T AppLiCATIONs 1. Schve for the orthogonal trayectories (a+x)y² = x*( 3a-x)

For the sphers x-12+y+22+z-42=36 and x2+y2+z2=64, find the ratio of their a surface areas. b volumes.

Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. The frustum of a right circular cone has a larger base area of 40.0 square centimeters and a smaller base area of 19.0 square centimeters. The height is 22.0 centimeters. Find the volume. Round the answer to the nearest cubic centimeter.

c) A cube has sides of length x cm and volume V cm3 . The volume is increaring at a rate of 1.5 cm's. Find the rate of increase of x when V 8 cm³. %3D

Need help. Show complete and thorough solution with good explanation.

2. A tank has 72 gallons of water. Brine solution with 2lbs of salt per gallon of solution enters at a rate of 2.5 gal/min and the well-stirred mixture is also withdrawn at the same rate. When will the concentration be 0.5lb/gal of solution? 20

dt tu2 >16? 92 dt 9ン14.4% 2. A rectangular lot is bounded on one side by a concrete wall. The owner wishes to put up fences on the 3 remaining sides. Give the length and the width of the largest lot that can be enclosed if the length of the available fencing material is 800 ft. 3. Sand is being sifted onto a conical pile at the rate of 0.3 ft³ /sec. It was also observed that at any instance, the base diameter of the pile is twice that of the height. How fast is the height of the pile increasing when the pile is 2 ft high?

= 5. Find the x-coordinate of the center of mass of the thin flat plate of constant density & located in the first quadrant bounded from the top by y 1 and from 28 the bottom by y = x². You may use the fact that the mass M of the plate is 3

6. A 100-gal tank is initially full of water containing 10 lb of salt in solution. The tank will overflow whenever additional water is added. A pump attached to a sensor pumps fresh water into the tank at a rate proportional to the concentration of salt in the tank. The constant of proportionality is 10 (gal) /lb - min. Find the amount and concentration of salt in the tank as functions of t.

4. Copy the following solution for the volume of a cylinder to the right of where it appears on the page. V = ar²h V = T(5)²(7) V = t(25)(7). V = 549.8 cm