The sides of an equilateral triangle are increasing at the rate of 5 centimeters per hour. At what rate is the area increasing when the side is 10 centimeters?

I have answered 4 of your 5 Calculus questions now.

Show me in this one that you have some kind of idea as to how to solve it.

50 cm2/hr

To find the rate at which the area is increasing, we can use the formula for the area of an equilateral triangle, which is given by:

Area = (√3/4) * side^2

where "side" represents the length of one side of the equilateral triangle.

Given that the sides of the equilateral triangle are increasing at a rate of 5 centimeters per hour, we can differentiate both sides of the area formula with respect to time (t):

d(Area)/dt = d(√3/4 * side^2)/dt

Now, let's substitute the given rate of change of the side (ds/dt = 5 cm/hr) and the value of the side when the area is desired (side = 10 cm) into the equation:

d(Area)/dt = d(√3/4 * (10 cm)^2)/dt

d(Area)/dt = d(√3/4 * 100 cm^2)/dt

d(Area)/dt = (√3/4) * 2 * 100 * d(side)/dt

Since we know d(side)/dt = 5 cm/hr, we can substitute this into the equation:

d(Area)/dt = (√3/4) * 2 * 100 * (5 cm/hr)

Simplifying further:

d(Area)/dt = (√3/4) * 2 * 100 * 5 cm/hr

Now, we can calculate the rate at which the area is increasing:

d(Area)/dt = (√3/4) * 2 * 100 * 5 cm/hr

d(Area)/dt = (√3/4) * 2 * 100 * 5 cm/hr

d(Area)/dt = (√3/4) * 1000 cm^2/hr

So, when the side of the equilateral triangle is 10 centimeters, the rate at which the area is increasing is (√3/4) * 1000 cm^2/hr.