Answer:
<h2><u><em>
36 - x</em></u></h2>
Step-by-step explanation:
A woman buys 3 dezen eggs. Later she discovers that x of them are broken. How many mang eggs are not broken
3 = 3
Dozen = 12
x = broken eggs
3 * 12 - x =
36 - x
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 .
The word inscribed means that the sphere is inside the cylinder and its diameter is equal to the height and diameter of the cylinder. The surface area of the sphere is equal to
SA (sphere) = πd²
where d is the diameter.
That of the cylinder is,
SA (cylinder) = πd(h + d/2)
Since h is also equal to d
SA (cylinder) = πd(d + d/2) = 3πd²/2
Therefore, the surface area of the cylinder is approximately 1.5 times that of the sphere.
Answer:
were is the circle to be to be equated
