Question
the side of an equilateral triangle decreases at a rate of 3cm/s. at what rate is the area decreasing when the area is 150cm squared?
Answers
Damon
altitude = (s/2)sqrt3
A = (s/2) (s/2) sqrt 3 = (s^2/4) sqrt3
dA/dt = (2 s/4) sqrt3 ds/dt
= (s/2) sqrt 3 * (-3)
= (-3s/2) sqrt 3
now what is s when A = 150?
(s^2/4) sqrt 3 = 150
s^2 = 600/sqrt3
so
dA/dt = (-3/2) sqrt3 (sqrt 600)/3^.25
= (-3/2)(sqrt600)(3^.25)
A = (s/2) (s/2) sqrt 3 = (s^2/4) sqrt3
dA/dt = (2 s/4) sqrt3 ds/dt
= (s/2) sqrt 3 * (-3)
= (-3s/2) sqrt 3
now what is s when A = 150?
(s^2/4) sqrt 3 = 150
s^2 = 600/sqrt3
so
dA/dt = (-3/2) sqrt3 (sqrt 600)/3^.25
= (-3/2)(sqrt600)(3^.25)