Compute the directional derivative of the function g(x, y)= sin(π(x−5y)).

Step-by-step explanation:

The directional derivative of a function in a particular direction u is given as the dot product of the unit vector in the direction of u and the gradient of the function

g(x,y) = sin(π(x−5y)

∇g = [(∂/∂x)î + (∂/∂y)j + (∂/∂z)ķ] [sin(π(x−5y))

(∂/∂x) g = (∂/∂x) sin (πx−5πy) = π [cos(π(x−5y))]

(∂/∂y) g = (∂/∂y) sin (πx−5πy) = - 5π [cos (π(x−5y))]

∇g = π [cos(π(x−5y))] î - 5π [cos (π(x−5y))] j

∇g = π [cos (π(x−5y))] [î - 5j]

So, the question requires a direction vector and a point to fully evaluate this directional derivative now.

y-1700=200(x+4)

step-by-step explanation:

200(x+4) is 200x + 800 she is saving 200 per week x is the weeks and the -1700 is. us that’s howmuch she already had

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i