If a snowball melts so that its surface area decreases at a rate of 3 cm^2/min, find the rate at which the diameter decreases when the diameter is 11 cm.

The diameter is decreasing at the rate of 0.0434 cm/min.

Step-by-step explanation:

A snowball is spherical, so it's area is given by the following formula:

The radius is half the diameter, so:

If a snowball melts so that its surface area decreases at a rate of 3 cm^2/min, find the rate at which the diameter decreases when the diameter is 11 cm.

This is when

Applying implicit differentiation:

We have to variables(A and d), so:

The diameter is decreasing at the rate of 0.0434 cm/min.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.