Answer:
The solution of this differential system is [tex]y(x) = x\cdot e^{3\cdot x}[/tex].
Step-by-step explanation:
This second-order differential equation is homogeneous and linear of the form:
[tex]y'' + p\cdot y' +q\cdot y = 0[/tex] (1)
Where:
[tex]p[/tex] - First-order constant coefficient, dimensionless.
[tex]q[/tex] - Zero-order constant coefficient, dimensionless.
Whose characteristic polynomial is:
[tex]\lambda^{2}+p\cdot \lambda + q = 0[/tex] (2)
Where [tex]\lambda[/tex] contains the roots associated with the solution of the differential equation.
If we know that [tex]p = 6[/tex] and [tex]q = 9[/tex], the roots of the characteristic equation are, respectively:
[tex]\lambda^{2}+6\cdot \lambda + 9 = 0[/tex]
[tex](\lambda +3)\cdot (\lambda + 3) = 0[/tex]
Which means that [tex]\lambda_{1} = \lambda_{2} = 3[/tex] and the solution of the differential equation is of the form:
[tex]y(x) = e^{3\cdot x}\cdot (c_{1}+c_{2}\cdot x)[/tex] (3)
Where [tex]c_{1}[/tex] and [tex]c_{2}[/tex] are integration constants.
The first derivative of the equation above is:
[tex]y'(x) = 3\cdot e^{3\cdot x}\cdot (c_{1}+c_{2}\cdot x)+c_{2}\cdot e^{3\cdot x}[/tex] (4)
Now, if we get that [tex]y(0) = 0[/tex] and [tex]y'(0) = 1[/tex], then the system of equations to the solved is:
[tex]c_{1} = 0[/tex] (3b)
[tex]c_{1}+c_{2} = 1[/tex] (4b)
The solution of this system is: [tex]c_{1} = 0[/tex], [tex]c_{2} = 1[/tex]. Therefore, the solution of this differential system is [tex]y(x) = x\cdot e^{3\cdot x}[/tex].
The derivative of the function f is given by f′(x)=−3x+4 for all x, and f(−1)=6. Which of the following is an equation of the line tangent to the graph of f at x=−1 ?
Answer:
The equation of the line tangent to the graph of f at x = -1 is [tex]y = 7\cdot x +13[/tex].
Step-by-step explanation:
From Analytical Geometry we know that the tangent line is a first order polynomial, whose form is defined by:
[tex]y = m\cdot x + b[/tex] (1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]b[/tex] - Intercept, dimensionless.
The slope of the tangent line at [tex]x = -1[/tex] is:
[tex]f'(x) = -3\cdot x +4[/tex] (2)
[tex]f'(-1) = -3\cdot (-1) +4[/tex]
[tex]f'(-1) = 7[/tex]
If we know that [tex]m = 7[/tex], [tex]x = -1[/tex] and [tex]y = 6[/tex], then the intercept of the equation of the line is:
[tex]b = y-m\cdot x[/tex]
[tex]b = 6-(7)\cdot (-1)[/tex]
[tex]b = 13[/tex]
The equation of the line tangent to the graph of f at x = -1 is [tex]y = 7\cdot x +13[/tex].
help pls
What is the solution to this system of equations?
x = 12 − y
2x + 3y = 29
Answer:
Step-by-step explanation:
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of business travelers follow.
2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9
6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9
7 10 7 9 9 9 9
Required:
Develop a confidence interval estimate of the population mean rating for Miami.
Answer: 6.8622 ; 8.1778
Step-by-step explanation:
Given the data:
2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9
6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9
7 10 7 9 9 9 9
Assume a confidence interval of 95%
Using calculator :
The mean of the distribution (m) = 7.52
Standard deviation (s) = 2.314
Sample size),
Obtaining the t score ;
Degree of freedom (df) = (n-1) = 50 - 1 = 49
t(1-α/2), 49 = t(0.025, 49) = 2.01 ( t distribution table)
Margin of Error :
2.01 * s/√n = 2.01 * 2.314/7.0710678
Margin of Error (E) = 0.6578
Confidence interval:
(Mean - E) ≤μ≤ (mean + E)
(7.52 - 0.6578) ≤μ≤ (7.52 + 0.6578)
6.8622 ≤μ≤ 8.1778
The mean age of several boys in a class is 12. The total is 156. How
many boys are there?
Answer:
13
Step-by-step explanation:
156/12
12. Write the EQUATION for 125 is what percent of 200.
A 125 = p x 200
B 125 = p/200
C 125/p = 200
D 125 = 200/2
Answer:
Step-by-step explanation:
125 =200p
125/p=200
So the answer is option D
The correct equation for 125 is what percent of 200 is:
C (125/p = 200).
To write the equation for 125 is what percent of 200, follow these steps:
Step 1: Identify the unknown value.
In this case, looking for the percent, which can represent as p.
Step 2: Set up the equation.
To express the relationship between 125 and 200 as a percent, use the equation: 125 = p/100 * 200.
Step 3: Simplify the equation.
To simplify, divide both sides of the equation by 200 to isolate p:
125/200 = p/100
Step 4: Simplify further.
To simplify the left side, divide both the numerator and denominator by 25:
5/8 = p/100
Step 5: Rewrite the equation.
Finally, rewrite the equation as:
125/p = 200
Therefore, the correct equation for 125 is what percent of 200 is:
C (125/p = 200).
Learn more about Percent there:
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1.5 m =_____ cm
a 15
b 0.015
c 1.5
d 150
Answer:
150
Step-by-step explanation:
Answer:
D.)150
Step-by-step explanation:
Hope I helped
What is the slope-intercept form of a line that contains the point (0,3) and a slope =-2?
PLZ HELPP MEEE!!
Answer:
C.
Step-by-step explanation:
-2 is in front of x so thats gonna be the slope
and +3 is the y-intercept
if 'HOPE' is called 3, ' GOVERNMENT' is called 9, ' PEACEFUL' is called 7, what would HAPPINESS 'be called??
Answer:
8
Step-by-step explanation:
Identifying the Pattern:
We are told that 'HOPE' is called 3
we can see that there are 4 characters in the word HOPE
So, we can see that the number is one less than the number of characters in the given word
Let's see if the observation we made still holds for the other Words:
We are also told that 'GOVERNMENT' is called 9
the number of characters = 10
Here, we once again notice that the code number is one less than the number of characters in our word
We are Given that 'PEACEFUL' is called 7
the number of characters = 8
Once again, our observation holds true
Hence, our observation holds true for all the words
Therefore, we can say with certainty that the pattern is:
code number = (number of characters of the word) - 1
Code number for 'HAPPINESS':
from the above, we know that:
code number = (number of characters of the word) - 1
we can see that 'HAPPINESS' has 9 words, plugging that value:
code number = 9 - 1
code number for 'HAPPINESS' = 8
Algebra!!!
3 Questions Only take if you know ALL Answers
PLZZZ QUICK
Answer:
1. -7.5
2. $1
3. 40
Step-by-step explanation:
For number 1, it can be solved by using the PEMDAS method, or see explanation below:
6x - 4x - 36 = 6 - 2x
2x - 36= -2x + 6
4x + 36 = 6
4x = -30
x = -15/2 or -7.5
For number 2, substitute 3 into both equations:
f(x) =1.50(3) + 2.00
and
f(x) = 2.00(3) + 1.50
This would get $6.50 and $7.50, which, if subtracted, gets $1.
For number 3, do something similar to the previous problem. Substitute 3 for x. It would be 5(2^3), or 40.
Hope this helps!
How would you graph the solution to 3x ≤ -15?
Draw an open circle on -5 and shade to the left.
Draw an open circle on -5 and shade to the right.
Draw a closed circle on -5 and shade to the left.
Draw a closed circle on -5 and shade to the right.
Answer: C) Closed circle at -5; shading to the left
The given inequality [tex]3x \le -15[/tex] solves to [tex]x \le -5[/tex] when we divide both sides by 3. The inequality sign does not change because we didn't divide both sides by a negative number.
The graph has a closed circle at -5 to include this value as part of the solution set. Shading is to the left to indicate values smaller than -5. Overall, the graph says "x can be -5 or smaller". If you wanted to exclude -5, you would say [tex]x < -5[/tex] and use an open circle; but that's not the case here.
Answer:
C) Closed circle at -5; shading to the left
Step-by-step explanation:
20 points.Cynthia has a bag of jellybeans. There are two red jellybeans, one yellow jellybean, and two black jellybeans in her bag. Cynthia grabs two jellybeans and gives them to her friend, Pedro, and he eats them. What is the probability that she gives him two red jellybeans?
Answer:
2/5
Step-by-step explanation:
Answer:
D. This is a dependent event because Pedro ate the jellybeans, and they cannot be replaced.
Step-by-step explanation:
Pretty much, dependent means it can’t be replaced and independent means it can be replaced.
A quadratic equation is written as a system of two quadratic functions. Select the number of possible ways the graphs can intersect.
Answer:
can I see the opinions and I will come
Step-by-step explanation:
back and edit my question and answer it for you
Answer:
0, 1, 2, infinite
Step-by-step explanation:
Please hurry. Please
Answer:
yes
Step-by-step explanation:
12p<=56
12*3<=56
36<=56
Correct.
Hope this helps :D
4) What are all the subsets of (3, 5, 7)?
ANSWER: 1 is a subset of 3,5,7
Answer:
X=(0,3) (3,0) Y=(0,5)(5,0) Z=(7,0) (0,7)
Step-by-step explanation:
suppose ,3=x ,5=y and 7=z
0 is the common number
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Answer:
This is a hw site pls dont post this, if you dont need help. I dont want your account to be deleted. :) Hope u have a great day tho, but in the future dont post this.
Step-by-step explanation:
The sum of two numbers is 12.
When three times the first number is added to 5 times the second number, the result is 44.
Find the two numbers.
A 9 and 3
B) 8 and 4
C) 10 and 2
D) 7 and 5
Answer:
b
Step-by-step explanation:
8*3
=24
4*5
=20
20+24
=44
Please help me asap this was due 5 days ago
Answer:
do 9.60 divided by 12
Step-by-step explanation:
Answer:
$0.80
Step-by-step explanation:
All that is needed for finding this answer is 9.60 ÷ 12 which gets us 0.80.
A weighted coin has a 0.599 probability of landing on heads. What is the probability that it takes 5 flips for the first head to occur?
Answer:
0.411^5 times 0.599
Step-by-step explanation:
0.599 chance of landing on heads.
0.411 chance of not landing on heads.
0.411 times 0.411 times 0.411 times 0.411 times 0.411 (for the 5 flips that do not land on heads) times 0.599 (for the time that it does land on heads).
6 x +4 + 10x - 9 + 8x - 7=
Answer:
24x - 12
Step-by-step explanation:
6x + 4 + 10x - 9 + 8x - 7
6x + 10x + 8x + 4 - 9 - 7
24x - 12
I'm doing system of equations and I have to solve using substitution
the equations are y=5x and xy=45
Answer: +3, -3
Step-by-step explanation:
ok so all you need to do is plug in that first equation into the second one.
x(5x) = 45
5x^2 = 45
x^2 = 9
x = +3, -3
Whats the slope and how do i / where do i graph it
Answer:
The slope is 3. graph it every time the line hits an exact point
Step-by-step explanation:
Why is the distributive property important in solving equations?
Answer:
it helps simplify difficult problems . it breaks down expressions into the difference or the sum
of two numbers.
simplify 32 L : 56L with whole numerator and denominator
Answer:
4L/7L
Step-by-step explanation:
32:56 is the same as 32/56
They can be divided by a maximum of 8
32/8=4
56/4=7
4/7
I needs help with this question pls
Answer:
Is it A
Step-by-step explanation:
Please help ASAP due soon I need help
Answer: 18
Step-by-step explanatio 18
5(2y-3)-4y=8-2y-15
Justify each step with a property of algebra. Drag the property to the correct row.
Which one are functions
Answer:
A
Step-by-step explanation:
PLEASE MARK BRAINLIEST IT WILL HELP SM
Answer:
its hard to see but I think all of them except the first and the last ones r
Step-by-step explanation:
an x can't repeat
answer fast!!!
A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 3100 seats. The students filled 32% of the seats in the theater. How many 6th graders went on the trip?
Answer:
992
Step-by-step explanation:
Answer:
38%
Step-by-step explanation:
1178 / 3100 = 0.38
38%
Tony is spending money at a constant rate. Suppose he initially has $1000, and after 4 months, he has $760,
Which of these expresses the rate at which Tony's amount of money is changing?
Answer:
$60 monthlyStep-by-step explanation:
Step one:
The initial amount that Tony has= $1000
final amount =$760
amount spent= 1000-760= $240
time taken is 4 months
Step two:
Required:
the rate of spending
we know that rate= quantity/time
rate= 240/4
rate= $60 per month
Hence Tony's amount is changing at $60 monthly
Answer: -60
Step-by-step explanation:
8
Find the circumference of the circle pictured above.
Round your answer to the nearest tenth