Question

you and a friend are riding your bikes to a restaurant that you think is east; your friend thinks the restaurant is north. you both leave from the same point, with you riding mph east and your friend riding mph north. after you have travelled mi, at what rate is the distance between you and your friend changing? after you have travelled mi, the distance between you and your friend is changing at a rate of mph.

Answer 1

The distance between you and your friend is changing at a rate of 20 miles per hour.

What is the Pythagorean theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we

Let the east direction is denoted by x and

the north direction is denoted by y.

dx / dt = 16 miles per hour

dy / dt = 12 miles per hour

x = 4 miles

Let the distance between both the friends be s.

Time is taken by you to travel 4 miles,

time = distance / speed = 4 / 12 = 1/4 hour

Distance traveled by your friend in time t,

y = speed x time = 12 x 1/4 = 3 miles

By Using the Pythagorean theorem,

x² + y²  = s²     ..... (1)

Substitute, x = 4 mile, y = 3 mile

s²  = 16 + 9 = 25

s = 5 miles

Now, Differentiate equation (1) with respect to t, we get

2x dx/dt + 2y dy/dt = 2s ds/dt

4 (16) + 3 (12) = 5 ds/dt

ds/dt = 20 miles per hour

Hence, the distance between you and your friend is changing at a rate of 20 miles per hour.

To learn more about the Pythagorean theorem from the given link

https://brainly.com/question/16176867

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