Answer:
6
Step-by-step explanation:
80- 34.34 = 45.66
45.66 ÷ 7.61 = 6
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
.
5(18-1)-(6+30)
85-36 = 49
Your answer if 49
Answer: The area of the mirror is 113.14 sq. inches [approx.].
Step-by-step explanation: Given that a circular can till 375 ft² of land in 15 min.
We are to find the area of the mirror in square inches.
The AREA of a circle with radius 'r' units is given by

The diameter of the circular mirror is 12 inches, so the radius of the mirror will be

Therefore, the area of the circular mirror is
![A=\pi r^2=\frac{22}{7}\times 6^2=\dfrac{22\times 36}{7}=113.14~\textup{sq inches}~\textup{[approx.]}](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E2%3D%5Cfrac%7B22%7D%7B7%7D%5Ctimes%206%5E2%3D%5Cdfrac%7B22%5Ctimes%2036%7D%7B7%7D%3D113.14~%5Ctextup%7Bsq%20inches%7D~%5Ctextup%7B%5Bapprox.%5D%7D)
Thus, the area of the mirror is 113.14 sq. inches [approx.].
So, the prime factors of 100 are written as 2 x 2 × 5 x 5 or 22 x 52, where 2 and 5 are the prime numbers. It is possible to find the exact number of factors of a number 100 with the help of prime factorisation. The prime factor of the 100 is 22 x 52.