R is partly constant and partly varies with e when r =530,e=1600 and r =730 e=3600find the formula that connects r and e find r when e=1300

Answer 1

To find the formula connecting r and e, we first need to determine the constant part of r when e = 1600 and 3600.

When r = 530 and e = 1600:
530 = k * 1600 + c (equation 1)

When r = 730 and e = 3600:
730 = k * 3600 + c (equation 2)

Subtracting equation 1 from equation 2:
730 - 530 = k*3600 - k*1600
200 = k*2000
k = 200/2000
k = 1/10

Substitute k = 1/10 back into equation 1:
530 = 1/10 * 1600 + c
530 = 160 + c
c = 530 - 160
c = 370

Therefore, the formula connecting r and e is:
r = (1/10) * e + 370

To find r when e = 1300:
r = (1/10)*1300 + 370
r = 130 + 370
r = 500

Therefore, when e = 1300, r = 500.