A skier is on a mountain, where the altitude (in feet) is given by A(x, y) = 898

Question

A skier is on a mountain, where the altitude (in feet) is given by A(x, y) = 8980 - x^2 -3y^2 origin representing the mountain peak and x and y are measured in hundreds of feet, with the The skier is located 100 feet east of the peak, and 200 feet north (i.e., (x,y) = (1,2)). In which direction should she point her skis so that she goes downhill as quickly as possible? If her skis were pointed in the direction (3,4), what would be the slope of the mountain in that direction? (You will get full credit without units, but I suggest you find the units to realize how this number even means anything.)

Explanation / Answer

A(x,y)= 8980 -x2-3y2

A =<-2x ,-6y>

A at (1,2)=<-2 ,-12>

a) down hill as quickly as possible ==>direction =-A=<2 ,12>

b)p(1,2) ,q(3,4)

pq =v =q-p=(3,4)-(1,2)=<2,2>

A at (1,2)=<-2 ,-12>

x=Ax*x =-2*2 =-4

y =Ay*y =-12*2 =-24

slope =y /x =-24/-4 =6

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