Calc I Implicit diff & Related Rates

SHOWING ALLLLLLL WORK! 

1. Use Implicit Differentiation to find dy/dx for x³y+yx²=2x

2. Use implicit differentiation to find equations of both tangent lines to the circle x² + y²=1
3. A spherical snowball of diameter 12 inches begins to melt at a rate of 4.5 cubic inches per minute.
a. How long before the snowball is completely gone?
b. At what rate is surface area changing at the start compared to when the radius
    is just one inch?

4. A cone-shaped coffee filter of radius 3 cm and depth 6 cm contains water, which drips out through a hole at the bottom as a constant rate of 2.5 cubic centimeter (cm³) per sec.
a. If the filter starts out full, how long does it take to empty?
b. Find the volume of water in the filter when the depth of the water is h cm ( This     means to write the formula for volume of the cone using h’s, to solve for r in     terms of h, use proportional reasoning.
c. How fast is the water level falling when the depth is 4 cm?