The probability that 1 < X ≤ 2 can then be computed as follows:

p(1 < X ≤ 2) = ∫₁² f(x) dx

Using the pdf defined above, we can evaluate the integral as follows:

p(1 < X ≤ 2) = ∫₁^(2/3) (31/6 - 79x/12) dx

= [(31/6)x - (79/24)x^2]₁^(2/3)

= (31/6)(2/3) - (79/24)(4/9) - (0) (substituting x = 2/3 and x = 1)

= 0.2222

Therefore, p(1 < X ≤ 2) ≈ 0.2222.

Learn more about cumulative distribution

https://brainly.com/question/19884447?referrer=searchResults

#SPJ11

Express cos M as a fraction in simplest terms.

Answers

Using the laws of simplification of fractions, we can find that in the simplest terms, cos M has a fraction value of 3/5.

Describe fraction?

In order to express a piece of a whole or a ratio of two numbers, a fraction requires a numerator (top number) and a denominator (bottom number) separated by a fraction bar.

The ratio of the neighbouring side to the hypotenuse of a right triangle is known as the cosine of an angle.

As a result, to calculate cos M, we must find the side that is perpendicular to M and divide it by the hypotenuse.

The length of the triangle's third side, KL, can be calculated using the Pythagorean theorem as shown below:

KL² + LM² = KM²

12² + 9² = 15²

144 + 81 = 225

225 = 15²

Taking the square root of both sides:

KL = √ (15² - 12²)

KL = √ (225 - 144)

KL = √81

KL = 9

As a result, angle M's neighbouring side, KL, has a length of 9. Therefore, by dividing 9 by 15, we can calculate cos M:

KL/KM = cos M = 9/15

To make this fraction simpler, divide the numerator and denominator by their 3 largest common factor:

cos M = (9/3)/ (15/3) = 3/5

To know more about Pythagorean theorem, visit:

brainly.com/question/30616230

#SPJ1

Solve for missing angle. round to the nearest degree

Answers

Answer:

Set your calculator to degree mode.

[tex] { \sin }^{ - 1} \frac{18}{20} = 64 [/tex]

So theta measures approximately 64 degrees.

find y' and y'' for x2 4xy − 3y2 = 8.

Answers

The derivatives are:

[tex]y' = (2x + 4y) / (4x - 6y)[/tex]

[tex]y'' = [(4x - 6y)(2 + 4((2x + 4y) / (4x - 6y))) - (2x + 4y)(4 - 6((2x + 4y) / (4x - 6y)))] / (4x - 6y)^2[/tex]

To find y' and y'' for the given equation x^2 + 4xy - 3y^2 = 8, follow these steps:

Step 1: Differentiate both sides of the equation with respect to x.
For the left side, use the product rule for 4xy and the chain rule for -3y^2.
[tex]d(x^2)/dx + d(4xy)/dx - d(3y^2)/dx = d(8)/dx[/tex]

Step 2: Calculate the derivatives.
[tex]2x + 4(dy/dx * x + y) - 6y(dy/dx) = 0[/tex]

Step 3: Solve for y'.
Rearrange the equation to isolate dy/dx (y'):
[tex]y' = (2x + 4y) / (4x - 6y)[/tex]

Step 4: Differentiate y' with respect to x to find y''.
Use the quotient rule: [tex](v * du/dx - u * dv/dx) / v^2[/tex],

where u = (2x + 4y) and v = (4x - 6y).
[tex]y'' = [(4x - 6y)(2 + 4(dy/dx)) - (2x + 4y)(4 - 6(dy/dx))] / (4x - 6y)^2[/tex]

Step 5: Substitute y' back into the equation for y''.
[tex]y'' = [(4x - 6y)(2 + 4((2x + 4y) / (4x - 6y))) - (2x + 4y)(4 - 6((2x + 4y) / (4x - 6y)))] / (4x - 6y)^2[/tex]

This is the expression for y'' in terms of x and y.

Learn more about differentiation:https://brainly.com/question/25081524

#SPJ11

exercise 0.2.7. let .y″ 2y′−8y=0. now try a solution of the form y=erx for some (unknown) constant .r. is this a solution for some ?r? if so, find all such .

Answers

The functions $y =[tex]e^{-4x}[/tex]$ and $y = [tex]e^{2x}[/tex] $ are solutions to the differential equation $y'' + 2y' - 8y = 0$.

Find if the function $y = e^{rx}$ is a solution to the differential equation $y'' + 2y' - 8y = 0$ can be substituted in place of $y$ and its derivatives?

To see if the function $y = e^{rx}$ is a solution to the differential equation $y'' + 2y' - 8y = 0$, we substitute it in place of $y$ and its derivatives:

y=[tex]e^{rx}[/tex]

y' = [tex]re^{rx}[/tex]

y" = [tex]r^{2} e^{rx}[/tex]

Substituting these expressions into the differential equation, we get:

[tex]r^{2} e^{rx} + 2re^{rx} - 8e^{rx} = 0[/tex]

Dividing both sides by $ [tex]$e^{rx}$[/tex] $, we get:

[tex]r^{2} + 2r - 8 = 0[/tex]

This is a quadratic equation in $r$. Solving for $r$, we get:

r = -4,2

Therefore, the functions $y =[tex]e^{-4x}[/tex]$ and $y = [tex]e^{2x}[/tex] $ are solutions to the differential equation $y'' + 2y' - 8y = 0$.

Learn more about differential equations

brainly.com/question/14620493

#SPJ11

consider the function (x)=3−6x2 f ( x ) = 3 − 6 x 2 on the interval [−6,4] [ − 6 , 4 ] . Find the average or mean slope of the function on this interval, i.e. (4)−(−6)4−(−6) f ( 4 ) − f ( − 6 ) 4 − ( − 6 ) Answer: By the Mean Value Theorem, we know there exists a c c in the open interval (−6,4) ( − 6 , 4 ) such that ′(c) f ′ ( c ) is equal to this mean slope. For this problem, there is only one c c that works. c= c = Note: You can earn partial credit on this problem

Answers

The average slope of f(x) on the interval [-6,4] is equal to f'(3.5) = -12(3.5) = -42.

How to find the average or mean slope of the function on given interval?

The Mean Value Theorem (MVT) for a function f(x) on the interval [a,b] states that there exists a point c in (a,b) such that f'(c) = (f(b) - f(a))/(b - a).

In this problem, we are asked to find the average slope of the function f(x) = 3 - 6x² on the interval [-6,4]. The average slope is:

(f(4) - f(-6))/(4 - (-6)) = (3 - 6(4)² - (3 - 6(-6)²))/(4 + 6) = -42

So, we need to find a point c in (-6,4) such that f'(c) = -42. The derivative of f(x) is:

f'(x) = -12x

Setting f'(c) = -42, we get:

-12c = -42

c = 3.5

Therefore, the point c = 3.5 satisfies the conditions of the Mean Value Theorem, and the average slope of f(x) on the interval [-6,4] is equal to f'(3.5) = -12(3.5) = -42.

Learn more about average slope.

brainly.com/question/31376837

#SPJ11

HURRY UP Please answer this question

Answers

Answer:

[tex] {6}^{2} + {b}^{2} = {10}^{2} [/tex]

[tex]36 + {b}^{2} = 100[/tex]

[tex] {b}^{2} = 64[/tex]

[tex]b = 8[/tex]

mong the following pairs of sets, identify the ones that are equal. (Check all that apply.) Check All That Apply (1,3, 3, 3, 5, 5, 5, 5, 5}, {5, 3, 1} {{1} }, {1, [1] ) 0.{0} [1, 2], [[1], [2])

Answers

Among the following pairs of sets, I'll help you identify the ones that are equal:

1. {1, 3, 3, 3, 5, 5, 5, 5, 5} and {5, 3, 1}:

These sets are equal because in set notation, repetitions are not counted.

Both sets have the unique elements {1, 3, 5}.

2. {{1}} and {1, [1]}:

These sets are not equal because the first set contains a single element which is the set {1}, while the second set contains two distinct elements, 1 and [1]

(assuming [1] is a different notation for an element).

3. {0} and [1, 2]:

These sets are not equal because they have different elements. The first set contains the single element 0, while the second set contains the elements 1 and 2.

4. [[1], [2]]:

This is not a pair of sets, so it cannot be compared for equality.

In summary, the equal pair of sets among the given options is {1, 3, 3, 3, 5, 5, 5, 5, 5} and {5, 3, 1}.

To know more about sets:

https://brainly.com/question/8053622

#SPJ11

A regular octagon has an area of 48 inches squared. If the scale factor of this octagon to a similar octagon is 4:5, then what is the area of the other pentagon?

Answers

The area of the other octagon is 75 square inches.

To find the area of the other octagon, we can use the concept of scale factors. The scale factor of 4:5 tells us that corresponding lengths of the two similar octagons are in a ratio of 4:5.

Since the scale factor applies to the lengths, it will also apply to the areas of the two octagons. The area of a shape is proportional to the square of its corresponding side length.

Let's assume the area of the other octagon (with the scale factor of 4:5) is A.

The ratio of the areas of the two octagons can be expressed as:

(Area of the given octagon) : A = (Side length of the given octagon)^2 : (Side length of the other octagon)^2

48 : A = (4/5)^2

48 : A = 16/25

Cross-multiplying:

25 * 48 = 16A

1200 = 16A

Dividing both sides by 16:

75 = A

Therefore, the area of the other octagon is 75 square inches.

For more such questions on area, click on:

https://brainly.com/question/22972014

#SPJ8

As reported by the Department of Agriculture in Crop Production, the mean yield of oats for U.S. farms is 58.4 bushels per acre. A farmer wants to estimate his mean yield using an organic method. He uses the method on a random sample of 25 1-acre plots and obtained a mean of 61.49 and a standard deviation of 3.754 bushels. Assume yield is normally distributed.
Refer to problem 2. Assume now that the standard deviation is a population standard deviation.
a. Find a 99% CI for the mean yield per acre, :, that this farmer will get on his land with the organic method.
b. Find the sample size required to have a margin of error of 1 bushel and a 99% confidence level?

Answers

The farmer would need to sample at least 108 1-acre plots to estimate the mean yield per acre with a margin of error of 1 bushel and a 99% confidence level.

What is Standard deviation ?

Standard deviation is a measure of how spread out a set of data is from the mean (average) value. It tells you how much the individual data points deviate from the mean. A smaller standard deviation indicates that the data points are clustered closer to the mean, while a larger standard deviation indicates that the data points are more spread out.

a. To find the 99% confidence interval (CI) for the mean yield per acre, we can use the formula:

CI = X' ± Zα÷2 * σ÷√n

where X' is the sample mean, σ is the population standard deviation, n is the sample size, and Zα÷2 is the critical value for a 99% confidence level, which can be found using a standard normal distribution table or calculator.

Zα÷2 = 2.576 (from a standard normal distribution table for a 99% confidence level)

Substituting the given values, we get:

CI = 61.49 ± 2.576 * 3.754÷√25

CI = 61.49 ± 1.529

CI = (59.96, 63.02)

Therefore, we are 99% confident that the true mean yield per acre for the farmer using the organic method is between 59.96 and 63.02 bushels.

b. To find the sample size required to have a margin of error of 1 bushel and a 99% confidence level, we can use the formula:

n = (Zα÷2 * σ÷E)²

where Zα÷2 is the critical value for a 99% confidence level (2.576), σ is the population standard deviation (which we assume to be 3.754), and E is the desired margin of error (1 bushel).

Substituting the given values, we get:

n = (2.576 * 3.754÷1)²

n ≈ 108

Therefore, the farmer would need to sample at least 108 1-acre plots to estimate the mean yield per acre with a margin of error of 1 bushel and a 99% confidence level.

To learn more about Standard deviation from given link.

https://brainly.com/question/13905583

#SPJ1

The mean of the following incomplete information is 16. 2 find the missing
frequencies. Class
Intervals
10-12 12-14 14-
16
16-
18
18-20 20-22 22-24 TOTAL
Frequencies 5 ? 10 ? 9 3 2 50

Answers

The missing frequency for the interval 10-12 is 21.

Let's call the missing frequencies as x and y for the intervals 10-12 and 16-18 respectively.

We know that the total number of observations is 50 and the mean is 16.

To find x and y, we can use the formula for the mean of grouped data:

Mean = (sum of (midpoint of each interval * frequency)) / (total number of observations)

16 = ((11+13)5 + (17+19)3 + 1410 + 202 + 21*y) / 50

Simplifying the above equation, we get:

800 + 21y = 800

y = 0

This means that the missing frequency for the interval 16-18 is 0.

To find the missing frequency for the interval 10-12, we can use the fact that the total number of observations is 50:

x + 5 + 10 + 9 + 3 + 2 + 0 = 50

x = 21

Therefore, the missing frequency for the interval 10-12 is 21.

So the complete frequency table is:

Class Intervals Frequencies

10-12 5 + 21 = 26

12-14 ?

14-16 10

16-18 0

18-20 9

20-22 3

22-24 2

TOTAL 50.

For similar question on frequency.

https://brainly.com/question/10613053

#SPJ11

The time it takes a mechanic to change the oil in a car is exponentially distributed with a mean of 5 minutes. (Please show work)
a. What is the probability density function for the time it takes to change the oil?
b. What is the probability that it will take a mechanic less than 6 minutes to change the oil?
c. What is the probability that it will take a mechanic between 3 and 5 minutes to change the oil?
d. What is the variance of the time it takes to change the oil?

Answers

The probability density function is f(x) = (1/5)e^(-x/5) for x >= 0, the probability it will take the mechanic less than 6 minutes to change oil is 0.699

What is the probability density function

a. The probability density function (PDF) for the time it takes a mechanic to change the oil in a car, given that it follows an exponential distribution with a mean of 5 minutes, is:

f(x) = (1/5)e^(-x/5) for x >= 0

b. The probability that it will take a mechanic less than 6 minutes to change the oil is given by:

P(X < 6) = ∫0^6 f(x) dx

= ∫0^6 (1/5)e^(-x/5) dx

= [-e^(-x/5)]_0^6

= 1 - e^(-6/5)

≈ 0.699

c. The probability that it will take a mechanic between 3 and 5 minutes to change the oil is given by:

P(3 < X < 5) = ∫3^5 f(x) dx

= ∫3^5 (1/5)e^(-x/5) dx

= [-e^(-x/5)]_3^5

= e^(-3/5) - e^(-1)

≈ 0.181

d. The variance of the time it takes to change the oil can be calculated using the formula:

Var(X) = σ^2 = 1/λ^2

where λ is the rate parameter of the exponential distribution, which is the reciprocal of the mean. Therefore, in this case:

λ = 1/5

σ^2 = (1/λ)^2 = 5^2 = 25

So, the variance of the time it takes to change the oil is 25.

Learn more on probability density function here;

https://brainly.com/question/30403935

#SPJ1

consider the following differential equation to be solved by the method of undetermined coefficients. y(4) 2y″ y = (x − 4)2

Answers

The particular solution to the differential equation by the method of undetermined coefficients is [tex]y \_p(x) = (-6x^2 - 16x - 80) + e^{(2x)}(x^2 + x - 44).[/tex]

How to find differential equation using the method of undetermined coefficients?

To solve this differential equation using the method of undetermined coefficients, we assume that the particular solution takes the form:

[tex]y \_ p(x) = (Ax^2 + Bx + C) + e^{(2x)}(Dx^2 + Ex + F)[/tex]

where A, B, C, D, E, and F are constants to be determined.

To determine the values of these constants, we differentiate y_p(x) four times and substitute the result into the differential equation. We get:

[tex]y \_p(x) = Ax^2 + Bx + C + e^{(2x)}(Dx^2 + Ex + F)[/tex]

[tex]y\_p'(x) = 2Ax + B + 2e^{(2x)}(Dx^2 + Ex + F) + 2e^{(2x)}(2Dx + E)[/tex]

[tex]y \_p''(x) = 2A + 4e^{(2x)}(Dx^2 + Ex + F) + 8e^{(2x)}(Dx + E) + 4e^{(2x)(2D)}[/tex]

[tex]y\_p''(x) = 8e^{(2x)}(Dx^2 + Ex + F) + 24e^{(2x)(Dx + E)} + 16e^{(2x)(D)}[/tex]

[tex]y \_p^4(x) = 32e^{(2x)(Dx + E) }+ 32e^{(2x)(D)}[/tex]

Substituting these into the original differential equation, we get:

[tex](32e^{(2x)(Dx + E)} + 32e^{(2x)(D))} - 2(8e^{(2x)}(Dx^2 + Ex + F) + 24e^{(2x)(Dx + E)} + 16e^{(2x)(D))} + (Ax^{2 }+ Bx + C + e^{(2x)}(Dx^2 + Ex + F))(x - 4)^2 = (x - 4)^2[/tex]

Simplifying this expression, we get:

[tex](-6D + A)x^4 + (4D - 8E + B)x^3 + (4D - 16E + 4F - 32D + C + 16E - 32D)x^2 + (-8D + 24E - 16F + 64D - 32E)x + (32D - 32E) = x^2 - 8x + 16[/tex]

Comparing the coefficients of like terms, we get the following system of equations:

-6D + A = 0

4D - 8E + B = 0

-24D + 4F - 32D + C = 16

-8D + 24E - 16F + 64D - 32E = 0

32D - 32E = 0

Solving this system of equations, we get:

D = E = 1

A = -6

B = -16

C = -80

F = -44

Therefore, the particular solution to the differential equation is:

[tex]y \_p(x) = (-6x^2 - 16x - 80) + e^{(2x)}(x^2 + x - 44)[/tex]

The general solution to the differential equation is the sum of the particular solution and the complementary function, which is the solution to the homogeneous equation:

[tex]y'''' - 2y'' + y = 0[/tex]

The characteristic equation of this homogeneous equation is:

[tex]r^4 - 2r^2 + 1 = 0[/tex]

Factoring the characteristic equation, we get:

[tex](r^2 - 1)^[/tex].

The particular solution to the differential equation by the method of undetermined coefficients is [tex]y \_p(x) = (-6x^2 - 16x - 80) + e^{(2x)}(x^2 + x - 44).[/tex]

Learn more about differential equation.

brainly.com/question/31396200

#SPJ11

Please help me with this (9/4x+6)-(-5/4x-24)

Answers

Answer:

7/2x+30

Step-by-step explanation:

(9/4x+6)-(-5/4x-24)

9/4x+6-(-5/4x)-(-24)

9/4x+6+5/4x+24

14/4x+30

7/2x+30

Find the missing dimension of the parallelogram.

Answers

Answer:

b=7

Step-by-step explanation:

We know that for a parallelogram, The formula is a=bh

so plug it in

28=b4

Divide both sides by 4:

b=7

Answer:

b = 7 m

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here h = 4 and A = 28 , then

28 = 4b ( divide both sides by 4 )

7 = b

find the derivative of the function. f(x) = (9x6 8x3)4

Answers

The derivative of the function f(x) = (9[tex]x^{6}[/tex] + 8x³)³ is f'(x) = 4(9[tex]x^{6}[/tex] + 8x³)³(54x³ + 24x²).

To find the derivative of the function f(x) = (9x² + 8x³)³, you need to apply the Chain Rule. The Chain Rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, let u = 9x + 8x.

First, find the derivative of the outer function with respect to u: d( u³ )/du = 4u³.
Next, find the derivative of the inner function with respect to x: d(9x² + 8x³)/dx = 54x³ + 24x².

Know more about derivative of the function here:

https://brainly.com/question/25752367

#SPJ11

URGENT PLS HELP!! Will give brainiest :)

Answers

you should put the question, there is not question to be answered?

change f(x) = 40(0.96)x to an exponential function with base e. and approximate the decay rate of f.

Answers

The decay rate of f is approximately 4.0822% per unit of x.

How to change [tex]f(x) = 40(0.96)^x[/tex] to an exponential function?

To change [tex]f(x) = 40(0.96)^x[/tex] to an exponential function with base e, we can use the fact that:

[tex]e^{ln(a)} = a[/tex], where a is a positive real number.

First, we can rewrite 0.96 as[tex]e^{ln(0.96)}[/tex]:

[tex]f(x) = 40(e^{ln(0.96)})^x[/tex]

Then, we can use the property of exponents to simplify this expression:

[tex]f(x) = 40e^{(x*ln(0.96))}[/tex]

This is an exponential function with base e.

To approximate the decay rate of f, we can look at the exponent x*ln(0.96).

The coefficient of x represents the rate of decay. In this case, the coefficient is ln(0.96).

Using a calculator, we can approximate ln(0.96) as -0.040822. This means that the decay rate of f is approximately 4.0822% per unit of x.

Learn more about exponential function

brainly.com/question/14355665

#SPJ11

Other Questions
Consider a password hash function that works as follows on a system where the password must contain only lower case letters: Step 1. Take each letter in the password and replace it with a number representing its place in the alphabet (a= 1, b=2, etc). Step 2. Take each number from Step 1, multiply it by 2, and add 1. Step 3. Combine the resulting numbers, separated by 0s, into a single string. This string is the encrypted password. 3. Given the user password "user", what would this hashing algorithm produce as the final encrypted password? 4. Is it possible for a hacker to reverse engineer a password encrypted in this manner to reveal the original cleartext password? 5. If so, write an algorithm in pseudocode to do the decryption Computers are assembled in a process with two resources.The first resource has a capacity of 10 computers per hour. The capacity of the second resource is 13 computers per hour.The first resource has 1 worker and the second resource has 7 workers.Demand for this process is 5.9 computers per hour. Wage are $12 per hour.What is the cost of direct labor? The first five terms of a sequence are shown3, 12, 48, 192, 768We are going to write an explicit function to model the value of nth term in the sequence such that f(1)=3.Our function will be written in this form: f(n)=a(b)^n-1What value will we substitute in for a? (blank box)What value will we substitute in for b? (blank box) For example, in cell B26 enter the formula " B5" Check your worksheet by changing the budgeted unit sales in Quarter 2 of Year 2 in cell C5 to 75,000 units. The total expected cash collections for the year should now be $2,085,000. If you do not get this answer, find the errors in your worksheet and correct them Data Year 2 Quarter Year 3 Quarter Budgeted unit sales 40,000 60,000 10 0,000 50,000 70,000 80,000 S8 per unit Selling price per unit Accounts receivable, beginning balance Sales collected in the quarter sales are made Sales collected in the quarter after sales are made Desired ending finished goods inventory is Finished goods inventory, beginning Raw materials required to produce one unit Desired ending inventory of raw materials is Raw materials inventory, beginning .Raw material costs Raw materials purchases are paid $65,000 75% 25% 30% of the budgeted unit sales of the next quarter 2,000 units 5 pounds 10% of the next quarter's production needs 23,000 pounds $0.80 per pound 60% in the quarter the purchases are made 40% in the quarter following purchase and Accounts payable for raw materials, beginning balance $81,500 Enter a formula into each of the cells marked with a? below Review Problem: Budget Schedules Construct the sales budget Year 2 Quarter Year 3 Quarter Budgeted unit sales Selling price per unit Total sales Construct the schedule of expected cash collections Year 2 Quarter Year Accounts receivable, beginning balance First-quarter sales Second-quarter sales Third-quarter sales Fourth-quarter sales Total cash collections Construct the production budget Year 2 Quarter Year 3 Quarter Year Budgeted unit sales Add desired finished goods inventory Total needs Less beginning inventory Required production Construct the raw materials purchases budget Year 2 Quarter Year 3 Quarter 3 Year Required production (units) Raw materials required to produce one unit Production needs (pounds) Add desired ending inventory of raw materials (pounds) Total needs (pounds) Less beginning inventory of raw materials (pounds) Raw materials to be purchase Cost of raw materials per pound Cost of raw materials to be purchased 2 2 2 2 Construct the schedule of expected cash payments Year 2 Quarter 3 Year Accounts payable, beginning balance First-quarter purchases Second-quarter purchases Third-quarter purchases Fourth-quarter purchases Total cash disbursements 2 2what is the total expected cash collections for the year when the budgeted unit sales in q2 of year 2 change to 75,000? A milling operation has historically produced an average thickness of 0.003 inch with an average range of 0.0015 inch. Currently, the first three items from each batch of 20 are inspected. Use Table 1. What is the value of the lower control limit for the x-bar chart?A) less than or equal to 0.00100B) greater than 0.00100 but less than or equal to 0.00299C) greater than 0.00299 but less than or equal to 0.00499D) greater than 0.00499Table 1 Factors for Calculating Three-Sigma Limits for the x Chart and R-ChartSize of SampleFactor for UCL and LCL for x-bar-ChartsA2Factor for LCL for R-ChartsD3Factor for UCL for R-ChartsD421.88003.26731.02302.57540.72902.28250.57702.11560.48302.00470.4190.0761.92480.3730.1361.86490.3370.1841.816100.3080.2231.777 A shopper in a supermarket pushes a buggy with a force of 50N directed at an angle 20 degrees below the horizontal. What work is done on the buggy if the shopper pushes it 30m? Use the fact that the change in the mechanical energy is equal to the work done by friction to find the value of the friction force acting on the cart. Use the electronic balance to find the mass of the friction block, and then find the coefficient of friction between the friction block and the track. Suppose that a random variable Y has a probability density function given by | ky3e-y/2, y > 0, f(y) = 0, elsewhere. a Find the value of k that makes f(y) a density function. b Does Y have a x2 distribution? If so, how many degrees of freedom? What are the mean and standard deviation of Y? d Applet Exercise What is the probability that Y lies within 2 standard deviations of its mean? What are the answer to the AR test for i survived the great Chicago fire? Rauls group has made little progress, and eddie acknowledges that raul "kind of does his own thing." which contextual factor related to team performance appears to be most lacking? Glucose synthesis can derive carbons from a variety of sources including [ Select] [ Select] [ Select) and [ Select] [ Select glycerol fatty acids Select amino acids cholesterol [ Select] lactate NADH Select, oxidative phosphorylation carbon dioxide, photosynthesis at stp how many liters of nh3 can be produced from the reaction of 6.00 mol of n2 with 6.00 mol of h2? n2(g) 3 h2(g) 2 nh3(g) It's been a year since Mark and Tracy broke up. Mark is still depressed and gets irate if anyone even mentions Tracy's name. Mark is experiencing: Evaluate the expression shown below and write your answer as a fraction. -5/9 -(-9/4) What tactic used in the early 1950s is described in this quotation? (Image)A. Massive RetaliationB. BrinksmanshipC. McCarthyismD. Containment cartels are difficult to maintain because a. cartel agreements are conducive to monopoly outcomes. b. there is always tension between cooperation and self-interest in a cartel. c. antitrust laws are difficult to enforce. d. firms pay little attention to the decisions made by other firms. Suppose you have a near point of typical value 25 cm.What is your range of accommodation?Express your answer in diopters. A 4.266 gram sample of a hydrocarbon, upon combustion in a combustion analysis apparatus, yielded 5.672 grams of water. The percent, by weight, of hydrogen in the hydrocarbon is therefore: A. 20.07% B. 17.24% C. 14.88% D. 08.62% E. 7.44% QUESTION 11 True or false: In a controlled experiment, an experimental group is the group that is exposed to the variable under study. a) true b) false a b QUESTION 12 The following is an example of what type of argument: "I was late to school because the bus broke down." (a) repeated observation argument (b) argument by analogy (C) causal argument (d) none of the above a b QUESTION 13 True or false: The conclusions of all non-deductive arguments follow with high probability from the premises? a) true b) false a QUESTION 14 True or false: Arguments by analogy are deductive arguments. a) true b) false a QUESTION 15 True or false: Valid arguments can contain premises that are derived from repeated observation arguments. a) true b) false a If the MPC in an economy is 0.75, government could shift the...If the MPC in an economy is 0.75, government could shift the aggregate demand curve rightward by $36 billion bya) decreasing taxes by $12 billion.b) increasing government spending by $12 billion.c) increasing government spending by $27 billion.d) decreasing taxes by $36 billion.