14. 1/5, 3/10, 12/25, 1/2,4/5
15. i suck at negatives whoops
16.
17.
18.
19. 6/5, 4/4, 29/20, 3/2
20. i suck :D
21. To compare 0.7 and 5/8, you would have to first turn the decimal into a fraction. After you have your fraction you want to simplify it down to the smallest fraction and compare with 5/8. You also want to find the common denominator.
I’m not positive this is right but try 26. I set 2x+1 and 3x-5 equal to each other and solved for x. I got x=6 then plugged it into both of the equations then added the equations together.
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:
x = ±2√10
Step-by-step explanation:
40 - x² = 0
⇌
(√40 - x)(√40 + x) = 0
⇌
x = √40 or x = -√40
we can go further and say that √40 = 2√10
