Answer:
Volume of the cone is increasing at the rate 
.
Step-by-step explanation:
Given: The radius of a right circular cone is increasing at a rate of 
in/s while its height is decreasing at a rate of 
in/s.
To find: The rate at which volume of the cone changing when the radius is 
in. and the height is 
in.
Solution:
We have,
, 
, 
, 
Now, let 
be the volume of the cone.
So, 
Differentiate with respect to 
.
![\frac{dv}{dt} =\frac{1}{3}\pi \left [ r^2\frac{dh}{dt}+h\left ( 2r \right )\frac{dr}{dt} \right ]](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%5Cleft%20%5B%20r%5E2%5Cfrac%7Bdh%7D%7Bdt%7D%2Bh%5Cleft%20%28%202r%20%5Cright%20%29%5Cfrac%7Bdr%7D%7Bdt%7D%20%5Cright%20%5D)
Now, on substituting the values, we get
![\frac{dv}{dt} =\frac{1}{3}\pi\left [ \left ( 134 \right )^2\left ( -2.2 \right )+\left ( 136\right )\left ( 2 \right )\left ( 134 \right )\left ( 1.9 \right ) \right ]](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Cleft%20%5B%20%5Cleft%20%28%20134%20%5Cright%20%29%5E2%5Cleft%20%28%20-2.2%20%5Cright%20%29%2B%5Cleft%20%28%20%20136%5Cright%20%29%5Cleft%20%28%202%20%5Cright%20%29%5Cleft%20%28%20134%20%5Cright%20%29%5Cleft%20%28%201.9%20%5Cright%20%29%20%5Cright%20%5D)
![\frac{dv}{dt} =\frac{1}{3}\pi\left [ -39503.2+69251.2 \right ]](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Cleft%20%5B%20%20-39503.2%2B69251.2%20%5Cright%20%5D)
![\frac{dv}{dt} =\frac{1}{3}\pi\left [ 29748 \right ]](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Cleft%20%5B%2029748%20%5Cright%20%5D)
Hence, the volume of the cone is increasing at the rate .
Answer:
1 Hour
250 + 150h = 500
Step-by-step explanation:
So, the fee for the meeting is 250. The hourly fee is 150. Let h equal the number of hours.
250 + 150h
If pablo has 500, then we cannot exceed that amount. So, our equation becomes
250 + 150h = 500
Subtract 250 from both sides
150h = 250
And divide by 50 on both sides. You get x = about 1.67. Since this is a question about time and money, you would round down to 1.
Answer:
yes he is correct for 13
peyton hikes. 6 1/80
no it would not be a greater distance because if you do 9/10 times 3 and turn the answer into a decimal the red trail is a greater distance.
Step-by-step explanation:
yes he is correct for 13
peyton hikes. 6 1/80
no it would not be a greater distance because if you do 9/10 times 3 and turn the answer into a decimal the red trail is a greater distance.
Answer:
w>-12
Step-by-step explanation:
6>w/-2 (Given)
6>-w/2 (Rewrite)
12>-w (Multiply both sides by 2)
-12<w (Remember to flip the sign when dividing or mulitplying by a negative)
w>-12 (Rewrite with w in front)
Therefore, w>-12 is the solution to the inequality.
Answer:
y>=x+1
Step-by-step explanation:
it will be y>= x+1 bcz the shaded area shows a straight line rather than a dotted line which means the line is part of the shaded region. so that's why y>=x+1
