Question

In: Math

Joe leaves an intersection traveling west in his car. He is 20 feet from the intersection...

Joe leaves an intersection traveling west in his car. He is 20 feet from the intersection 4 seconds later. At the same time, Joshua leaves the intersection heading north in his car so that his position 4 seconds later is 26 feet from the intersection. If, at that instant time, Joe's speed is 8 feet per second and Joshuas' speed is 12 feet per second, find the rate at which the distance between the two cars is changing to the nearest tenth.

Solutions

Expert Solution

Let the Distance travelled by Joe be x feet and the distance travelled by Joshua be y feet and let the distance between the two cars is r and then the rate of change between them is

We know x=20 feet and y=26 feet

Applying Pythagorean theorem to get r

Then, starting with , take the derivative with respect to time on both sides to get

Dividing Both sides with 2

We Know

and

Also x=20 feet and y=26 feet

We were unable to transcribe this image

North r=distance between two cars y feet by at any Joshua timet, West x feet by Joe

We were unable to transcribe this image

C dc dt +y dy dt dr = T- dt

We were unable to transcribe this image

milcah answered 1 year ago

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