When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, dS/dt = rS, where r is the annual rate of interest. a. Find the amount of money accrued at the end of 7 years when $6000 is deposited in a savings account drawing 5 and 3/4% annual interest compounded continuously?
b. In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.)
c. Use a calculator to compare the amount obtained in part (a) with the amount S=6000 (1+1/4(0.0575))^7 that is accrued when interest is compounded quarterly.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

i need more details sorry

step-by-step explanation:

it would rotate about 180 degrees.