The figure consists of a tangent and a secant to the circle. Find the value of x. Leave your answer in simplest radical form

Gravel is being dumped from a conveyor belt at a rate of 15 ft3/min, and its coarseness is such that it forms a pile in the shap

gayaneshka [121]

Answer:

0.13 ft/min

Step-by-step explanation:

We are given that

$\frac{dV}{dt}=15ft^3/min$

We have to find the increasing rate of change of height of pile when the pile is 12 ft high.

Let d be the diameter of pile

Height of pile=h

d=h

Radius of pile,r= $\frac{d}{2}=\frac{h}{2}$

Volume of pile= $\frac{1}{3}\pi r^2 h=\frac{1}{12}\pi h^3$

$\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}$

h=12 ft

Substitute the values

$15=\frac{1}{4}\pi(12)^2\frac{dh}{dt}$

$\frac{dh}{dt}=\frac{15\times 4}{\pi(12)^2}$

$\frac{dh}{dt}=0.13ft/min$

7 0

3 years ago

A three-dimensional model of lucia’s apartment is shown. to cool the whole apartment, an air conditioner must provide 2.5 btus p

SashulF [63]

The number of btus which are needed to cool Lucia’s apartment shown in the three-dimensional model are 20,400 btus.

<h3>What is of volume of rectangular prism?</h3>

Volume of rectangular prism is the amount of quantity, which is obtained in it in the 3 dimensional space.

Volume of a rectangular prism is the product of its width, height and length.

$V=w\times h\times l$

Here, (w) is the width of the base (l) is the length and (h) is the height of the rectangular prism.

A three-dimensional model of Lucia’s apartment is shown. The image is attached below for the apartment. The three section are there in the apartment. The volume of this apartment is,

$V=[(20\times12)+(20-9)\times16+(20\times20)]\times10\\V=8160\rm\; ft^3$

To cool the whole apartment, an air conditioner must provide 2.5 btus per cubic foot. To cool, the 8160 cubic foot apartment the btus needed are,

$n=8160\times2.5\\n=20400\rm\; btus$