The distance between a point

on the given plane and the point (0, 2, 4) is

but since

and

share critical points, we can instead consider the problem of optimizing

subject to

.
The Lagrangian is

with partial derivatives (set equal to 0)




Solve for

:


which gives the critical point

We can confirm that this is a minimum by checking the Hessian matrix of

:


is positive definite (we see its determinant and the determinants of its leading principal minors are positive), which indicates that there is a minimum at this critical point.
At this point, we get a distance from (0, 2, 4) of
Ok. Something times 90 = 7200.
Let something = x
90x = 7200
Divide both sides by 90.
90x/90 = 7200/90
x = 80
The other factor is 80.
Step-by-step explanation:
15. If f(x) = 20x, adding a $10 fee for cleaning would be
g(x) = 20x + 10
The graph of g(x) is shifted 10 units up from the graph of f(x).
16. f(x) = 2x + 1
g(x) = (2x + 1) + 5
h(x) = 3f(2x + 1)
g(x) shifted f(x) 5 units to the right.
h(x) is 3 times steeper than f(x).
If this is the correct answer, then please give it the brainliest.
Answer:
I need points, sorry, i cant help
Step-by-step explanation: