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2 years ago

The figure will be dilated by a scale factor of 1.2. Find the new length. W: 25 in L: 40 in

Mathematics

1 answer:

Ghella [55]2 years ago

3 0

The new length and width is 48in and 40in respectively

<h3>Dilation</h3>

Given the following information

Width = 25in
Length = 40in

If the length and the width are dilated by a factor of 1.2, the new length and width is expressed as;

W = 25(1.2) = 30in

L = 40(1.2)

L = 48 in

Hence the new length and width is 48in and 40in respectively

Learn more on dilation here: brainly.com/question/10253650

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3 years ago

A car is traveling at a rate of 99 kilometers per hour. what is the car's rate in kilometers per minute? how many kilometers wil

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3 years ago

The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi

inessss [21]

Answer:

The height of cone is decreasing at a rate of 0.085131 inch per second.

Step-by-step explanation:

We are given the following information in the question:

The radius of a cone is decreasing at a constant rate.

$\displaystyle\frac{dr}{dt} = -7\text{ inch per second}$

The volume is decreasing at a constant rate.

$\displaystyle\frac{dV}{dt} = -948\text{ cubic inch per second}$

Instant radius = 99 inch

Instant Volume = 525 cubic inches

We have to find the rate of change of height with respect to time.

Volume of cone =

$V = \displaystyle\frac{1}{3}\pi r^2 h$

Instant volume =

$525 = \displaystyle\frac{1}{3}\pi r^2h = \frac{1}{3}\pi (99)^2h\\\\\text{Instant heigth} = h = \frac{525\times 3}{\pi(99)^2}$

Differentiating with respect to t,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)$

Putting all the values, we get,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)\\\\-948 = \frac{1}{3}\pi\bigg(2(99)(-7)(\frac{525\times 3}{\pi(99)^2}) + (99)(99)\frac{dh}{dt}\bigg)\\\\\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi} = (99)^2\frac{dh}{dt}\\\\\frac{1}{(99)^2}\bigg(\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi}\bigg) = \frac{dh}{dt}\\\\\frac{dh}{dt} = -0.085131$

Thus, the height of cone is decreasing at a rate of 0.085131 inch per second.

3 0

2 years ago

- ignore this :)<br><br> thank you v much.

yan [13]

Answer:

i dont know what you mean by ignore this and it looks like you got it

Step-by-step explanation:

8 0

2 years ago

The figure will be dilated by a scale factor of 1.2. Find the new length. W: 25 in L: 40 in​

The figure will be dilated by a scale factor of 1.2. Find the new length. W: 25 in L: 40 in