Evaluate the integral. (Use C for the constant of integration.)
cos(x) (8 + 7 sin^2(x)) dx

Answers

Answer 1

Answer: [tex]8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]

Step-by-step explanation:

Consider [tex]\int \cos(x) (8+7 \sin^2(x)) \, dx[/tex]

Substitute  t= sinx

then dt = cos x dx

[tex]\int \cos(x) (8+7 \sin^2(x)) \, dx = \int (8+7t^2)dt\\\\ =8t+7(\dfrac{t^3}{3})+C[/tex]

[tex][\int x^ndx=\dfrac{x^{n+1}}{n+1}+C][/tex]

[tex]=8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]

Hence, [tex]\int \cos(x) (8+7 \sin^2(x)) \, dx=8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]


Related Questions

If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are given by the vector functions for t 0. Do the particles collide? If they collide find t. If not enter NONE.
r1(t) = t^2, 8t − 15, t^2
r2(t) = 11t − 30, t^2, 13t − 40
t=

Answers

Answer:

Step-by-step explanation:

[tex]r_1(t) = < t^2 , 8t-15,t^2> \\ \\ r_2(t) = < 11t-30, \ t^2 , \ 13t-40> \\ \\ at \ r_1 = r_2 \\ \\ t^2 = 11t - 30 , \ \ \ \ \ \ \ \ \ \ \ \ 8t - 15 = t^2 , \ \ \ \ \ \ \ \ \ t^2 = 13t -40 \\ \\ t^2 - 11t + 30\ \ \ \ \ \ \ \ \ \ \ \ t^2 -8t + 15 , \ \ \ \ \ \ \ \ \ \ \ \ t^2 -13t + 40 \\ \\ t^2 -8t-3t + 30=0 \ \ \ \ \ \ t^2 - 2t -4t + 15=0 \ \ \ \ \ \ t^2 - 1t - 13t + 40 =0[/tex]

[tex](t-6)(t-5) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-3) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-8)[/tex]

[tex]\mathbf{The \ common \ value \ of \ t \ = \ 5}[/tex]

The square pyramid has a base area of 144 square centimeters and a height of 12 centimeters. Find the volume.

Answers

Step-by-step explanation:

the answer is 576 cubic centimetre.

Answer:

Its 576 cubic centimeters

Step-by-step explanation:

Find cos (P)
Q
74
70
P
24
R
A.
37
12
В.
35
37
C.
12

Answers

Answer:

cos P = 71.09

Step-by-step explanation:

cos = [tex]\frac{adajcent}{hypotenuse}[/tex]

cos P = [tex]\frac{24}{74}[/tex]

cos P = 0.324

cos-1 of 0.324 is 71.09

cos P = 71.09

Figure A is a scale image of Figure B. Figure A: 7.2 , 4. Figure B: 3 , x. What is the value of x

Answers

Answer: 5.4

Step-by-step explanation:

Answer:

5.2

Step-by-step explanation:

What is the value of 8+(7+1)^2÷4(1/2)^4​

Will Mark Brainliest

^=exponents

Answers

Answer:

264

Step-by-step explanation:

8+(7+1)^2 / 4(1/2)^4

8+ 8^2 / 4(1/2)^4

8+64/4(1/16)

8+64 / 1/4

8 + (64*4)

8+256

264

The number line is 0 to 1 true or false 2/8 is close to 0

Answers

Answer:

True

Step-by-step explanation:

from the scale 0-1, 2/8 is closer to 0 because you round 2 down to 0, which gives you 0.

Maurice Luken deposited $3,021 in a savings account that paid 5.5 percent interest
compounded daily. How much interest did he earn in 31 days?

Answers

9514 1404 393

Answer:

  $14.14

Step-by-step explanation:

The amount of interest earned is ...

  I = P((1 +r/365)^n -1) . . . . interest on principal P at annual rate r compounded daily for n days

  I = 3021(1 +0.055/365)^31 -1) ≈ 14.14

$14.14 in interest is earned in 31 days.

Combine like terms
x + 10x-30= -8

Answers

Answer: x=2

Isolate the variable by dividing each side by the factors that don't contain variables.

4
Which of the following is a function?
А
B
C
D

Answers

Answer:

B)

Step-by-step explanation:

A function is when every input has one output.

Easiest way is to do the "vertical line test" and "horizonal line test."

Basically you draw a vertical line and a horizontal line.

If either line passes through more than one point, then it is not a function.

The only one that passes them is B, the line.

Answer:

B

Step-by-step explanation:

A function is when every input has one output.

Easiest way is to do the "vertical line test" and "horizonal line test."

Basically you draw a vertical line and a horizontal line.

If either line passes through more than one point, then it is not a function.

The only one that passes them is B, the line.

which set of measurements would NOT creat a triangle?


A) 3in,8in,6in
B) 14in,6in,20in
C)11in,12in,22in
D)9in,8in,16in​

Answers

Answer is b because thats the answers

what is the simplified expression of 6h +(-7.1d)-15+4d-3.4h

Answers

Answer:

6h+ (-7.1d) -15+4d-3.4h

Step-by-step explanation:

tell what place the digit is in for the following number 14,632.708



4
0
7​

Answers

Thousands
Hundredths
Tenths

Answer:

4 is in the one thousands place. The 0 is in the hundredths place. The 7 is in the tenths place.

To compare the dry braking distances from 30 to 0 miles per hour for two makes of​ automobiles, a safety engineer conducts braking tests for 35models of Make A and 35 models of Make B. The mean braking distance for Make A is 41feet. Assume the population standard deviation is 4.6 feet.The mean braking distance for Make B is 45feet. Assume the population standard deviation is 4.3 feet.At alphaequals0.10​,can the engineer support the claim that the mean braking distances are different for the two makes of​ automobiles

Answers

Answer:

There is sufficient evidence to support the claim.

Step-by-step explanation:

Given

[tex]\alpha = 0.10[/tex]

Make A

[tex]\bar x_1 = 41[/tex]

[tex]\sigma_1= 4.6[/tex]

[tex]n = 35[/tex]

Make B

[tex]\bar x_2 = 45[/tex]

[tex]\sigma_2 = 4.3[/tex]

[tex]n = 35[/tex]

First, we state the null and alternate hypothesis

[tex]H_0 : \mu_1 = \mu_2[/tex]

[tex]H_1 : \mu_1 \ne \mu_2[/tex]

Next, calculate test statistic:

[tex]z = \frac{(\bar x_1 - \bar x_2)-(\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}[/tex]

[tex]z = \frac{(41- 45)-0}{\sqrt{\frac{4.6^2}{35}+\frac{4.3^2}{35}}}[/tex]

[tex]z = \frac{-4}{\sqrt{0.6046+0.5283}}[/tex]

[tex]z = \frac{-4}{\sqrt{1.1329}}[/tex]

[tex]z = \frac{-4}{1.0643}[/tex]

[tex]z = -3.7583[/tex]

The critical value at [tex]\alpha = 0.10[/tex] is: [tex]\±1.282[/tex]

[tex]-3.7583 < -1.282[/tex]

So, we reject [tex]H_0[/tex]

This implies that; there is sufficient evidence to support the claim.

Stuck on this problem, can't find 3x​

Answers

Answer:

x equals 10, angle measure is 30°

Step-by-step explanation:

By using the Vertical Angles Theorem which states that opposite angles formed by 2 intersecting lines are congruent we can find that the measure of the angle with 3x is equal to the measure of it's opposite angle or 30°. Using this we can make an equation that can find us our answer.

3x = 30

Divide both sides by 3

3x/3 = 30/3

x = 10

For each ordered pair determine if it is a solution to 7x+5y=9
(-4,-3)
(-3,6)
(5,0)
(2,-1)

Answers

Answer
2,-1

Explanation
Because ik

9
On a field trip, there are 3 adults for every 45 students. Which graph models a relationship with
the same unit rate?
А
с
101
9
10
9
8
7
7
6
5
4
b
6.
5
4
3
2
3
2
1
0
30
60
90 120 150
30
60 90 120 156
B
D
10T
9
8
10
9
6
5

Answers

Answer:

I believe the answer is C

A rock is thrown upward from the top of a high cliff overlooking the ocean at a speed of 96 feet per second . The rock's height above ocean can be modeled by the equation H(t) = - 16t ^ 2 + 96t + 112 . How long will it take seconds for the rock to hit the ocean? Do not include units in your answer.

Answers

Answer:

7

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

The height of the rock after t seconds is given by the following equation:

[tex]H(t) = -16t^2 + 96t + 112[/tex]

How long will it take in seconds for the rock to hit the ocean?

This is t for which:

[tex]H(t) = 0[/tex]

So

[tex]-16t^2 + 96t + 112 = 0[/tex]

Simplifying by -16

[tex]t^2 - 6t - 7 = 0[/tex]

So a quadratic equation with [tex]a = 1, b = -6, c = -7[/tex]

[tex]\Delta = b^{2} - 4ac = (-6)^2 - 4*1*(-7) = 36 + 28 = 64[/tex]

[tex]t_{1} = \frac{-(-6) + \sqrt{64}}{2*1} = 7[/tex]

[tex]t_{2} = \frac{-(-6) - \sqrt{64}}{2*1} = -1[/tex]

Since time is a positive measure, it will take 6 seconds for the rock to hit the ocean, and the answer is 7.

In ΔGHI, i = 64 inches, g = 91 inches and ∠H=134°. Find the length of h, to the nearest inch.

Answers

Answer:

143

Step-by-step explanation:

delta math

The  length of h, to the nearest inch. is 57.4 inch.

What is triangle?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

Here, given that,

In ΔGHI, i = 64 inches, g = 91 inches and ∠H=134°

Now. we know that,

a sinA =b sinB =c sinC

We get,

length of h = 57.4 inch.

hence, The  length of h, to the nearest inch. is 57.4 inch.

To learn more on triangle click:

brainly.com/question/29126067

#SPJ2

True or False: x is the same/equal to 1x

Answers

Answer:

Yes

Step-by-step explanation:

Because you're multiplying by 1 so it stays the same value

Can someone please help meeee I’m desperateeee

Answers

A = 3x cause if you look they are across from each other in an x shape so they would be the same

Answer:

Step-by-step explanation:

1)(-3x+10)(50-x)=180

-4x+60=180

-4x=120

x=-30

2)6x+2+2x=90

8x=88

x=11

larger angle: 68°

3) a=3x°

4)(7x-5)=-2x+22

9x=27

x=3

DBE=16°

5)(x-39)=2x-59)

x=20

What is the answer to
2x squared?

Answers

Answer:

it’s just 2x^2

it’s not factorable

A container has 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, put it back in the container and draw another marble. What is the probability of pulling out a yellow marble, followed by a blue marble?

Answers

Sorry I don’t know about that
7/9
There are 9 marbles all together and 4+3 is 7 so there for the answer should be 7/9.....(I may be wrong‍♀️)




Hope this helps.!

POV: you procrasiant a lot and dont pay attention on online school and ur failing ur classes, so now ur on brainly, just me?

also someone pls answer my other question will make brainliest!

Answers

Answer:

its true i cant pay attention in class cuz its boring but im

not failing it thank god

Answer:

sameeee but im currently not failing, lets hope it stays like that ;-;

Step-by-step explanation:

im smart

A researcher found that 55% of families in the United States have one child under the age of 21, 22% have two children under the age of 21, 15% have three children under the age of 21, 5% have 4 children under the age of 21and 3% have 5 or more children under the age of 21. If a family is selected at random, what is the probability the family has at least 3 children under the age of 21? (Express your answer as a percent, Please include the % symbol.)

Answers

Answer:

23% probability the family has at least 3 children under the age of 21.

Step-by-step explanation:

If a family is selected at random, what is the probability the family has at least 3 children under the age of 21?

15% have three children under the age of 21

5% have 4 children under the age of 21

3% have 5 or more children under the age of 21.

So:

15% + 5% + 3% = 23%

23% probability the family has at least 3 children under the age of 21.

What is the total surface of the pyramid in square centimeters? A: 17.5 B:70 C:140 D:35

Answers

Answer:

C:140

Step-by-step explanation:

because 7 x 5 in the tiangle.

PLEASE HELP
determine the intercepts of the line
x intercept (__ , __)
y intercept (__ , __) ​

Answers

Answer:

i think y=2 and x=-7

Step-by-step explanation:

Alice has $90 to spend on
new clothes. She wants to buy
some shirts for $20 each. If
she has a coupon for $10 off
her total purchase, how many
shirts can she buy?

Answers

Answer:

5

step by step explanation:

if she gets $10 off of her purchase that means she would have a little extra money to another shirt

Kylee bought a backpack at Tilly's for $32. The same backpack is on sale today for $24. What is the percent
of change? Round your answer to the nearest tenth.

Answers

Answer:

25

Step-by-step explanation:

32-24=8
8/32= 0.25
* 100%
= 25%

Definition the value of a number regardless of its sign Definition

Answers

are you asking for a definition


Please help, I’ve looked everywhere and haven’t found any answers!

Answers

Answer:

m = 4 + (2n)/(3)

Step-by-step explanation:

Move all terms that contain m to the right side and solve it.

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