Calculus Story Problem?
I have never been able to do story problems, can you break it down for me step by step? When a certain comodity is sold for p dollars per unit, consumers will buy D(p) = 31,500/p units per month. It is estimated that t months from now, the price of the commodity will be p(t) = t^2/3 + 5.15 dollars per unit. The approximate rate at which the monthly demand will be changing with respect to time in 27 months is
Work done on an object?
Work is found with a vector calculus line integral W = ∫F · dr Don't use the period to indicate dot product, it looks confusing. Represent both vectors in component form: F = <4*x, 3*y> Newtons dr =
Can anyone help me with a math problem? (Calculus)?
calling the dock (0,0), east is +x, north is +y the position of the first boat is (0 , -20t) (where t is time from 2:00 in hours) the position of the second boat is (15(t-1), 0) this is derived from the 15 km /hr, but it doesn't get to (0,0) until t = 1 (1 hour after 2:00) using the distance formula squared, d^2 = [15(t - 1) - 0]^2 + (-20t - 0)^2 d^2 = 225(t - 1)^2 + 400t^2 this is the equation to minimize d^2 = 225(t^2 - 2t + 1) + 400t^2 d^2 = 625t^2 - 450t + 225 d^2 = 25(25t^2 - 18t + 9) (d^2)' = 50t - 18 (d^2)' = 0 at 50t = 18, or t = 9/25 hr = .36 hr , or about 21.6 minutes so at 2:21:26, the distance between them will be at a minimum (arithmetic mistake corrected....doh, I can't multiply!) check: (d^2)" = 50, so yes, this is a minimum