I have the first two solved. I'll display them here step by step, and while you ponder them over, I'll try to figure out #3.
You're given a rectangle with a length of 20 m and a width of 16 m. You're also given two rates:
What you're asked to find is find the rate of the width: .
First, find a formula for a rectangle that includes area, width, and length. That formula is A = lw. Of course, we can't plug in the rates to just that, so take the derivative of the formula. Notice that we have to use the product rule on the right side.
Now plug in everything you know, and solve for the missing variable.
Simplify, and you'll get.
Be sure to include the second unit.
Ok, this is a right triangle. x = 36 km/h and y = 48 km/h. There is no rate here except the one we need to find (the hypotenuse, which I'm going to call w). However, notice that the problem is asking for the rate after ten minutes have passed, so what you can do, is take x and y, and divide each of those by 60, in order to convert it to minutes. That'll give you your dx and dy.
Here's what we know now.
x = 36 km/h
y = 48 km/h
Now, we need to find a formula for this triangle. To find the missing side, we will need to use the Pythagorean Theorm. Before we get into anything, lets go ahead and find w (trust me on this).
Ok, we found w. Lets go ahead and take the derivative of the Pythagorean Theorem.
Notice that we now need w to solve the equation. At this point, plug everything you know in.
Solve for the missing variable.
Keep in mind that this is in kilometers/minute after one minute has passed. To find it at the 10 minute mark, we have to multiply by 10 to find the total distance.
1(10) = 10 km
Thats your solution.