The rate of change of the volume of a snowball that is melting is proportional to the surface area of the snowball. suppose the snowball is perfectly spherical. then the volume (in centimeters cubed) of a ball of radius r centimeters is 4/3πr3. the surface area is 4πr2. set up the differential equation for how r is changing. then, suppose that at time t = 0 minutes, the radius is 10 centimeters. after 5 minutes, the radius is 8 centimeters. at what time t will the snowball be completely melted.

According to the passage, we have the next equation:

where "K" is a proportional constant

Leaving at the end with the next equation:

Integrating the equation, we have:

where "C" is a constant

Then, we have the 2 conditions for the problem:

1) t=0 → r=10

Replacing in the equation, we have C = 10

2) t=5 → r=8

Replacing in the equation, we have K = -0.4

Finally, the time which the snowball will be completely melted will be when r = 0. So replacing in the equation

t = 25 minutes

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )

answer: the answer is one

step-by-step explanation:

pemdas, in this situation there is no parenthesis or exponents so you go to multiplication, 1x1=1, then division 1/1= 1 then addition 1+1=2 then subtraction 2-1=1