Can you please answer the following questions: 1. A point is moving along y = x^2 + 3x - 6 at a rate of dx/dt = 3 mm/s, find dy/dt , when x = 2. a.) dy/dt= 18 mm/s b.) dy/dt= 12 mm/s c.) dy/dt= 16 mm/s d.) dy/dt= 21 mm/s 2. A rectangle with area A=bh is expanding with time such that the length of the base, b(t)=t^2+2, and the height of the rectangle is constant at h = 4. What is the formula for the rate of change of the area of the rectangle with respect to time? a.) dA/dt=(db/dt)=2t b.) dA/dt=(dh/dt)(db/dt)=0 c.) dA/dt=h(db/dt)=8t d.) dA/dt=b(t)=t^2+2 3. Sue is filling up a grain elevator that is shaped like a circular cylinder. Assume that the volume of the cylinder is V=r^2h, let r = 4 m, and h(t) = t^2. What is the formula for the rate of change of the volume of the cylinder, with respect to time? a.) dV/dt= 32t b.) dV/dt= 16t c.) dV/dt= 32t2 d.) dV/dt= 16t2 4. A triangle, whose h = 2b, has an area A =1/2 b h =1/2 b (2b) = b^2 is expanding with time. If dA/dt = 4 cm2/s, what is db/dt when b = 1? a.) db/dt= 2cm/s b.) db/dt= 13cm/s c.) db/dt= 6cm/s d.) db/dt= 12cm/s 5. A sphere is expanding at the rate of 6 cm^3/sec. The formula for the volume of a sphere is: V=4/3 r^3 . What is dr/dt when r = 2? a.) dr/dt= 3/8 c m/s b.) dr/dt= 3/4 c m/s c.) dr/dt= 1/2 c m/s d.) dr/dt= 1/4 c m/s 6. A cylinder is being filled such that the height of the contents is increasing at a rate of 2 cm/sec. What is the rate of change of the volume if r = 3 and V = r^2h? a.) dV/dt= 18 cm^3/s b.) dV/dt= 8 cm^3/s c.) dV/dt= 2 cm^3/s d.) dV/dt= 9 cm^3/s 7. A ladder is 36 feet long and is leaning against the side of a house. The base is moved away at 2 ft per min. At what rate is the ladder moving down the wall when the base is 5 feet from the wall? a.) dh/dt = -0.460 ft/m b.) dh/dt= -0.560 ft/m c.) dh/dt = -0.280 ft/m d.) dh/dt = -0.251ft/m