Question

help please :)
Two wave fronts off the coast of Sydney meet at the coast. The height at the coast (in cm) of the two wave forms are given by:
h1 = 7 + 2 sin t and h2 = 17 + 7cos t .
Find the exact value of the initial rate of change of h. ( h = h1 + h2)

Answer 1

i found that \[h = 24 + \sqrt{53} \sin (t + (\tan^{-1} \frac{ 7 }{ 2 }))\]
But i am unsure how to find the initial rate of change.

Answer 2

me neither

Answer 3

ty.

Answer 4

with h= h1 + h2
h1 = 7 + 2 sin t and h2 = 17 + 7cos t

I would leave h(t) a sum:
h(t) = 24 + 2 sin t + 7 cos t

and h' = 2 cos t - 7 sin t

Answer 5

by exact value of the initial rate of change, I assume they mean evaluate that expression at t=0
we get
h'(0)= 2 (cm/sec ?) not sure of the units

Answer 6

ohh i see. I totally missed that. Thank you!:)