Answer:
x= 0,1+3i, 1-3i
Step-by-step explanation:
So the first option
[tex] \rm \int_0^ \infty \frac{1}{(1 + {x}^{ \phi} {)}^{ \phi} } dx \\ [/tex]
Recall that [tex]\phi = 1 + \frac1\phi[/tex].
In the integral, substitute [tex]y=1+x^\phi[/tex], so that [tex]x=(y-1)^{1/\phi} = (y-1)^{\phi-1}[/tex] and [tex]dx = (\phi-1) (y-1)^{\phi-2} \, dy[/tex]. We have
[tex]\displaystyle I = \int_0^\infty \frac{dx}{(1+x^\phi)^\phi} \\\\ ~~~~ = \frac1\phi \int_1^\infty \frac{(y-1)^{\phi-2}}{y^\phi} \, dy[/tex]
Substitute [tex]y=\frac1z[/tex] and [tex]dy=-\frac{dz}{z^2}[/tex] to transform [tex]I[/tex] to
[tex]\displaystyle I = \frac1\phi \int_0^1 \left(\frac1z-1\right)^{\phi-2} z^{\phi-2} \, dz \\\\ ~~~~ = \frac1\phi \int_0^1 (1-z)^{\phi-2} \, dz[/tex]
Finally, substitute [tex]u=1-z[/tex].
[tex]\displaystyle I = \frac1\phi \int_0^1 u^{\phi-2} \, du \\\\ ~~~~ = \frac1\phi \cdot \frac1{\phi-1} = \frac{\phi-1}{\phi-1} = \boxed{1}[/tex]
Use the drawing tools to form the correct answer on the number line
Graph the solution set to this inequality.
-2(x + 6) > -4x
Answer:
Step-by-step explanation:
Answer:
x > 6 with an open point
Hope this helps!
Step-by-step explanation:
-2 ( x + 6 ) > -4x
-2x - 12 > -4x
-(-4x) - 2x > -(-12)
4x - 2x > 12
2x > 12
x > 6
Find k with the given information.
m=-3/5 (k,-9) and (1,-6
Using the slope formula, the value of k in the coordinates of the point given is: k = 6.
How to Find the Slope of a Line?If we are given two points that lie on a line, (x1, y1) and (x2, y2), the formula that is used to find the slope (m) of the line is given as:
Slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = change in y / change in x..
Given the following:
(k, -9) = (x1, y1)
(1, -6) = (x2, y2)
Slope (m) = -3/5
Plug in the values into the formula used for calculating the slope of a line:
(-6 -(-9))/(1 - k) = -3/5
3/(1 - k) = -3/5
Cross multiply and solve for the value of k
-3(1 - k) = 3(5)
-3 + 3k = 15
Add 3 to both sides
-3 + 3k + 3 = 15 + 3 [subtraction property of equality]
3k = 18
Divide both sides by 3
3k/3 = 18/3 [division property of equality]
k = 6
The value of k is: 6. Therefore, the points on the line that have a slope of -3/5 are (6, -9) and (1, -6).
Learn more about the slope of a line on:
https://brainly.com/question/16949303
#SPJ1
The quantity of six and a number, times
five
Find the missing integer that makes the following addition statement true.
+ 3 = 2+3=2
The missing integer that makes the following addition statement true is -1.
What is the commutative law of addition?The commutative law of addition is also known as the law of cumulative addition and it states that when two numbers are added together, then, the outcome is equal to the addition of their interchanged position because addition is considered as a binary operation.
Mathematically, the commutative law of addition can be represented using the following formula:
A + B = B + A.
What is an integer?An integer can be defined as a whole number that may either be positive, negative, or zero such as -1, 0, 1, 2, 3, etc.
Now, we would determine the missing number:
x + 3 = 2
x = 2 - 3
x = -1.
Read more on missing numbers here: https://brainly.com/question/603901
#SPJ1
Complete Question:
Find the missing integer that makes the following addition statement true.
+ 3 = 2
The position, d, in metres of an object
in motion as it travels is given by:
d= (t + 2) (t + 1.2)
It is the time in seconds.
This is an equation of motion.
By looking at it, we can learn about
how the object started moving.
First, expand the brackets.
t2+2.4+3.2t
The initial height is the constant
(no t) term.
What is the initial height?
Answer:
2.4m
Step-by-step explanation:
The question has already done most of the work for you. To find the initial height, simply set t = 0 and substitute it into the function.
[tex]d(0) = {0}^{2} + 2.4 + 3.2(0) \\ = 2.4m[/tex]
To pay for a $22,800car, Mai made a down payment of $3,800and took out a loan for the rest. On the loan, she paid monthly payments of $420for 4 years. (a) What was the total amount Mai ended up paying for the car (including the down payment and monthly payments)? (b) How much interest did Mai pay on the loan?
1. The total amount that was paid for the car will be $23960.
2. The interest that Mai pay on the loan will be $1160.
How to calculate the value?1. From the information, in order to pay for a $22,800 car, Mai made a down payment of $3,800 and took out a loan for the rest and on the loan, she paid monthly payments of $420for 4 years.
The total amount that was paid for the car will be:
= $3800 + ($420 × 4 years)
= $3800 + ($420 × 48)
= $3800 + $20160
= $23960
2. The interest that Mai pay on the loan will be:
= $23960 - $22800
= $1160
Learn more about interest on:
brainly.com/question/25793394
#SPJ1
Match the polar equations to their rectangular forms-
Applying the rules for the polar equations, the correct pairs are given in the image at the end of the answer.
What are polar equations?
The most well known polar equation rules are given as follows:
For the first pair, when x = 2, we have that:
rcos(θ) = 2.
r = 2/cos(θ)
r = 2 sec(θ), as one divided by the cosine is the secant.
For the second pair, we have that:
x² + y² = 36.
x² + y² = r², hence:
r² = 36
r = 6.
For the third pair, we have that:
x² + y² = 2y
r² = 2rsin(θ).
r²/r = 2sin(θ).
r = 2sin(θ).
For the fourth pair, we have that:
[tex]x = \sqrt{3}y[/tex]
[tex]\frac{y}{x} = \frac{1}{\sqrt{3}}[/tex]
[tex]\frac{y}{x} = \frac{\sqrt{3}}{3}[/tex]
Then the angle theta is given as follows:
θ = arctan(sqrt(3)/3) = pi/6.
For the fifth pair, we have an angle in which the sine and the cosine are equal, hence this angle is of 45º = pi/4.
The image at the end of the answer shows all the matched pairs.
More can be learned about polar equations at https://brainly.com/question/9363127
#SPJ1
(b) y = x²+2x9 dx = 11x¹⁰ + 10x¹, where 10 dy is the derived function. dx Find the value of p and the value of q.
The expression y=[tex]x^{p} +2x^{q}[/tex]. [tex]\frac{dy}{dx}=11x^{10}+10x^{4}[/tex], where dy/dx is derived function. The p and q values are 11 and 5.
Given that,
The expression y=[tex]x^{p} +2x^{q}[/tex]
[tex]\frac{dy}{dx}=11x^{10}+10x^{4}[/tex], where dy/dx is derived function.
Derived function means for any value of the independent variable, the value of another function is the instantaneous rate of change of the specified function at that value of the independent variable.
We have to find the p and q values.
Take expression
y=[tex]x^{p} +2x^{q}[/tex]
[tex]\frac{dy}{dx}=px^{p-1}+2qx^{q-1}[/tex]
[tex]11x^{10}+10x^{4}=px^{p-1}+2qx^{q-1}[/tex]
Here,
we can see p=11 and
2q=10
q=5
Therefore, the p and q values are 11 and 5.
To learn more about derived visit: https://brainly.com/question/25324584
#SPJ1
10 less than the quotient of a number and 2 is -18"
The representation of the expression is x/2 - 10 = -18
How to translate the algebraic expression?The mathematical statement is given as
"10 less than the quotient of a number and 2 is -18"
In expressions, quotient mean divide i.e. /
So, we have the following representation
"10 less than the quotient of a number and 2 is -18" ⇒ 10 less than a number/2 is -18"
Let the number be x
So, we have
"10 less than the quotient of a number and 2 is -18" ⇒ 10 less than x/2 is -18"
Less than as used here means minus
So, we have
"10 less than the quotient of a number and 2 is -18" ⇒ x/2 - 10 is -18
Rewrite as
"10 less than the quotient of a number and 2 is -18" ⇒ x/2 - 10 = -18
Hence, the expression represented by "10 less than the quotient of a number and 2 is -18" is x/2 - 10 = -18
Read more about expressions at
https://brainly.com/question/4344214
#SPJ1
)) 24 cups 5) 3 cups
Answer: 12 cups
Explanation
Anna needs 6 pint of milk to produce yoghurt
1 pint = 2 cups
let cups of milk be x
1 pint of milk will give 2 cups
6 pints of milk will give x cups of milk
1 pint = 2cups
6 pints = x cups
Cross multiply
1 * x = 2 * 6
x = 12 cups
Therefore, Anna will need 12 cups of milk to produce a yoghurt.
I need help with this problem
We have the following function:
[tex]H(t)=10\sin (2\pi(t-\frac{1}{4}))+15[/tex]a) The initial height occurs at t=0. By substituting this value into the function, we get
[tex]H(0)=10\sin (2\pi(0-\frac{1}{4}))+15[/tex]which gives
[tex]\begin{gathered} H(0)=10\sin (-2\pi\frac{1}{4})+15 \\ H(0)=10\sin (-\frac{2\pi}{4})+15 \\ H(0)=10\sin (-\frac{\pi}{2})+15 \end{gathered}[/tex]since sin(-Pi/2) is equal to -1, we have
[tex]H(0)=-10+15[/tex]Then, H(0)= 5, so the height is 5 feets.
b) The car will make a full rotation when the argument is shifted 2Pi:
[tex]H(t)=10\sin (2\pi(t-\frac{1}{4})+2\pi)+15[/tex]at this point H(t) must be equal to 5 feets. Then, we have
[tex]5=10\sin (2\pi(t-\frac{1}{4})-2\pi)+15[/tex]and we must find t. If we move +15 to the left hand side, we obtain
[tex]\begin{gathered} 5-15=10\sin (2\pi(t-\frac{1}{4})-2\pi) \\ \text{then} \\ 10\sin (2\pi(t-\frac{1}{4})-2\pi)=-10 \end{gathered}[/tex]By moving the coefficient 10 the the right hand side, we get
[tex]\begin{gathered} \sin (2\pi(t-\frac{1}{4})-2\pi)=-\frac{10}{10} \\ \sin (2\pi(t-\frac{1}{4})-2\pi)=-1 \end{gathered}[/tex]we can note that when
[tex]\sin \theta=-1\Rightarrow\theta=-90=-\frac{\pi}{2}[/tex]this implies that the argument of our last result is
[tex]2\pi(t-\frac{1}{4})-2\pi=-\frac{\pi}{2}[/tex]By moving 2Pi to the right hand side, we have
[tex]\begin{gathered} 2\pi(t-\frac{1}{4})=-\frac{\pi}{2}+2\pi \\ 2\pi(t-\frac{1}{4})=\frac{3\pi}{2} \end{gathered}[/tex]Now, by moving 2Pi to the right hand side, we have
[tex]t-\frac{1}{4}=-\frac{\frac{3\pi}{2}}{2\pi}[/tex]which gives
[tex]t-\frac{1}{4}=\frac{3}{4}[/tex]so, t is given by
[tex]\begin{gathered} t=\frac{3}{4}+\frac{1}{4} \\ t=1 \end{gathered}[/tex]That is, n 1 minute, the car will take one full rotation.
c) The maximum height of the car ocurrs at t=0.5 min because in one minute it take one full rotation. Then, at t=1/2 we get
[tex]H(\frac{1}{2})=10\sin (2\pi(\frac{1}{2}-\frac{1}{4}))+15[/tex]which gives
[tex]\begin{gathered} H(\frac{1}{2})=10\sin (2\pi(\frac{1}{4}))+15 \\ H(\frac{1}{2})=10\sin (\frac{\pi}{2})+15 \\ H(\frac{1}{2})=10(1)+15 \\ H(\frac{1}{2})=25 \end{gathered}[/tex]that is, the maximum height is 25 feets
Convert the following phrase into a mathematical expression use x as the variable combine like terms when possible A number multiplied by -8 subtracted from the sum of 8 and two times the number
ANSWER:
[tex]-8x-(8+2x)[/tex]STEP-BY-STEP EXPLANATION:
We must convert the following statement "A number multiplied by -8 subtracted from the sum of 8 and two times the number" into a mathematical expression.
We know that "a number" would be x.
Therefore:
[tex]-8x-(8+2x)[/tex]The analysis of a data set last year produced a line of best fit with equation y = 2.108x - 0.3818. Data was collected from the same sample this year and produced a line of best fit with equation y= 2.107x + 1.7455. Explain the verticalchange in going from last year's data to this year's data.
The slope of the line has increased, meaning it has become a positive number. This shift means that this year the data points were placed higher than the previous year.
A florist sells a dozen roses for $35.40. She sells individual roses for the same unit cost. How much would 18 roses cost?
Answer: 53.1
Step-by-step explanation: Divide 35.40 by 2 to get 17.7. now add 35.40 with 17.7 and you get 53.1
The set of all numbers greater than or equal to -10 and less than 9
The The set of all numbers greater than or equal to -10 and less than 9 will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.
How to illustrate the information?It should be noted that from the information, we are to find the set of all numbers greater than or equal to -10 and less than 9.
This simply means the numbers from -10 to 8.
Therefore, the numbers will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.
Learn more about numbers on:
brainly.com/question/17200227
#SPJ1
Mary has 65 roses and 104 tulips. What is
the greatest number of bouquets they can be
divided into if there will be the same number
of roses in each bouquet and the same
number of tulips in each bouquet?
The greatest number of bouquets they can be divided into if there will be the same number of roses in each bouquet and the same number of tulips in each bouquet is 5.
Given that:-
Number of roses Mary has = 65
Number of tulips Mary has = 104
We have to find the greatest number of bouquets they can be divided into if there will be the same number of roses in each bouquet and the same number of tulips in each bouquet.
HCF (65, 104) = 13
Hence, the groups of 13 roses and 13 tulips will together make a bouquet.
From 65 roses, 65/13 = 5 bouquets can be made.
From 104 tulips, 104/13 = 8 bouquets can be made.
Min (5,8) = 5.
To learn more about HCF, here:-
https://brainly.com/question/17240111
#SPJ1
In geometry,you can use deductive rules to
A
b
c
d
In geometry, you can use deductive rules to prove conjectures.
What is geometry?Geometry is defined as a subfield of mathematics that examines the measurement and relationships of surfaces, solids, solid surfaces, angles, and points. The calculation of a triangle's angles is a geometry example.
Geometry will categorize, quantify, and lack a counterexample. Once a concept has been defined, it can be utilized in subsequent definitions; for instance, parallel lines can be used in the definition of a parallelogram once they have been defined. classification, counterexample, quantification, and parallelogram.
Given Data
In geometry, you can use deductive rules to
In geometry, you can use deductive rules to prove conjectures.
In geometry, deductive rules can be used to demonstrate whether a particular assertion or conjecture is true or untrue. We narrow down a result proving a statement must be true or untrue by using deductive principles, such as definitions, postulates, and other theorems, in a logical order.
To learn more about geometry, visit:
https://brainly.com/question/3410069
#SPJ9
given: P(A) = 0.45, P(B) = 0.65, and P(A and B) = 0.35.
Find:
P (A or B)
P(A OR B) ( line on top)
P(A|B)
P(B|A)
Answer:
P(A or B) = 0.75P(A or B)' = 0.25P(A|B) = 0.54P(B|A) = 0.78Step-by-step explanation:
Normally we use the symbols U for set union corresponding to or and ∩ for set intersection corresponding to and.
But here i will use and and or
By the rules of probability
P(A or B) = P(A) + P(B) - P( A and B)
So P(A or b ) = 0.45 + 0.65 - 0.35 = 0.75
The complement of a set A is all the elements not in A
P(A') = 1 - P(A)
If we denote the complement of a set A as A' then your second expression is asking What is the complement of A or B or P(A or B)'
P(A and B)' = 1 - P(A or B) = 1- 0.75 = 0.25
P(A|B) = P(A and B)/P(B) = 0.35/0.65 = 0.54
P(B|A) = P(A and B)/P(A) = 0.35/0.45 = 0.78
Please help with the following question:
Using it's concept, the probabilities are given as follows:
a) Both go off on schedule: 0.30 = 30%.
b) Both go off on schedule: 0.2 = 20%.
What is a probability?A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.
From the text of the problem, the probability of A and not B is of 0.2, that is:
A x (1 - B) = 0.2.
We can multiply the probabilities as the events are independent.
In item a, the probability of neither is of 0.2, hence:
(1 - A) x (1 - B) = 0.2.
From the first equation, we have that:
A = 0.2/(1 - B).
From the second equation, we have that:
(1 - A) = 0.2/(1 - B).
Hence:
A = 1 - A
2A = 1
A = 0.5.
Then we can find B as follows:
(1 - A) x (1 - B) = 0.2.
1 - B = 0.2/0.5
1 - B = 0.4
B = 0.6.
The probability of both is:
A x B = 0.5 x 0.6 = 0.30 = 30%.
For item b, we consider that:
(1 - A) x B = 0.3.
We also have that:
A x (1 - B) = 0.2.
From the first equation:
B = 0.3/(1 - A).
Then, replacing on the second:
A x (1 - 0.3/(1 - A)) = 0.2
Which has a solution of:
A = 0.5, B = 0.4.
Hence the probability of both is:
0.4 x 0.5 = 0.2 = 20%.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
Consider the function f(x) = -2/3x +5.
What is ƒ ( − 1/2 ) ?
After substituting x = -1/2 in f(x), the value of the function f(-1/2) is found to be 5.333.
What exactly is function?A function from a set X to a set Y assigns exactly one element of Y to each element of X.
What is the function's domain and codomain?The set X is known as the function's domain, and the set Y is known as the function's codomain.
The given function is f(x) = -2/3x +5.
To obtain f(-1/2), we must substitute the value of x with -(1/2).
f(x) = -2/3x +5
f(-1/2) = -2/3×(-1/2) + 5
f(-1/2) = (2/6) + 5
f(-1/2) = 0.333 + 5
∴ f(-1/2) = 5.3333
Therefore, the value of the function f(-1/2) obtained after substituting x = -1/2 is 5.333.
Learn more about problems based on domain and codomain here:
https://brainly.com/question/2264373
#SPJ9
7. Write a biconditional for the following conditional. Determine the truth value
of the new statement. If two lines have the same slope, then they are parallel.
Line AB is parallel to CD, for instance, as indicated by the formula AB ll CD.
How do parallel lines work?
Lines in a plane that are regularly spaced apart are known as parallel lines. Parallel lines don't overlap each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.Only if the slopes of two lines are equal can they be said to be parallel. If two lines have different y-intercepts and equal slopes, they are said to be parallel. In a plane, parallel lines are two lines that never cross (meaning they will continue on forever without ever touching). The equal slopes of parallel lines are a distinctive feature. The rise (change in Y coordinates) over the run (change in X coordinates) of a line, or its steepness, is referred to as the slope of a line. The most typical way to depict parallel lines is with two vertical lines (ll). Line AB is parallel to CD, for instance, as indicated by the formula AB ll CD.Learn more about parallel lines
brainly.com/question/16701300
#SPJ13
Question 1 options:
Is the relation in this set of points a function?
{(-2, 6) , (4, 5) , (3, -3) , (6, 9), (4, -4)}
State whether the statement is true of false.
1. The relation is a function.
2. An element from the domain is paired with more than one element from the range.
Answer:
1.4 Relations and Functions
A relation is a correspondence between two sets. If x and y are two
elements in these sets and if a relation exists between x and y, then x
corresponds to y, or y depends on x.
DEFINITION OF A FUNCTION:
Let X and Y two nonempty sets. A function from X into Y is a relation that
associates with each element of X, exactly one element of Y.
However, an element of Y may have more than one elements of X
associated with it.
That is for each ordered pair (x,y), there is exactly one y value for each x,
but there may be multiple x values for each y. The variable x is called the
independent variable (also sometimes called the argument of the
function), and the variable y is called dependent variable (also
sometimes called the image of the function.) x = y2 is not a function from X into Y, because there
is not exactly one y value for each x.
Solving for y, you get y =
which means there are two possible values for y
Step-by-step explanation:
Can the angle measures of a triangle be 46°, 82°and 50°
Answer:Explanation:
No
The sum of the interior angles of a triangle is always 180°. in this case, the sum is:
Then,
46 + 82 + 50 = 178
Since 178 and 180 are distinct, 46°, 82°and 50° can't be the angle measures of a triangle.
PLEASE HELP- Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 25 gallons of fuel, the airplane weighs 2060 pounds. When carrying 45 gallons of fuel, it weights 2188 pounds. How much does the airplane weigh if it is carrying 60 gallons of fuel?
The linear function which can be used to represent the situation is y = 6.4x + 1900 and airplane weight if it is carrying 60 gallons of fuel is 2,284 pounds
How to find linear functiony = mx + b
where,
x = the number of gallons and y = the weight of the aircraft in pounds.Now, we can use the two sets of data points given to us to first solve for the slope m as:
m = (2188 - 2060) / (45 - 25)
= 128 / 20
= 6.4
y - yo = m(x - xo)
y - 2060 = 6.4(x - 25)
y - 2060 = 6.4x - 160
y = 6.4x - 160 + 2060
y = 6.4x + 1900
if it is carrying 60 gallons of fuelx = 60
So,
y = 6.4x + 1900
y = 6.4(60) + 1900
y = 384 + 1900
y = 2,284 pounds
Therefore, the weight of the airplane if it is carrying 60 gallons of fuel is 2,284 pounds
Read more on linear function:
https://brainly.com/question/4025726
#SPJ1
Select the correct answer. Based on these segment lengths, which group of segments can form a triangle? A. 3, 10, 14 B. 8, 7, 13 C. 3, 2, 5 D. 20, 7, 13
Answer:
B
Step-by-step explanation:
By the triangle inequality theorem, the sum of the lengths of the two shorter sides needs to be greater than the length of the longest side.
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar. y = -x² + 64x - 292
Answer:
what
Step-by-step explanation:
i think maybe like… actually
Isabelle is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $9, and her grandmother has pledged $1 per mile. If Isabelle walks a certain distance, the two donors will end up owing the same amount. How much will each donor owe?
Answer:
9 mileds
Step-by-step explanation:
Find the length of the arc on a circle with a radius of 2.4 kilometers and is intercepted by a central angle measuring 150°. Leave your answer in terms of π. A. 6π/5kmB. 6 kmC. 12π/5kmD. 2π km
Given:
The radius of the circle = 2.4 kilometers
The measure of the arc = 150°
The length of the arc is given by the formula:
[tex]A=\theta\cdot r[/tex]Note: we will convert the angle from degrees to radian
So, the length of the arc =
[tex](150\cdot\frac{\pi}{180})\cdot2.4=\frac{150}{180}\cdot2.4\cdot\pi=2\pi[/tex]So, the answer will be option D. 2π km
Hi, I need to send you the question as I have written
recall the formula for velocity, which involves distance and time:
velocity = distance / time
since the woman's velocity is: 4.5 Km/h, then in order to cover 10 km, we need to find the time in the equation:
4.5 km/h = 10 km / t
multiply both sides by the time (t)
4.5 * t = 10
divide both sides by 4.5 in order to isolate t completely
t = 10 / 4.5
then
t = 2 hours and 0.2222 hours which can be translated into minutes by multiplying this by 60: 40/3 = 13 minutes and 0.33333 minutes. which can be converted into seconds by multiplying it by 60: 20 seconds
Then she will cover that distance in 2 hours, 13 minutes and 20 seconds.