HELP PLS I WILL GIVE BRAINLIEST<br><br><br> 10 + x

g Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min, and its coarseness is such that it forms a pile in the sh

Maslowich

Answer:

0.3537 feet per minute.

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=10$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

If the Base Diameter = Height of the Cone

The radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10$

We want to determine how fast is the height of the pile is increasing when the pile is 6 feet high.

$When h=6$ feet$\\\dfrac{3\pi *6^2}{12}\dfrac{dh}{dt}=10\\9\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{9\pi}\\ \dfrac{dh}{dt}=0.3537$ feet per minute$

When the pile is 6 feet high, the height of the pile is increasing at a rate of 0.3537 feet per minute.

7 0

4 years ago

Confused on this one. I need someone to help me out.

Arlecino [84]

The answer is T=PV/nR

Hope this helps!

6 0

3 years ago

if theta is in the first quadrant sin left parenthesis t h e t a right parenthesis equals 0.17 then what is tan left parenthesis

Kazeer [188]

The value of $tan\theta$ in the first quadrant is approximately 0.173.

There are 4 quadrants inside the cartesian aircraft. All trigonometric ratios of sin, cos, tan are high quality inside the first quadrant.in the 2nd quadrant simplest sin is advantageous rest are negative. within the 1/3 quadrant simplest tan is wonderful inside the fourth quadrant best cos is fantastic.

Given $sin \theta=0.17$ and $\theta$ is in the first quadrant.