Solve for the highlighted items (#1, #2, #4, #6). Provide a clear and complete solutions.

Supplementary Problems 1. Let :1: and y be differentiable functions of t and suppose that they are related by the equation my 1 = y2. Find (tr/d1? when 1: = 2, and dy/dt = 1. 220 All ghts reserved. No part of this material may be reproduced or transmitted in any form or by any means - electronic or mechanical including photocopying without written permission from the DepEd Central Office. First Edition, 331?. 2. Let r, h, and A be differentiable functions of t and A = 27er + 27rrh. Find dA/dt when r = 2, h = 5, dr/dt = 2 and dh/dt =1. l 3. Starting from the same point, Royden starts walking eastward at 5 m/s while Nilo starts running towards southward at 2 m / s. How fast is the distance between Royden and Nilo increasing after 3 s? 4. A ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed towards the wall at the rate of 20 m/min, how fast is the top of the ladder moving up the wall when the top of the ladder is 6 meters from the ground? 5. Car A leaves a parking lot at 9 am and travels eastward at the rate of 60 kph. Another vehicle, car B, leaves the same parking lot at 10 am and travels southward at 40 kph. How fast is the distance between these two cars changing at 11 am? 6. A spherical balloon is being inated in such a way that the radius is increasing at the rate of 1 111 /s What is the rate of change of its volume when its radius is 5 111