What is the total surface area of this rectangular prism?

If a bicycle wheel has a diameter of 28 inches how many revolutions does it take to travel 3 miles

KatRina [158]

The circumference of the tire would be: 28 x PI = 87.96 inches = 88 inches.

88 inches / 12 inches = 7.33 feet

Every revolution the tire would travel 7.33 feet.

1 mile = 5,280 feet

3 miles = 5280 x 3 = 15,840 feet total.

Divide total feet by the circumference of the tire:

15,840 / 7.33 = 2,161 revolutions.

8 0

3 years ago

What is the value of z in the equation 3z + 5 = 4z − 8?<br> hurry

Bad White [126]

Z=13 I had a similar problem before and I've gotten it right.

8 0

3 years ago

Read 2 more answers

Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the curves about the given

kondor19780726 [428]

Answer:

The volume is $\frac{16\pi}{e}$

Step-by-step explanation:

* Lets talk about the shell method

- The shell method is to finding the volume by decomposing

a solid of revolution into cylindrical shells

- Consider a region in the plane that is divided into thin vertical

rectangle

- If each vertical rectangle is revolved about the y-axis, we

obtain a cylindrical shell, with the top and bottom removed.

- The resulting volume of the cylindrical shell is the surface area

of the cylinder times the thickness of the cylinder

- The formula for the volume will be: $V=\int\limits^b_a {2\pi xf(x)} \, dx$

where 2πx · f(x) is the surface area of the cylinder shell and dx is its

thickness

* Lets solve the problem

- To find the volume V generated by rotating the region bounded

by the curves y = 4e^x and y = 4e^-x about the y-axis by use

cylindrical shells

- Consider that the height of the cylinder is y = (4e^x - 4e^-x)

- Consider that the radius of the cylinder is x

- The limits are x = 0 and x = 1

- Lets take 2π and 4 as a common factor out the integration

∴ $V=\int\limits^1_0 {2\pi x(4e^{x}-4e^{-x})} \, dx$

∴ $V=2\pi(4)\int\limits^1_0 ({xe^{x}-xe^{-x})} \, dx$

- To integrate $xe^{x}$ and $xe^{-x}$ we will use

integration by parts methods $\int\ {uv'=uv-\int{v}\,u' }\,$

∵ u = x

∴ u' = du/dx = 1 ⇒ differentiation x with respect to x is 1

∵ v' = dv/dx = e^x

- The integration e^x is e^x ÷ differentiation of x (1)

∴ $v=\int\ {e^{x}}\, dx= e^{x}$

∴ $\int\ {xe^{x}} \, dx=xe^{x}-\int\ e^{x}\, dx=xe^{x}-e^{x}$

- Similar we will integrate xe^-x

∵ u = x

∴ u' = du/dx = 1

∵ v' = dv/dx = e^-x

- The integration e^-x is e^x ÷ differentiation of -x (-1)

∴ $v=\int\ {e^{-x}} \, dx=-e^{-x}$

∴ $\int\ {x}e^{-x}\, dx=-xe^{-x}+\int\ {e^{-x}} \, dx=-xe^{-x}-e^{-x}$

∴ V = $8\pi \int\limits^1_0 ({xe^{x}-xe^{-x})} \, dx=8\pi[xe^{x}-e^{x}+xe^{-x}+e^{-x}]$ from 0 to 1

- Lets substitute x = 1 minus x = 0

∴ $V=8\pi[(1)(e^{1})-(e^{1})+(1)(e^{-1})+(e^{-1})-(0)(e^{0})+(e^{0})-(0)(e^{0})-(e^{0})]$

∴ $V=8\pi[e^{1}-e^{1}+e^{-1}+e^{-1}-0+1-0-1]=8\pi[2e^{-1}]=16\pi e^{-1}$

∵ $e^{-1}=\frac{1}{e}$

∴ $V=\frac{16\pi}{e}$

3 0

4 years ago

The high temperature in Rockport over the weekend was 55 1/4 °F. Write this as a decimal

Hoochie [10]

55.25 °F
I believe this is right

6 0

3 years ago

After 6 hours, 4 inches of snow have fallen. Assume it continues just know at a constant rate complete the table to show how muc

ANEK [815]

Answer:

Step-by-step explanation:

For 6 hrs and 4 inches that's 2/3 an inch for every hr

1 hr 2/3 inches

2 hrs 1.3 or 1 1/3 inches

6 hrs 4 inches

8 hrs 5.3 or 5 1/3 inches

6 0

3 years ago