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- Can the average rate of change of a function be constant?Estimate the average rate of change from x=3 to x=4. Enter your estimate as a decimal number (not as a fraction), rounded to one decimal place.A particle moves on the line y = 2x + 1 in such a way that its x−coordinate changes at a constant rate of 4 units per second. A right triangle is formed by the vertical line from the particle to the x−axis, the line connecting the particle to the origin, and the x−axis. At what rate is the area of the right triangle changing when x = 4?
- The sides of an equilateral triangle extend at a rate of two cm per second. I drew a half-circle inside this triangle that touches two of its sides and began to expand with it. Find the rate of change of the area between the triangle and the half-circle when the length of the side of the triangle is 16 cm4. The volume of a sphere is changing at a constant rate. Show that the surface area changes at a rate which varies inversely as the radius.What is the average rate of change of the height of water in the vase with respect to the volume of water in the base as the volume changes from 2.5 cups to 4.25 cups? The average rate of change is?
- When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is increasingat the rate of 0.02 cm/s, at what rate is the area of the top surface increasing when the radius is 3 cm?The time rate of change of the radius of a sphere is 1/2π, when its radius is 5 cm , find the rate of change of the area of the surface of the sphere with time.The length of a rectangle is increasing at a rate of 5 meters per minute and the width is increasing at a rate of 4 meters per minute. When the length is 14 meters and the width is 23 meters, then how fast is the AREA changing?? (Enter answer as an integar)
- The volume of a cube decreases at a rate of 10 meters33 per second. Find the rate at which the side of the cube changes when the side of the cube is 3 meters.The sides of an equilateral triangle are increasing at the rate of 3 cm/min. Find the rate of the perimeter and the rate of change of the area when the side is 3 cm long.If we know the rate of growth of a patch of moss, how can we calculate the area the moss covers?