Question

Ali is hiking on the hill, whose height is given by f(u,v)=n^2 e^((u+n)/(v+n)). Currently, he is positioned at point (3, 5). Find the direction at which he moves down the hills quickly. Take n =12

Answer 1

Answer:

Step-by-step explanation:

We are given that

$f(u,v)=n^2e^{\frac{u+n}{v+n}}$

Point=(3,5)

n=12

We have to find the direction at which he moves down the hills quickly.

$f(u,v)=144e^{\frac{u+12}{v+12}}$

$f_u(u,v)=144e^{\frac{u+12}{v+12}}$

$f_u(3,5)=144e^{\frac{3+12}{5+12}}$

$f_u(3,5)=144e^{\frac{15}{17}}=144e^{0.88}$

$f_v(u,v)=144e^{\frac{u+12}{v+12}}\times (-\frac{u+12}{(v+12)^2})$

$f_v(3,5)=144e^{\frac{15}{17}}(-\frac{15}{(17)^2}$

$f_v(3,5)=-\frac{2160}{289}e^{\frac{15}{17}}=-7.47e^{0.88}$

$\Delta f(3,5)=$

$\Delta f(3,5)=$

The direction at which he moves down the hills quickly=-$\Delta f(3,5)$

The direction at which he moves down the hills quickly=