Answer:
184.8
Step-by-step explanation:
y =kx
k=y/x
k=42/5=8.4
y=8.4*22
Find hypotenuse,perpendicular and base
Answer:
Hypotenuse = XY = 17 cm
Base = YZ = 15 cm
Perpendicular = XZ = 8 cm
[tex]\int\limits^a_b {(1-x^{2} )^{3/2} } \, dx[/tex]
First integrate the indefinite integral,
[tex]\int(1-x^2)^{3/2}dx[/tex]
Let [tex]x=\sin(u)[/tex] which will make [tex]dx=\cos(u)du[/tex].
Then
[tex](1-x^2)^{3/2}=(1-\sin^2(u))^{3/2}=\cos^3(u)[/tex] which makes [tex]u=\arcsin(x)[/tex] and our integral is reshaped,
[tex]\int\cos^4(u)du[/tex]
Use reduction formula,
[tex]\int\cos^m(u)du=\frac{1}{m}\sin(u)\cos^{m-1}(u)+\frac{m-1}{m}\int\cos^{m-2}(u)du[/tex]
to get,
[tex]\int\cos^4(u)du=\frac{1}{4}\sin(u)\cos^3(u)+\frac{3}{4}\int\cos^2(u)du[/tex]
Notice that,
[tex]\cos^2(u)=\frac{1}{2}(\cos(2u)+1)[/tex]
Then integrate the obtained sum,
[tex]\frac{1}{4}\sin(u)\cos^3(u)+\frac{3}{8}\int\cos(2u)du+\frac{3}{8}\int1du[/tex]
Now introduce [tex]s=2u\implies ds=2du[/tex] and substitute and integrate to get,
[tex]\frac{3\sin(s)}{16}+\frac{1}{4}\sin(u)\cos^3(u)+\frac{3}{8}\int1du[/tex]
[tex]\frac{3\sin(s)}{16}+\frac{3u}{4}+\frac{1}{4}\sin(u)\cos^3(u)+C[/tex]
Substitute 2u back for s,
[tex]\frac{3u}{8}+\frac{1}{4}\sin(u)\cos^3(u)+\frac{3}{8}\sin(u)\cos(u)+C[/tex]
Substitute [tex]\sin^{-1}[/tex] for u and simplify with [tex]\cos(\arcsin(x))=\sqrt{1-x^2}[/tex] to get the result,
[tex]\boxed{\frac{1}{8}(x\sqrt{1-x^2}(5-2x^2)+3\arcsin(x))+C}[/tex]
Let [tex]F(x)=\frac{1}{8}(x\sqrt{1-x^2}(5-2x^2)+3\arcsin(x))+C[/tex]
Apply definite integral evaluation from b to a, [tex]F(x)\Big|_b^a[/tex],
[tex]F(x)\Big|_b^a=F(a)-F(b)=\boxed{\frac{1}{8}(a\sqrt{1-a^2}(5-2a^2)+3\arcsin(a))-\frac{1}{8}(b\sqrt{1-b^2}(5-2b^2)+3\arcsin(b))}[/tex]
Hope this helps :)
Answer:[tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{3arcsin(a) + 2a(1 - a^2)^\Big{\frac{3}{2}} + 3a\sqrt{1 - a^2}}{8} - \frac{3arcsin(b) + 2b(1 - b^2)^\Big{\frac{3}{2}} + 3b\sqrt{1 - b^2}}{8}[/tex]General Formulas and Concepts:
Pre-Calculus
Trigonometric IdentitiesCalculus
Differentiation
DerivativesDerivative NotationIntegration
IntegralsDefinite/Indefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
U-Substitution
Trigonometric SubstitutionReduction Formula: [tex]\displaystyle \int {cos^n(x)} \, dx = \frac{n - 1}{n}\int {cos^{n - 2}(x)} \, dx + \frac{cos^{n - 1}(x)sin(x)}{n}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for u-substitution (trigonometric substitution).
Set u: [tex]\displaystyle x = sin(u)[/tex][u] Differentiate [Trigonometric Differentiation]: [tex]\displaystyle dx = cos(u) \ du[/tex]Rewrite u: [tex]\displaystyle u = arcsin(x)[/tex]Step 3: Integrate Pt. 2
[Integral] Trigonometric Substitution: [tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos(u)[1 - sin^2(u)]^\Big{\frac{3}{2}} \, du[/tex][Integrand] Rewrite: [tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos(u)[cos^2(u)]^\Big{\frac{3}{2}} \, du[/tex][Integrand] Simplify: [tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos^4(u)} \, du[/tex][Integral] Reduction Formula: [tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{4 - 1}{4}\int \limits^a_b {cos^{4 - 2}(x)} \, dx + \frac{cos^{4 - 1}(u)sin(u)}{4} \bigg| \limits^a_b[/tex][Integral] Simplify: [tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4}\int\limits^a_b {cos^2(u)} \, du[/tex][Integral] Reduction Formula: [tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg|\limits^a_b + \frac{3}{4} \bigg[ \frac{2 - 1}{2}\int\limits^a_b {cos^{2 - 2}(u)} \, du + \frac{cos^{2 - 1}(u)sin(u)}{2} \bigg| \limits^a_b \bigg][/tex][Integral] Simplify: [tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4} \bigg[ \frac{1}{2}\int\limits^a_b {} \, du + \frac{cos(u)sin(u)}{2} \bigg| \limits^a_b \bigg][/tex][Integral] Reverse Power Rule: [tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4} \bigg[ \frac{1}{2}(u) \bigg| \limits^a_b + \frac{cos(u)sin(u)}{2} \bigg| \limits^a_b \bigg][/tex]Simplify: [tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3cos(u)sin(u)}{8} \bigg| \limits^a_b + \frac{3}{8}(u) \bigg| \limits^a_b[/tex]Back-Substitute: [tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(arcsin(x))sin(arcsin(x))}{4} \bigg| \limits^a_b + \frac{3cos(arcsin(x))sin(arcsin(x))}{8} \bigg| \limits^a_b + \frac{3}{8}(arcsin(x)) \bigg| \limits^a_b[/tex]Simplify: [tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{3arcsin(x)}{8} \bigg| \limits^a_b + \frac{x(1 - x^2)^\Big{\frac{3}{2}}}{4} \bigg| \limits^a_b + \frac{3x\sqrt{1 - x^2}}{8} \bigg| \limits^a_b[/tex]Rewrite: [tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{3arcsin(x) + 2x(1 - x^2)^\Big{\frac{3}{2}} + 3x\sqrt{1 - x^2}}{8} \bigg| \limits^a_b[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{3arcsin(a) + 2a(1 - a^2)^\Big{\frac{3}{2}} + 3a\sqrt{1 - a^2}}{8} - \frac{3arcsin(b) + 2b(1 - b^2)^\Big{\frac{3}{2}} + 3b\sqrt{1 - b^2}}{8}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Can someone help me find the answer?
Answer:
a. x = 3/a
Step-by-step explanation:
Add all like terms on left hand side of the equation:
5 ax + 3 ax => 8 ax
Bring like term 4ax on left hand side
8ax - 4ax
=> 4ax
Therefore we get 4ax = 12
ax = 12/4
ax = 3
x = 3/a
Solve the equation by factoring: 5x^2 - x = 0
Answer:
Step-by-step explanation:
x = 0, 1/5
.Part D. Analyze the residuals.
Birth weight
(pounds)
Adult weight
(pounds)
Predicted
adult weight
Residual
1.5
10
3
17
1
8
2.5
14
0.75
5
a. Use the linear regression equation from Part C to calculate the predicted adult weight for each birth weight. Round to the nearest hundredth. Enter these in the third column of the table.
b. Find the residual for each birth weight. Round to the nearest hundredth. Enter these in the fourth column of the table.
c. Plot the residuals.
d. Based on the residuals, is your regression line a reasonable model for the data? Why or why not?
Answer:
Hi there! The answers will be in the explanation :D
Step-by-step explanation:
a) I'll attach a doc for the table so it'll basically answer a and b.
c) I'll also attach the graph.
d) I'm not entirely sure for this question, but I'll do my best to answer it correctly for you. I would say no, because we can see that the residuals are all positive, but the graph we're looking is going down which means it's negative. We can also see the table is increasing a bit so it doesn't really make any sense...
Hope this helped you!
A photographer bought 35 rolls for $136.44 what was the price of one roll
Answer:
$3.90
Step-by-step explanation:
136.44/35= (rounded tot the nearest hundredth) $3.90
Answer:
136.44÷36 =3.79
3.79×36=136.44
Step-by-step explanation:
So one ball cost 3. 79
Which equation has a graph that is a parabola with a vertex at (-2, 0)?
y= -2x^2
y = (x + 2)^2
y= (x – 2)^2
y= x^2 – 2
A square prism and a cylinder have the same height. The area of the cross-section of the square prism is 628 square units, and the area of the cross-section of the cylinder is 200π square units. Based on this information, which argument can be made?
The volume of the square prism is one third the volume of the cylinder.
The volume of the square prism is half the volume of the cylinder.
The volume of the square prism is equal to the volume of the cylinder.
The volume of the square prism is twice the volume of the cylinder.
Answer:
C. The volume of the square prism is equal to the volume of the cylinder.
Step-by-step explanation:
I took the test and it was right
A car is advertised with a price of $16336. The payment plan to own a car is $474 per month for 8 years. What is the
amount of interest paid?
Graph the complex numbers in the complex plane
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The imaginary value is plotted on the vertical axis in the same way that the y-coordinate would be for an ordered pair (x, y). Similarly, the real value is plotted on the horizontal axis.
__
I find it helpful to think of the complex number a+bi as equivalent to the ordered pair (x, y) = (a, b) when it comes to graphing.
What is the volume of the cylinder below?
Answer:
A
Step-by-step explanation:
v=πr2h
r=(3)²* 5
45π unit³
For f(x) = 4x2 + 13x + 10, find all values of a for which f(a) = 7.
the solution set is ???
Answer:
f(7)=109
Step-by-step explanation:
Since f(a)=7 then you just imput 7 on each x like this f(7)=8+13(7)+10= 109
I need help answering this question thank guys
Write –0.38 as a fraction.
Answer:
-19/50
Step-by-step explanation:
Answer:
-19/50
Step-by-step explanation:
The population of a town is decreasing exponentially according to the formula
P = 7,285(0.97)t, where t is measured in years from the present date. Find the population in 2 years, 9 months. (Round your answer to the nearest whole number.)
Answer: 6669
Step-by-step explanation:
I hope I did this right... anyways,
t, is represented by years, which is given to us by 2 years and 9 months. Assuming you would put 2.9 for t.
Additionally, as you can't have a decimal for a person, and they've asked for it to be rounded to the nearest whole number, there would be 6669 people in 2 years and 9 months.
The formula used is:
[tex]7285(0.97)^2^.^9[/tex]
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
3x + 6y = -42
Answer:
y = -1/2x -7
Step-by-step explanation:
3x + 6y = -42
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
Subtract 3x from each side
3x-3x+6y = -3x-42
6y = -3x-42
Divide each side by 6
6y/6 = -3x/6 - 42/6
y = -1/2x -7
What is the x intercept of the graph that is shown below? Please help me
Answer:
(-2,0)
Step-by-step explanation:
The x intercept is the value when it crosses the x axis ( the y value is zero)
x = -2 and y =0
(-2,0)
Triangles ABC and DEF are similar. Find the
perimeter of triangle DEF.
a. 34.7 cm
b. 25.3 cm
c. 15 cm
d. 38 cm
Please show work to help me understand.
If Both triangles are similar the ratio of sides will be same
[tex]\\ \sf\longmapsto \dfrac{AB}{AC}=\dfrac{DE}{DF}[/tex]
[tex]\\ \sf\longmapsto \dfrac{8}{10}=\dfrac{12}{DF}[/tex]
[tex]\\ \sf\longmapsto 8DF=120[/tex]
[tex]\\ \sf\longmapsto DF=\dfrac{120}{8}[/tex]
[tex]\\ \sf\longmapsto DF=15cm[/tex]
Now
[tex]\\ \sf\longmapsto Perimeter=DF+DE+EF[/tex]
[tex]\\ \sf\longmapsto Perimeter=15+11+12[/tex]
[tex]\\ \sf\longmapsto Perimeter=38cm[/tex]
I need help in understanding and solving quadratic equations using the quadratic formula
x^2+8x+1=0
Answer:
Exact Form: -4⊥√15
Decimal Form:
0.12701665
7.87298334
…
A rational expression is _______ for those values of the variable(s) that make the denominator zero.
9514 1404 393
Answer:
undefined
Step-by-step explanation:
A rational expression is undefined when its denominator is zero.
Can I pleaseee have help with all 3 parts of this ? Thank you :D
Answer:
Part A:
the first step is to work out the brackets by multiplying the coefficients outside the brackets by everything in the brackets.
Part B:
5(3x-4)=-2(6x-9)
15x-20=-12x+18
Part C:
15x-20=-12x+18
15x+12x=18+20
27x/27=38/27
x=1.407
I hope this helps
A circle P is circumscribed about a regular hexagon ABCDEF
If segment AE is drawn, triangle AEF is a/n ____________ triangle. Select one:
a. isosceles
b. scalene
c. equilateral
d. right
i’ll mark u as brainliest:))
9514 1404 393
Answer:
a. isosceles
Step-by-step explanation:
Segments EF and FA of the hexagon are the same length, so the triangle is an isosceles triangle.
Find the area of each figure one of the sides are 8.3cm it’s a square btw
Answer:
68.89 cm
Step-by-step explanation:
8.3 X 8.3 would equal 68.89 cm. We can see that one side is 8.3 cm, and the other sides don't say their sides, so the only number we will use for multiplying is 8.3, and all sides of the square will be 8.3. The equation is L X W, where L is the length, and W is the width. Since 8.3 is on all four sides, it will also be the length and the width on the equation. As a result, 68.89 cm would be the final answer.
Answer:
I don't real know if this is right, but I think its this:
68.89 cm2 is the area.
write your answer in simplest radical form
9514 1404 393
Answer:
4√2
Step-by-step explanation:
In a 30°-60°-90° triangle, the ratio of side lengths is ...
1 : √3 : 2
That is, the hypotenuse (c) is double the short side (2√2).
c = 4√2
Bà B đến ngân hàng ngày 05/05/2019 để gửi tiết kiệm 250 triệu đồng thời hạn 3 tháng, lãi suất 7%/năm, NH trả lãi định kỳ hàng tháng (kỳ lĩnh lãi đầu tiên là ngày 05/05/2019). Đến ngày 05/08/2019, bà B tất toán sổ tiết kiệm trên. Tính số tiền bà B nhận được vào ngày đáo hạn sổ tiết kiệm là? (Cơ sở công bố lãi suất là 365 ngày)
Answer:
Ask in English then I can help u
Answer pleaseeeeeeee
Answer:
17x^2-9x-9 -->B
Step-by-step explanation:
7x^2 -12x +3 +10x^2+3x-12
There are 5 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?
Answer:
60
Step-by-step explanation:
To begin, we can look at combinations and permutations. A permutation or combination is when we need to find how many possibilities there are to choose a certain amount of objects (in this case, candidates) given an array of options (members on the board)
Combinations are when the order doesn't matter, and permutations are when the order does matter. Here, we know that we care whether someone is chairperson or secretary. If we were to just choose three for an "elite" board, and there were no specific positions in the board, then order would not matter. However, because it does matter which person gets which role, order does matter.
Assuming that someone cannot have more than one role, we know that this is a permutation without repetition. The formula for this is
(n!) / (n-r)!, where we have to choose from n number of people and choose r number of people. We have 5 members to choose from, and 3 people to choose, making our equation
(5!) / (5-3)! = 120 / 2! = 120/2 = 60
The prices of paperbacks sold at a used bookstore are approximately Normally distributed, with a mean of $7.85 and a standard deviation of $1.25.
Use the z-table to answer the question.
If the probability that Joel randomly selects a book in the D dollars or less range is 56%, what is the value of D?
$4.46
$7.75
$8.04
$8.10
(C) 8.04
Answer:
The answer you want is indeed, (C).
8.04
ED2021
Answer:
C) 8.04
Step-by-step explanation:
edge 2023
5 oranges weigh 1.5 kg, 8 apples weigh 2 kg. What would be the total weight of 3 apples and 4 oranges?
Answer: oranges 1.2 Kg and apples 0.75 Kg.
Step-by-step explanation:
Oranges (4)(1.5)/5
Apples (3)(2)/8
Of the respondents, 502 replied that America is doing about the right amount. What is the 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment?
Answer:
The 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment is (0.461, 0.543), considering [tex]n = 1000[/tex]
Step-by-step explanation:
Incomplete question, so i will suppose this is a sample of 1000.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Of the n respondents, 502 replied that America is doing about the right amount.
Supposing [tex]n = 1000[/tex], so [tex]\pi = \frac{502}{1000} = 0.502[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.502 - 2.575\sqrt{\frac{0.502*0.498}{1000}} = 0.461[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.502 + 2.575\sqrt{\frac{0.502*0.498}{1000}} = 0.543[/tex]
The 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment is (0.461, 0.543), considering [tex]n = 1000[/tex]
