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1 / 2 90% + Answer each of the problems. Make sure to show all your work. 1. A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute, at what rate is the volume increasing when the radius is 5 inches? 2. A particle moves in a circular orbit x? + y? = 16. As it passes through the point (2, 2:/3 ), its y-coordinate decreases at a rate of 3 units per second. At what rate is the x- coordinate changing? 3. A point moves along the straight line x + 3y = 6. Find the rate of change of the y-coordinate, given that the x-coordinate is increasing at a rate of 3 units per second. 4. If a point is moving along y = 3x? - 4x - 6 at a rate of an = 4 m/s, find dy , when x = 3. 5. A heap of garbage in the shape of a cube is being compacted. Given that the volume decreases at a rate of 2 cubic meters per minute, find the rate of change of an edge of the cube when the volume is exactly 27 cubic meters. 2/2 90% + 6. A circle with area A = xr is expanding with time. If JA = 5 cm'/s, what is of when r = 6? 7. A triangle, whose h = 2b, has an area A = -bh - _b(2b) = b is expanding with time. If dA= 8 cm'/s, what is when b = 2? ' dt 8. A sphere is expanding at the rate of 8 cm'/sec, the formula for volume of a sphere is V = = n'. what is s " when r = 5? dt 9. A cone is expanding at the rate of 9 cm /sec, the formula for volume of a cone is: V = arch, let 3 h = 2r, what is - when r = 3? 10. A cylinder is being filled such that the height of its contents is increasing at a rate of 5 cm /s. What is the rate of change of the volume if r = 3 and V = mirh