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Here\'s the problem statement: I can\'t seem to get the answer at all. I know th

ID: 2828596 • Letter: H

Question

Here's the problem statement:


I can't seem to get the answer at all.

I know the process goes:

1) law of cosines  z^2 = x^2 + y^2 - xycos(theta) <- solve for z

2) take derivative of this, solve for dz/ dt (subbing in 6/4 for x, 6 for dx/dt, 3/4 for y, and 3 for dy/dt)


If anyone can figure out where I'm going wrong and what the exact answer is in mi/h, that would be perfect and I will rate perfect.  Thank You!

Two people start from the same point. One walks east at 6 mi/h and the other walks northeast at 3 mi/h. How fast is the distance between the people changing after 15 minutes? aw of cosines z^2 = x^2 + y^2 - xycos(theta)

Explanation / Answer

Let x = distance travelled by person heading east
dx/dt = 6
x = 6t

Let y = distance travelled by person heading northeast
dy/dt = 3
y = 3t

Let d = distance between these two people

We can draw triangle to illustrate the situation, with side lengths x, y, and d, and angle between sides x and y = 45 degrees (east = 0 degrees, northeast = 45 degrees)
Now we can express d in terms of x and y using cosine rule:
d