MATH PEOPLE, help with a function word problem!?

Question

A person leaves home and walks due west for a time and then walks due north.

a- The person walks ten miles in total. If W represents the (variable) distance west she walks, and D represents her (variable) from home at the end of her walk, is D a fuction of W? Why or why not?
b- Suppose now that X is the distance that she walks in total. Is D a function of X? Why or why not?


PLEASE DO NOT USE COS OR TAN. I KNOW YOU HAVE TO USE THE DISTANCE FORMULA BUT I DON'T KNOW HOW TO APPROACH THE PROBLEM

THANKS A LOT!

Answer 1

You can solve this with the Pythagoran Theorem.

Note that W+S = 10

If he walks west, then south & then heads straight for home, his path forms a right triangle. The Pythagorean Theorem tells us that:

W^2 + S^2 = D^2

But since S = 10-W, we get:

W^2 + (10-W)^2 = D^2

So, as a function, you get:

D(W) = SQRT[W^2 + (10-W)^2]

Not a sin or cos in sight.

Answer 2

a) If the person walks 10 miles total, and W miles west, then the amount walked north is 10 - W. Using the distance formula (or the Pythagorean theorem, really), the distance from the starting point to the final point is √[ 10^2 + (10-W)^2 ]. So D is equal to this expression. And yes, it is a function. If you plug in W you get one and only one value back for D.

b) Then D = √[ X^2 + (X - W)^2 ]. You still only get one value for D back from a given X value. It's a function of both X and (if you want to make it a variable) W.

Answer 3

Let X = W + N (N is the distance walked north)

a. Yes, the distance D involves W. In fact, D = sqrt(N^2 + D^2).

b. No, the distance from home D is expressed as a function of W and N.

Answer 4

a) D is function of W, because for each W you will have only one D.
D=sqrt(W^2+(10-W)^2)

b) D is not the function of X because for
a single X value, you'll have different values
for D.
for example consider these two sets:
W=4, N=3 then X=7 and D=5
W=2, N=5 then X=7 and D=5.3
as you can see for X=7 you get
D=5 and/or D=5.3