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2 years ago

HELP ME OUT PLEASE!!!

Mathematics

1 answer:

ANTONII [103]2 years ago

7 0

Answer:

D) y= 4x - 1

Step-by-step explanation:

We are basically trying to see which of the equations provided are true on both sides of the equal sign when you plug in the x and y values.

Let's start!

Choice A:

plug in 0 for x and -1 for y

-1 = 4(0)

And you are left with...

-1 = 0

This equation is false! Therefore it does not match the function in the table

Choice B:

plug in the values again

-1 = 0 + 1

-1 = 1

False!

Choice C:

-1 = 0 + 5

-1 = 5

False!

Lastly...Choice D:

-1 = 4(0) -1

Multiply 4 and 0 which is 0, so you are left with...

-1 = -1

This equation is true!!

So your answer is D

Hope this helps :D

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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,

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