A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min. At what rate is the volume of the snowball decreasing when the radius is 17 cm. (Note the answer is a positive number).

726.34 cm/min

Step-by-step explanation:

Volume of a sphere:

The volume of a sphere is given by the following equation:

In which r is the radius.

Implicit derivatives:

This question is solving by implicit derivatives. We derivate V and r, implicitly as function of t. So

A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min.

This means that

At what rate is the volume of the snowball decreasing when the radius is 17 cm.

This is when

This means that the volume of the snowball is decreasing at a rate of 726.34 cm/min when the radius is 17 cm.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions