The wave heights h in the open sea depend on the speed v of the wind and the len
ID: 1591328 • Letter: T
Question
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 = f(v, t) are recorded in feet in the following table Use the table to find a linear approximation to the wave height function when v is near 40 knots and t is near 20 hours. (Round your numerical coefficients to two decimal places.) f(v, t) = Estimate the wave heights when the wind has been blowing for 24 hours at 42 knots. (Round your answer to two decimal places.)Explanation / Answer
The equation for the height at (v,t)=(a1,a2) is the expression
f(v,t)=h(a1,a2)+[h/v(a1,a2)](va1)+[h/t(a1,a2)](ta2)....standard result for multivariable linear approximation
Here, a1=40knots, a2=20hour, h(a1,a2)= 28, h/v(a1,a2)= [40-28]/[50/40]=1.2, h/t(a1,a2)= [31-28]/10=0.3
Hence,
f(v,t)=28+1.2(v40)+0.3(t20)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.