Answer to Question #237876 in Mechanics | Relativity for Emma

Question

Q6. Find the gradient of the following functions

f(x, y, z) = x2y3z4.

f(x, y, z) = exsin(y) ln(z).

Q7. The height of certain hill (in feet) is given by h(x,y)=10(2xy−3x2 −4y2 −18x+28y+12)

Where y is the distance in north, x is the distance in east.

a. Where is the top of the hill located?

b. How high is the hill?

c. How steep is the slope (in feet per mile) at a point 1-mile north and 1- mile east, in what

direction is the slope steepest?

Q8. Calculate the divergence and Curl, of the following functions

a. V= x2 i+3xy^2 j -2xyz k

b. V=xyi+2yz j+3zx k

c. V= y2i +(2xy+z2)j+ 2yz k , where i , j , k are unit vectors along x, y and z axis

Answer 1

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