I can’t remember how to do this if I try a bit longer I can probably figure it out but not sure exactly. Please If anyone can help so I can come back and check it later

===========================================================

Explanation:

Check out figure 1 in the attached images below. In this figure, I've plotted the function y = 6/(2x-3) on a 2D grid system. The function curve is in blue. Then I've plotted (2,0) and (3,0) on the x axis. Point A is somewhere between those endpoints. Point A is also on the x axis. Directly above A is point B such that B is on the blue function curve.

The distance from A to B is found by subtracting the y values of each point.

The y coordinate of A is y = 0. The y coordinate of B is y = 6/(2x-3)

Therefore, the distance from A to B is 6/(2x-3) units. This will form the radius of each cylindrical slice as figure 2 shows. Note the color coding to help see how the 2D view corresponds to the 3D view. The xy plane has been laid flat on the floor. So we're viewing the function curve at a downward angle now. Each of those gray cylinders combine to form an approximate 3D volume. The more cylinders we have, and the finer the cuts, the more accurate the total volume.

So it comes down to finding the volume of each cylindrical slice and adding up the volumes. This is effectively what integral calculus is all about.

------------------------------------

Since the radius of each cylinder is y = 6/(2x-3), this means r = 6/(2x-3) is plugged into the formula

V = pi*r^2*h

which is the volume of a cylinder formula

The height of each cylinder is delta x, which we'll use dx for short. So this is where the dx comes from in integrals.

This is what the integral will look like

[tex]\displaystyle V = \int_{2}^{3} \pi*\left(\frac{6}{2x-3}\right)^2dx[/tex]

which turns into

[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx[/tex]

after a bit of algebra. We're able to factor the 36pi out because it's a constant

From here we use u-substitution. Let u = 2x-3

This leads to du/dx = 2 which can be solved to dx = du/2

Since u = 2x-3, the lower endpoint x = 2 leads to

u = 2x-3 = 2*2-3 = 1

and x = 3 leads to

u = 2x-3 = 2*3-3 = 3

So the interval 2 < x < 3 turns into 1 < u < 3

After using u-sub, making the proper replacements, and integrating, we get

[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx\\\\\\\displaystyle V = 36\pi\int_{1}^{3}\frac{1}{u^2}\frac{du}{2}\\\\\\\displaystyle V = 36\pi*\frac{1}{2}\int_{1}^{3}\frac{1}{u^2}du\\\\\\\displaystyle V = 18\pi\int_{1}^{3}u^{-2}du\\\\\\\displaystyle V = 18\pi\left[-u^{-1}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\[/tex]

Let's evaluate that to get the following

[tex]\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[\left(-\frac{1}{3}+C\right)-\left(-\frac{1}{1}+C\right)\right]\\\\\\\displaystyle V = 18\pi\left(-\frac{1}{3}+1\right)\\\\\\\displaystyle V = 18\pi\left(\frac{2}{3}\right)\\\\\\\displaystyle V = 12\pi\\\\\\[/tex]

So the 3D volume formed by rotating that region (under the curve from x = 2 to x = 3) is exactly 12pi cubic units

Answer:

3x-8y=32

Step-by-step explanation:

Answer:

The longest side length b is approximately 13.172 cm

Step-by-step explanation:

The given parameters are;

The area of the triangle = 22.4 cm²

The given angles of the triangle = ∠97°

The given side of the triangle = 3.7 cm

The formula for the area of a triangle, A = 1/2 × a × b × sin(C)

Where;

a, and b are the side legs forming the angle C

Therefore,  we have;

A = 22.4 = 1/2 × 3.7 × a × sin(97°)

a =  22.4/(1/2 × 3.7 × sin(97°)) ≈ 12.199

a ≈ 12.199 cm

Therefore, by cosine rule, we have;

b² = a² + c² - 2 × a × c × Cos(B)

Substituting the values, gives;

b² = 12.199² + 3.7² - 2 × 12.199 × 3.7 × Cos(97°)

b² ≈ 173.507

∴ b ≈ √173.507 ≈ 13.172

b ≈ 13.172 cm

Answer:

Step-by-step explanation:

Answer:

2 + 0.1 + 0.06

2 + 0.16

two and sixteen hundredths

Answer:

[tex]S.A.=90\pi~cm^2[/tex]

Step-by-step explanation:

Surface Area of a Cone

Given a cone of base area B and slant height L, the surface area can be calculated with the formula:

[tex]S.A.=\pi rL +B[/tex]

The cone presented in the image has a circular base of radius r=5 cm, thus its base area is:

[tex]B=\pi r^2[/tex]

[tex]B=\pi 5^2[/tex]

[tex]B=25\pi~cm^2[/tex]

The slant height can be calculated as the hypotenuse of a right triangle with legs 5 cm and 12 cm by using Pythatgora's Theorem:

[tex]L^2=5^2+12^2[/tex]

[tex]L^2=25+144=169[/tex]

Taking square roots

[tex]L = \sqrt{169}[/tex]

L = 13 cm

The surface area is:

[tex]S.A.=\pi (5~cm)*13~cm +25\pi~cm^2[/tex]

Operating:

[tex]S.A.=65\pi~cm^2 +25\pi~cm^2[/tex]

[tex]\mathbf{S.A.=90\pi~cm^2}[/tex]

Answer:

90

Step-by-step explanation:

Answer:

-7/1

Step-by-step explanation:

Answer:

X= 9

Y = -6

Step-by-step explanation:

first of all setting up the equation and solve it like a system of linear equations

5x+4y=21

-3x+2y=-39

then multiply -2 on the entire second equation

5x+4y = 21

6x-4y= 78

then eliminate the 4ys and you get

11x = 99

x = 9

lastly subsititue the 9 back into one of the original equations

5(9) + 4y =21

45 + 4y = 21

4y = -24

y = -6

Answer:

-3x+2y=-39

2y=-39+3x

y=-39+3x÷2 equation 1

5x+4y=21 equation 2

5x+4(-39+3x)÷2=21

5x+2(-39+3x)=21

5x+(-78)+6x=21

5x-78+6x=21

5x+6x-78=21

11x-78=21

11x=21+78

11x=99

x=99÷11

x=9

putting value of equation 2 in equation 1

y=-39+3x÷2

y=-39+3×9÷2

y=-39+27÷2

y=-12÷2

y=-6

x=9 and y=-6 answer

hope this may help you !!!!

Answer:

29

Step-by-step explanation:

The squares cannot be very big. For example the difference between 10^ and 11^2 = 100 to 121 which is a difference of 21.

What you are talking about is x + 4 prime + 7 next square.

Write the squares

1

4

9

16

25

36

add 4 to get to the prime, add 7 to get to the next square. That's 12

1 and 4 have a difference of 3 too small

4 and 9 have a difference of 5 too small

9 and 16 have a difference of 7 which is too small

16 and 25 have a difference of 9 which just a little too small.

25 and 36 has a difference of 11. Just right

25 + 4 = 29

29 + 7 = 36

Just right.

Answer:

The expression for the area of the given triangle is 5x^4+4x^3units

Step-by-step explanation:

c. 4/6

This is the answer

Answer:

C. 4/6

Step-by-step explanation:

2*2=4

3*2=6

4/6

Answer:

$9,724.05

Step-by-step explanation:

8000(1+.05)^4= 9724.05

sry if im wrong :)

The amount after 4 years will be equal to $9,724.05

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest.

Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-

Given that Mr.Turner invested $8,000 in an account for his daughter’s college education. The account pays 5% interest, compounded yearly.

The amount after 4 years will be calculated as:-

[tex]A = P ( 1 + \dfrac{r}{100})^{nt}[/tex]

[tex]A = 8000 ( 1 + \dfrac{5}{100})^{4}[/tex]

A =  9724.05

Therefore, the amount after 4 years will be equal to $9,724.05.

To know more about Compound interest follow

https://brainly.com/question/24924853

#SPJ5

Answer:

4,5

Step-by-step explanation:

I think it is 4,5. It says reflection of it across the line, and it is in the 4th quadrent, so that -5 will become a positive 5, and the 4 will stay the same.

Answer:

Its d i took the class

Step-by-step explanation:

Answer:

B) 35 divided by 7 = 5

Step-by-step explanation:

You have 35 blocks, you are devideding them in groups of 7, how many groups do you have?

Answer:

x=81

Step-by-step explanation:

I am 100% sure you can go with it

Answer:

1:

m=4/3

2:

-2

3:

First, you want to set up a proportion.

8/24 = 10/y

Cross multiply to get

240 = 8y, then divide 8 from both sides to get y = 30.

Answer: It is point B

Step-by-step explanation:

Answer: point b

Step-by-step explanation:

answer:

y=11x+11?

Step-by-step explanation:

from what i got from the equation it sounds like this might be the answer doory ^^'

Answer:

C is your y intercept 3.99b is your slope

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Begin by isolating y

-6y = - x - 1

Divide everything by -6

y = -x/-6 - 1/-6

y = x/6 + 1/6

Now you want the perpendicular

m1 * m2 = - 1

m1 = 1/6

1/6 * m2 = -1

multiply by 6

m2 = - 6

That's C

Answer:

48 hours

Step-by-step explanation:

The number of hours that Carrie must tutor to earn $408 will be 48 hours.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Carrie earns $8.50 per hour for tutoring her little brother.

Let x be the number of hours. Then the equation is given as,

8.50x = 408

Simplify the equation, then we have

x = 408 / 8.50

x = 48 hours

The number of hours that Carrie must tutor to earn $408 will be 48 hours.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

Answer:

the answer is located in the screenshot that is attached.

Step-by-step explanation:

The work is also in the screenshot attached. Hoped this helped!

The value of x if f(x) = 15 in the given function is 3

From the question,

We were given the function f(x) = 2x + 9

To determine the value of x if f(x) = 15, we will put f(x) to be equals to 15 and then solve for x in the equation

That is,

f(x) = 2x + 9

Since f(x) = 15

∴ 15 = 2x + 9

Now, to solve the above equation,

First, subtract 9 from both sides

That is,

15 - 9 = 2x +9 -9

6 = 2x

Then, we can write that

2x = 6

∴ x = 6 ÷ 2

x = 3

Hence, the value of x if f(x) = 15 in the given function is 3

Learn more here: https://brainly.com/question/19872526

Answer:

it's 8 inches luvvvv

Step-by-step explanation:

hope this helps

Answer:

101.76

Step-by-step explanation:

Answer:

(12.9 - 3.1) i'm in middle school so if i can do it you can

Step-by-step explanation:

Answer :need the options you choose frome

Step-by-step explanation: