Chelsea wants to rearrange her room. She makes a scale drawing of the room and cuts out

4. Four friends went on a trip to Mexico. They rented a car for eight days which cost

nlexa [21]

Explanation:

So, I know a lot of people won't do it this way, but this is how I would do it.

First, multiply each expense by eight (eight for the eight days)

$55 x 8 = 440

$25 x 8 = 200

$129 x 8 = 1032

Next, take the three answers and add them together:

440 + 200 + 1032 = 1672

Lastly, divide 1672 by four (four for the four friends)

1672/4 = 418

There you go! Here is your answer. Each friend paid $418

Hope I helped! :D

3 0

3 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y =

miss Akunina [59]

Answer:

381.18 cubic units

Step-by-step explanation:

Graph the region:

desmos.com/calculator/iwvreqjz2m

The region is a trapezoid. When we rotate it about x = 1, we get a hollow cylinder shape. We can either use washer method or shell method to find the volume.

If we find the volume using washer method, we'll have to use two integrals, one for the triangular part of the trapezoid and one for rectangular part. If we use shell method, we only need one integral. So let's use shell method.

Cut a thin, vertical slice of the region. The width of this slice is dx. The height of the slice is y₂ − y₁ = x − 0 = x. The radius of the shell is x − 1.

The volume of the shell is:

dV = 2π (x − 1) (x) dx

dV = 2π (x² − x) dx

The total volume is the sum of all the shells from x=5 to x=7.

V = ∫ dV

V = ∫₅⁷ 2π (x² − x) dx

V = 2π ∫₅⁷ (x² − x) dx

V = 2π (⅓ x³ − ½ x² + C) |₅⁷

V = 2π [(⅓ 7³ − ½ 7² + C) − (⅓ 5³ − ½ 5² + C)]

V = 2π [⅓ 7³ − ½ 7² − ⅓ 5³ + ½ 5²]

V = 2π [⅓ (7³ − 5³) + ½ (5² − 7²)]

V = 2π [⅓ (218) + ½ (-24)]