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Tools Window Help signment 3.pdf Q Search ing out this form. AMAT 112 Calculus 1 Written Assignment 3 Question 1) 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 at 16 mph east and your friend riding at 12 mph north. After you travel 4 miles, at what rate is the distance between you and your friend changing? (5 points) Question 2) You are constructing a box for your cat to sleep in. The plush material for the square bottom of the box costs $5/ft^2$ and the material for the sides costs $2/ft^2$. You need a box with

Transcript

00:01 So it's given that you and a friend are riding your bikes to a restaurant that you think it is in east.

00:06 So and your friend thinks that restaurant is in north.

00:09 You both live from the same point.

00:10 So we are living from the same point.

00:12 With you riding at 16 miles per hour east.

00:15 So let's say one person is riding in this direction at speed of, let's say this is a distance or x dot since we are moving in the x direction.

00:27 16 miles per hour.

00:30 This can x dot nothing but dx by d t.

00:33 Now similarly your friend is riding as 12 miles per our north from the same point so let's have here which can be written as d y by dt since there is a vertical height change that is equals to 12 miles per hour.

00:47 Now we need to find after four miles so after a distance of four miles sorry it's minutes not mile so after t equals to four minutes we need to find at water it is a distance between you changing so we need to find this distance at water it is changing so let name this as x now since this is north and this is east it must be perpendicular now if you apply pythogamous let this length be y and this length be x after sorry let take this length as d so after time t we have length y, x and d.

01:26 So by pythagoras we'll have y square plus x square is equal to d square and we have to find rate of change of d so we'll differentiate this entire equation with time so we'll have 2 y, d y, d y, since y is changing with respect to time...

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