Find the volume of the composite figure shown

Answer:

[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) + \rm C[/tex]

Step-by-step explanation:

we would like to integrate the following integration:

[tex] \displaystyle \int \frac{ \cos(2x) - \cos(2 \alpha ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]

notice that you can simplify the integrand

recall that,

[tex] \displaystyle \cos(2 \theta) = 2 \cos(\theta) ^{2} - 1[/tex]

thus substitute:

[tex]\displaystyle \int \frac{ 2\cos^{2} (x)- 1 - \{2\cos ^{2} (\alpha ) - 1 \} }{ \cos(x) - \cos( \alpha ) } dx[/tex]

remove parentheses:

[tex]\displaystyle \int \frac{ 2\cos^{2} (x)- 1 - 2\cos ^{2} (\alpha ) + 1}{ \cos(x) - \cos( \alpha ) } dx[/tex]

[tex]\displaystyle \int \frac{ 2\cos^{2} (x) - 2\cos ^{2} (\alpha ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]

factor out 2:

[tex]\displaystyle \int \frac{ 2(\cos^{2} (x) - \cos ^{2} (\alpha )) }{ \cos(x) - \cos( \alpha ) } dx[/tex]

we can use algebraic identity i.e

a²-b²=(a+b)(a-b) to factor the denominator

[tex]\displaystyle \int \frac{ 2(\cos^{} (x) + \cos ^{} (\alpha ))( \cos(x) - \cos( \alpha ) ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]

reduce fraction:

[tex]\displaystyle \int \frac{ 2(\cos^{} (x) + \cos ^{} (\alpha ))( \cancel{\cos(x) - \cos( \alpha ) ) }}{ \cancel{\cos(x) - \cos( \alpha ) }} dx[/tex]

[tex] \displaystyle \int 2( \cos(x) + \cos( \alpha ) )dx[/tex]

distribute:

[tex] \displaystyle \int 2 \cos(x) + 2\cos( \alpha ) dx[/tex]

use sum integration formula:

[tex] \rm \displaystyle \int 2 \cos(x) dx+ \int2\cos( \alpha ) dx[/tex]

recall integration rules:

[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) [/tex]

and we of course have to add constant of integration

[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) + \rm C[/tex]

Answer:

-4.7

Step-by-step explanation:

Answer:

Length of RU is 20 units.

Step-by-step explanation:

In ΔRSt and ΔRUT,

ST ≅ TU [Given]

RT ≅ RT [Reflexive property]

∠RTS ≅ ∠RTU [Both the angles are the right angles]

ΔRTS ≅ ΔRTU [By SAS property of congruence]

Therefore, RS ≅ RU [By CPCTC (corresponding parts of the congruent triangles are congruent]

8x = 6x + 5

8x - 6x = 5

2x = 5

x = 2.5

Length of RU = (6x + 5)

                      = 6(2.5) + 5

                      = 15 + 5

                      = 20

Length of RU is 20 units.

Answer:

B. <

Brainlist Pls!

Look at the example pics below:

Answer:

[tex]\frac{n^4p+n^2}{p^3} \\[/tex]

Step-by-step explanation:

We are given the equation [tex]\frac{n^4}{p^2} + \frac{n^2}{p^3}[/tex]

To solve we need to first find the LCM of the denominators, which would be [tex]p^3[/tex].

[tex]\frac{n^4p}{p^3} + \frac{n^2}{p^3}[/tex]

Now combine the fractions to get the final answer :

[tex]\frac{n^4p+n^2}{p^3} \\[/tex]

Answer:

They both are correct

Step-by-step explanation:

It is given that :

The length of the trail is = 1/4 of a mile

Angelo rode his bike around the trail = 8 times

So Angelo said that he rode his bike around the trail for = 8/4 miles

Terresa says Angelo actually rode his bike = 2 miles

They both are correct as 8/4 mile is equal to 2 miles in the simplified form.

So both of them are correct.

Answer:

91 used

65 new

Step-by-step explanation:

7 + 5 = 12

156/12 = 13

7(13) = 91

5(13) = 65

Answer:

61 pennies

Step-by-step explanation:

d + p = 99

0.1d + 0.01p = 4.41

d = 99 - p

0.1(99 - p) + 0.01p = 4.41

9.9 - 0.1p + 0.01p = 4.41

-0.09p = -5.49

p = 61

Answer: 61 pennies

solution,

slope(m) = y2-y1/ x2-x1

= 4+7/1+3

=11/4

I hope this is correct, the formula can be wrong so pls double check if u have formula.

Answer:

ba is the correct answer

Answer:

CA

Step-by-step explanation:

sana makatulong po ❤❤

Answer:

15min

Step-by-step explanation:

1hr15min=60min+15min=75min

Street dance: Tap Dance =3:2 =3x:2x

Difference:3x-2x=x

3x+2x=75

5x=75

x=15

Answer:

78

Step-by-step explanation:

[tex]400-224=156\\156/2=78[/tex]

Mrs. Kim is 78 years old

Step-by-step explanation:

400-2x=244

 400-244=156

  156=2x

   x=78

Answer:

x= 12.33333333333

Answer:

[tex]7^{x}[/tex]=[tex]\frac{1}{49}[/tex]

Step-by-step explanation:

Answer:

hope this helps you out five is a little harder to read sorry

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the net of the prism is not shown.

However, I will give a general explanation on how to determine the net of the three popular prisms.

(1) Rectangular prism.

It is made up of 6 rectangles

(2) Triangular prism

It consists of 3 rectangles and 2 triangles

(3) Square prism

It is made up of 6 squares

See attachment for the net of each prism

Answer:

2x + 2x + x - 8 = 4 (x + 2)

x = 16

Step-by-step explanation:

Because that's a square, the perimeter would be 4s where s is the measure of the side:

2x + 2x + x - 8 = 4 (x + 2)

To solve, refer below:

2x + 2x + x - 8 = 4x + 8

5x - 8 = 4x + 8

5x = 4x + 8 + 8

x = 16

Answer:

$332

Step-by-step explanation:

Simple interest is the type of interest that is earned on the principal amount only.

Interest in simple terms is the extra amount that you have to pay if you borrow money or the extra money you get if you lend the money.

Simple interest is one of the type of interest.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Suppose that, a certain transaction has an annual interest rate of 2% for a period of 10 years.

If the principal amount is P, then in simple interest, interest will be a fixed amount, that is, 2% of P, in the whole period.

In compound interest, the interest will be compounded each of the year or month or quarterly depending on the criterion.

Hence the type of interest described here is simple interest.

Learn more about Simple Interest here :

https://brainly.com/question/25663053

#SPJ6

Answer:

5 cm approx

Step-by-step explanation:

Given data

Diameter= 20cm

radius= 10cm

Volume= 1570cm^3

We know that the expression for the volume of the container/cylinder is

V= πr^2h

1570= 3.142*10^2*h

1570=3.142*100*h

1570=314.2h

h= 1570/314.2

h=4.99 cm

Hence the height is 5 cm approx

Answer:

C:  Exponential function

Step-by-step explanation:

This is an exponential function.  While the terms decrease steadily, they do not decrease by subtraction of any common difference.  Definitely not a linear function (y = mx + b) or a quadratic (ax^2 + bx + c) either.

Answer:

I think option (B) is right answer

Answer:

71

Step-by-step explanation:

64+3×5-8

64+15-8

79-8

71

Answer:

71

Step-by-step explanation:

4^3 = 64 + 15 = 79 - 8 = 71

Give me my brainllest

Answer:

arrange 3+4=5

Step-by-step explanation:

because 3 square = 9 and 4 square =16 and their sum is 25 and the square of 5 is 25 . both are same .

Hence proved

Answer:0.351

Step-by-step explanation:

Answer:

RQ = 5 cm

ST = 8 cm

Answer: A.3

Step-by-step explanation:

Answer:

They are called vertical angles but are also known as "Vertically Opposite Angles"

Step-by-step explanation:

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Answer:

"Vertical" refers to the vertex

Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.

Step-by-step explanation:

The angles opposite each other when two lines cross. They are always equal. In this example a° and b° are vertical angles. "Vertical" refers to the vertex (where they cross), NOT up/down. They are also called vertically opposite angles.