Question

A plane flying horizontally at an altitude of 4 mi and a speed fo 465mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 10 mi away from the station. Round the result to the nearest integer.

Answer 1

still there?

Answer 2

yes

Answer 3

you can use calculus for this one if it does make it easier.

Answer 4

first off, you'd want to know what the hypotenuse is
notice, the rate of change of the plane or "x" is not decreasing, thus is +465
thus \(\bf h^2=x^2+y^2\implies \cfrac{d}{dt}[h^2]=\cfrac{d}{dt}[x^2+y^2]\)

keep in mind that, all the while the plane is moving, and base is there, the "4" never changes, so, "y" is really a constant

Answer 5

\(\bf h^2=x^2+y^2\implies h^2=x^2+4^2\implies \cfrac{d}{dt}[h^2]=\cfrac{d}{dt}[x^2+4^2]\)

don't forget to chain-rule as you take the derivatives of "h" and "x"

Answer 6

ok wait, so the height of the plane is 4 mi and the distance is 10 mi and now the rate of increase is actually negative?

Answer 7

well... not quite
the plane at the very beginning just passed the radar station, so, is moving away from it
not to it
so the 465 is positive or +465
the 10 miles are the horizontal distance the plane has travelled

now the distance between the plane and the radar station, or hypotenuse, that one is increasing
but "y" is not, the plane is going steady at 4 miles height al along, it's just moving horizontally further only

Answer 8

ahh i see what you mean, care to help me with another one

Answer 9

sure.. post anew, thus, if I dunno, someone else may know :), more eyes

Answer 10

The volume of a cube is increasing at a rate of \[10cm ^{3}\] per minute. How fast is the surface area increasing when the lenght of an edge is 30cm?