Question

3. The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function h(v, t) have been experimentally determined and the results are recorded in feet in the following table. Here wind speed v is measured in knots and the duration t is measured in hours h(t, v)t 5 t-10 t 15 t 20 t 30 t-40 t-50 v205 9 19 13 21 29 37 16 25 36 47 17 28 40 54 18 31 45 62 19 v- 4014 v-50 19 v 60 24 48 67 50 69 i. Find an approximation to h, (40,20) and ht(40,20). Hint: Use an average rate of change/slope In your writeup you have to be clear about which slope you are using ii. Find a formula for the (approximate) tangent plane of h(v, t) at v- 40 knots and t-20 hours.

Answer 1

ven lo 40-2s 10 A by deincken 4o,D)

=31-98 (외 1o 1D -10 (40, 2o)二 28t lo15/40-40) +0-5(20-20) h(40, 20) = 28