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)

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)

butterflydreamer · Answer

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.

fantageplayer · Answer

me neither

butterflydreamer · Answer

ty.

phi · Answer

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

phi · Answer

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

butterflydreamer · Answer

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