Answer:
A
Step-by-step explanation:
=
2x5−8x4
/(6x3+30x2)
= 2x3−8x2
/(6x+30
)
=
x3−4x2
/(3x+15)
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 [ 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:
m - 1
c - 6
Step-by-step explanation:

The equation is in slope-intercept form.
y = mx + c
m - slope
c (or b) - y -intercept
Usually if the slope is one it will not be written.
y = 1x + 6
The slope is one.
6 takes 'c's place, so it is the y-intercept.
Hope this helps.
Step-by-step explanation:
Ans: b<3. I hope this helps.
Answer:
30 inches squared
Step-by-step explanation:
First, find the area of the entire frame using length times height. 9*6 is 54 inches squared. Then, find the area of the middle space the same way. 6*4 is 24 inches squared. Lastly, subtract the middle from the entire frame's area. 54-24 is 30 inches squared.