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]
How many feet of chain fence are necessary to
enclose a dog pen that is square and has an area of
144 square feet?
Answer:
48 feet
Step-by-step explanation:
Areas of a square is the length times the width. In a square the length and width are the same number because all the sides of a square have the same length.
12 x 12 = 144, so each side of the pen is 12 feet. We want to find the perimeter (the distance around the square). 4(12) = 48
b. Evaluate 2w-60 when w=140.
Answer: 220
Step-by-step explanation: quick maths ;)
Customers are charge a late fee of 20% of their bill . This person is a week late on a bill of 200$ what should we charge for late fee
Answer:
Step-by-step explanation:
20$
Your original grades on your exams were: 75, 85, 90, 90, 100, 75, 80, 100, 90. You retake the exams and now your scores are: 85, 85, 100, 90, 100, 85, 80, 100, 90. By how many percentage points did you improve your average score? Hint: Find the mean of both sets of data. Then find the difference between the two. Round to the nearest %.
Based on your original grades in your exams and the scores after you retake your exams, the percentage points you improved your average score by is 3.83%
How to find the percentage improvement?To find the percentage that you improved by, the first thing to do is to find your average score in the first exam:
= (75 + 85 + 90 + 90 + 100 + 75 + 80 + 100 + 90) / 9
= 785 / 9
= 87.22
The average score after the exam was retaken was:
= (85 + 85 + 100 + 90 + 100 + 85 + 80 + 100 + 90) / 9
= 815 / 9
= 90.56
The percentage increase is:
= (90.56 - 87.22) / 87.22 x 100%
= 0.0382939692731024994267369869296 x 100%
= 3.83%
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Which equation shows a slope of -5 and a y-intercept of (0,1)?
Answer: second option
y= -5x +1
Mia used a pattern to create figures with building blocks. The first three figures are shown.
Figure 1
Mia needs
Assuming the building pattern continued, how many blocks would be needed to build the 6th figure?
Figure 2
AX blocks to build the 6th figure.
Figure 3
Answer:
I think the answer would be 33
Find the average rate of change of f(x)=x^2-4x+1 from x=2 to x=6
Answer:
The answer is 4
Plot the points (-8, 7) and (5, 7) on the coordinate plane below.
What is the distance between these two points?
The distance between two points is 15.
What is distance between two points?The length of the line segment bridging two points on a plane is known as the distance between the points. Counting each number in between them is a quick and easy approach to determine how far apart two numbers are on a number line. Finding the distance by taking the absolute value of the values' difference is a quicker method. For instance, |4| and |-4| have the same absolute value of 4, which is 4.
Given Data
Points (-8,7) and (5,7)
Formula of distance between two points
d = [tex]\sqrt{(x_{2} - x_{1})^{2}+(y_{2} - y_{1})^{2} }[/tex]
x₂= 7 x₁= -8
y₂ = 7 y₁ = 7
d = [tex]\sqrt{(7-(-8))^{2}+(7-7)^{2} }[/tex]
d = [tex]\sqrt{(7+8)^{2}(0) }[/tex]
d = [tex]\sqrt{15^{2} }[/tex]
d = 15
The distance between two points is 15.
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In the figure, m/RPZ= 95 and TU || RQ || VW. Find the measure of angle UZP.
The measure of the corresponding angle; ∠UZP = 95°.
What is defined as the term corresponding angle?The definition of corresponding angles states that when two parallel lines intersect with a third, the angles that take up its same relative position at every intersection are said to be corresponding angles to one another. The statement "If a line intersects parallel lines, therefore the corresponding angles with in two intersection regions are congruent" is true either way, based on the corresponding angles theorem.For the given question;
Lines TU || RQ || VW are parallel.
The measure of the ∠RPZ= 95.
Thus, from the diagram,
∠UZP = ∠RPZ= 95
As both angles are corresponding angle so equal.
Therefore, the measure of the ∠UZP = 95°.
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f the gradient of a line is 3, what is the gradient of the line which is perpendicular to A
Answer:
-1/3
Step-by-step explanation:
gradients of perpendicular lines= m1 × m2=-1
hence , 3 × m2 = -1
m2 -1/3
10. Supose you bought a digital album from your favorite artist and set iTunes to play
the album in random order without repeats. The album has 10 songs and it turns
out you really like 5 of them. Find the following probabilities for the first 2 songs
played at random.
a) You like both of them 2
b) B) you like neither of the songs ,
c) C) you like at least one of the songs
Probability to like both of them is 0.02.
Probability to like neither of the songs is 0.62.
Probability to like at least one of the songs is 0.44
What is probability?
Probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Given Data
The album has 10 songs and
it turns out you really like 5 of them.
a) You like both of them
P(like both of them )
= [tex]\frac{2}{10}[/tex] ×[tex]\frac{1}{9}[/tex]
= 0.02
Probability to like both of them is 0.02.
b )you like neither of the songs
P(like neither of the songs)
= [tex]\frac{8}{10}[/tex] ×[tex]\frac{7}{9}[/tex]
= 0.62
Probability to like neither of the songs is 0.62.
c) you like at least one of the songs
P( like at least one of the songs)
2 ×[tex]\frac{2}{10}[/tex] ×[tex]\frac{1}{9}[/tex]
= 0.44
Probability to like at least one of the songs is 0.44
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I am a product of three different prime numbers, my largest factor is 13. I am between 185 and 200 who am I ?
The product of three different prime numbers that has largest factor is 13 and is between 185 and 200 is 195.
What are prime numbers?It should be noted that prime numbers are the numbers that can be divisible by only 1 and itself. They include 2, 3, 5, 7, 11, 13, etc.
It should be noted that the information illustrated that the prime numbers are 3, 5 and 13. The multiplication will be:
= 3 × 5 × 13
= 195
The number is between 185 and 200.
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Find the contrapositive and determine if it is true or false.
Statement : Obtuse angles are not right angles.
The contrapositive statement is If an angle is a right angle, then is not an obtuse angle True. Option B
What is a contrapositive statement?
A contrapositive statement can be defined as a theorem created by contradicting the hypothesis and conclusion of a statement.
It involves exchanging both the hypothesis and conclusion of a given conditional statement and then negating both hypothesis and conclusion.
It is a combination of an inverse and converse statements.
The hypothesis and conclusion are interchanged or switched.
A contrapositive statement is written as;
a b is equivalent to b ~a
Given the statement;
Obtuse angles are not right angles.
The contrapositive statement is :
If an angle is a right angle, then is not an obtuse angle
Thus, the contrapositive statement is true
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3.A car starts from A and is driven 50km to B on a bearing of 072 0 . It is then driven 30km to C on a bearing of 326 0 .
Answer:
aaaaaaaaaa
Step-by-step explanation:
aaaaaaaa
Solve the following linear equation using equivalent equations to isolate the variable. Express youranswer as an integer, as a simplified fraction, or as a decimal number rounded to two places.3y - y = -5AnswerHow to enter your answer (opens in new window)KeypadKeyboard Shortcutsy =
3y - y= -5
2y= -5
y= -5/2
y= -2.5
rounded of answer is 3
Mr. Vigrass was driving at a constant speed he drove 168 miles in 3 1/2 hours at that speed how many miles will he drive in one hour
Using speed, distance and time relation, Mr. Vigrass will travel 48 miles in an hours.
What is the relation between speed, distance and time?If we know how far something travels and how long it takes, we can determine how fast something is moving in a straight line. This equation illustrates the link between journey time, distance, and speed:
Distance divided by travel time equals speed.
Distance equals Time * Speed
Time = Speed / Distance
Distance x Time equals Speed
Given,
distance = 168 miles
time = 3 1/2 hours
speed = distance / time
speed = 168 × 2/7
speed = 48 miles/hour
At same speed,
distance travelled in 1 hour will be
distance = speed × time
distance = 48 × 1
distance = 48 miles.
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Can someone help me with this geometry question?
4/5 is the probability that jack will win at least 30 points in a throw.
What do we mean by probability?The probability is the likelihood that something will happen, to put it simply.The likelihood or likelihood of various outcomes can be discussed when we don't know how an event will turn out.The study of events that fit into a probability distribution is known as statistics.The probability is determined by dividing the total number of outcomes by the total number of potential events.Odds and probability are two different concepts.Calculating odds involves dividing the probability of an event by the probability that it won't happen.So, the probability formula:
P = favourable events/Total number of eventsFavorable events: (At least 30 points) ⇒ 30 + 40 + 50Total events: (Sum of all points) ⇒ 150Now, insert values in the formula as follows:
P = favourable events/Total number of eventsP = 120/150P = 12/15P = 4/5Therefore, 4/5 is the probability that jack will win at least 30 points in a throw.
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A school event requires 4 adults for every 35 kids. 12 adults are available. How many kids can attend?
Answer:
105 and five kids can attend
Step-by-step explanation:
12 divide by 4=3
this means that 3 groups of kids can go
so 35 x 3=105
therefore
Answer:
105 and five kids can attend
Step-by-step explanation:
12 divide by 4=3
this means that 3 groups of kids can go
so 35 x 3=105
So the answer is 105
The functions f and g are defined as follows.
f (x) = -2x^3 - 3 g (x) = 2x + 4
Find f (-2) and g (-6).
Simplify your answers as much as possible.
If the function are f(x) = [tex]-2x^{3}-3[/tex] and g(x)= 2x+4, then the values of
f(-2) = 13
g(-6) = -8
The functions are
f(x) = [tex]-2x^{3}-3[/tex]
g(x) = 2x+4
The function is an expression that represents the relationship between one variable and another variable. if one variable is independent variable another variable will be dependent variable.
First we have to find the value of f(-2)
Substitute the value of x= -2 in the given function
f(-2) = [tex]-2(-2)^3-3[/tex]
= -2×-8-3
= 16-3
= 13
Next we have to find the value of g(-6)
Substitute the value of x= -6 in the given function
g(-6) = 2×-6+4
= -12+4
= -8
Hence, if the function are f(x) = [tex]-2x^{3}-3[/tex] and g(x)= 2x+4 then the values of
f(-2) = 13
g(-6) = -8
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if f(x)= 2x(1-x) ^2 then f(1)=
The value of f(1) is the value of function f(x) at x = 1 which is 0.
What is function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
So,
We have given that the function
f(x)=[tex]2x(1-x)^2[/tex]
So, when x = 1
f(x)= [tex]2(1)(1-1)^2[/tex]
f(x)= 2(1)(0)
f(x)= 0
Therefore, The value of function f(x ) at x = 1 is f(1) 0.
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What’s the correct answer answer asap for brainlist
Answer:
answer a
Step-by-step explanation:
spongy bone in the center
Q/ evaluate.
(27) 2 over 3
Harlan is preparing a dip for a party the recipe calls for 4 cups of sour cream and three packages of onion soup mix he doesn’t want to prepare that my street decides to use only 2 cups of sour cream and one and a half packages of onion soup mix is this a proportional relationship
Yes!, This is a proportional relationship.
A proportional relationship means that the ratios of two variables are equal.
According to the question, the requirements of the recipe are
Number of cups of sour cream required be x1 = 4
Number of packages of onion soup mix required be y1 = 3
Used products by Harlan,
Cups used by Harlan of sour cream be x2 = 2
Packages of onion soup mix used by Harlan be y2 = 1.5
As we can see that,
x1/x2 = y1/y2
4/2 = 3/1.5
2 = 2
L.H.S = R.H.S ( ratio is same)
Therefore, we conclude that the above case is a proportional relationship.
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How do you write 0.083 as a fraction?
Answer: 83/1000 should be the answer
Step-by-step explanation:
0.083 goes to the thousandths place. Which would mean the denominator would be 1000, and in the hundredths and thousandths place it says 83, so the numerator would be 83. Resulting in the answer, 83/100.
The solution of the expression 0.083 in form of fraction is,
⇒ 83/1000
We have to given that,
Write a number 0.083 as a fraction.
Here, The number is,
⇒ 0.083
⇒ 0.083 x 1000 / 1000
⇒ 83/1000
Therefore, The solution of the expression 0.083 in form of fraction is,
⇒ 83/1000
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F(x)=|x|-7 describe the transformation of each function compared to its parent function
Compared to the parent function f(x)=|x|, the graph of F(x) is a translation 7 units down.
1. What is the value of 10/0?2. Which of the following fractions is equivalent to 3/4?
Answer:
1. Undefined
2. A
Explanation:
Part 1
[tex]\frac{10}{0}=\text{Undefined}[/tex]The value of 10/0 is undefined because you cannot divide by 0.
Part 2
From the given options:
[tex]\begin{gathered} \frac{-3}{-4}=\frac{3}{4}\text{ (Cancel the minus on both the top and bottom)} \\ -(\frac{3}{4})=-\frac{3}{4} \\ -(\frac{-3}{-4})=-\frac{3}{4} \\ \frac{-3}{4}=-\frac{3}{4} \end{gathered}[/tex]Therefore, A is the correct choice.
How can the rational zero theorem be used to find the zeros of polynomials
P is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P if P(x) is a polynomial with integer coefficients and if is a zero of P(x) (P() = 0). (x).
The Reasonable Zeros Theorem can be used to locate every rational zero in a polynomial.
What does the theorem of rational zeros state?According to the Rational Zeros Theorem, if P(x) is an integer-coefficient polynomial and is its zero (P() = 0), then p is a factor of P(xconstant )'s term and q is a factor of P's leading coefficient (x).
What does rational number theorem determines?Finding the rational solutions to a polynomial equation is done using the rational root theorem, as its name suggests (or zeros or roots of a polynomial function). The answers obtained from any polynomial equation are referred to as the roots or zeros of polynomials. It's not necessary for a polynomial to have rational zeros.
So, to find rational zero theorem states:
If P(x) is a polynomial with integers coefficients and if is a zero of P(x)(P()=0), then
P is a factor of the constant term of P(x) and q is a factor of of the leading coefficient
Of P(x).
To find all the rational zero of a polynomial we can use the rational zeros theorem
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Explain why when multiplying powers you add rather than multiply the exponents.
use real numbers for the proof
3^3 times 3^2 =
27 times 9 =
243 which is
3^5
Assume that A TUVE AWXY. Which of the following congruence statements
are correct? Check all that apply.
A. VU a YX
B. TV WY
C. ZY ZV
D. LT LX
E. ZWLV
F. ZX=ZU
For the congruent triangles TUV ≅ WXY, the correct statement are-
option B; TV ≅ WYoption c: ∠Y = ∠Voption f: ∠x = ∠UWhat is defined as the congruent triangles?The dimensions of the sides and angles of two or even more triangles determine their congruence. A triangle's size is determined by its three sides, and its shape is determined by its three angles. Two triangles have been shown to be congruent if the pairs of their corresponding sides and angles are equal.For the congruent triangles TUV ≅ WXY
By the property of congruency, the respective side and angles of each triangles are equal.
Thus, the correct option described the property of congruency are-
option B; TV ≅ WYoption c: ∠Y = ∠Voption f: ∠x = ∠UThus, the correct statement for congruent triangles are obtained.
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a movie theater is offering a special summer pass.passholders pay $8 per movie for the first 5 movies and watch additional movies for free up to maximum of 15 movies. the function c gives the total cost in dollars for a pass holder to watch n movies. describe as completely as possible the range of c
The function that completely describes the condition is a piecewise function;
[tex]\begin{cases}c=8n\text{ }\mleft\lbrace1\leq n\leq5\mright? \\ c=0\text{ }\mleft\lbrace n>5\mright?\end{cases}[/tex]