16. If the radius of a circle is increasing at the rate of 4 cm/s, find the rate of the increase in its area when the radius is 12 cm.

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 3 ft/min.…

A: The given data is: Initial radius ri=50 ft Radius is decreasing at the rate of drdt=3ft/min To find…

Q: 7. A triangle with a base of 20 inches has a height that is decreasing at a rate of 3 inches per…

A:

Q: Water is poured into a conical paper cup at the rate of 3/2 in/sec (similar to Example 4 in Section…

A: I will use the formula V=13πr2h and differentiation method to solve this problem.

Q: if the base of triangle is constantly 4 cm find the rate at which the area of the triangle is…

A:

Q: 2. A water heater that has the shape of a right cylindrical tank with a radius of 2 ft and a height…

A:

Q: There is a constant outflow of a liquid into a inverted conical vessel 15 m deep and 7.5 m in…

A: Find the rate of change of volume of water in the cone, with respect to time:…

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: lets the size of square is l so the rate of change of length = dl/dt = 3 m/sec area of square = l2…

Q: Suppose the radius of a sphere is increasing at a rate of 5 in/second.  At what rate is the surface…

A: Given that radius of a sphere is increasing at an of 5 in/sec. Let r be the initial radius of the…

Q: 1. The sides of a square decrease in length at rate 2 m/sec. At what rate is the area of the square…

A:

Q: 3. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a…

A:

Q: 9. When a particular plate of metal is heated in an oven, its radius increases at the rate of…

A:

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 4 ft/min.…

A: Area of a circle of radius r is given by  A = πr2                ...(1) Differentiate with respect…

Q: If the rate of change of the surface area of a sphere with respect to its radius is 16pi sq cm, find…

A:

Q: 11. If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at…

A:

Q: Find the rate of change. Volume of a cube with respect to its sides when s = 5

A: The volume of a cube with side s is V=s3 Differentiate with respect to s dVds=ddss3=3s2

Q: If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at what…

A: (a)Given:

Q: If the radius of a circle increases at a rate of o.01 inch per second, find the rate of change of…

A: Let the radius be r, The rate of change of radius , drdt=0.01 inch per secondArea of the circle is…

Q: The radius of a circle is increasing at the rate of 0.7 cm/s. what is the rate of

A:

Q: The radius of a circle is increasing at the rate of 0.7 cm/c.what isthe rate of oncreasing of its…

A: Differentiate circumference wrt t

Q: How fast is the surface area of a circular oil spill in the ocean changing when the radius is 10ft…

A:

Q: If the rate of change in volume of a sphere is equal to its rate of change of its radius. What is…

A: if we let the radius of square = r unit then volume of the square =4/3 πr3 unit3

Q: A softball diamond is a square whose sides are 60 ft long. Suppose that a player running from first…

A: Suppose , y is the distance from the home and x is the distance from first base. Given that ,…

Q: If the volume of a cube is increasing at a rate of 24 in'/min and each edge is increasing at 2…

A: The volume of cube is given by V=a3 where a edge of cube. Given that volume of cube increasing at a…

Q: If the sides of an equilateral triangle are increasing at a rate of 6 m/min. How fast is the area of…

A:

Q: The radius of a circle is increasing at the rate of 0.7 cm/sec.what is the rate of increase of its…

A: The radius of a circle is increasing at the rate drdt= 0.7 cm/sec r = radius of the circle

Q: A cylinder is leaking water but you are unable to determine at what rate. The cylinder has a height…

A: Given, Radius is 2m, height is 2m. Height is decreasing at 10 cm/min when height is 1m.

Q: When a circular plate is heated on an oven its radius increases at a rate of 0.03 cm/ min at what…

A:

Q: Show that the rate of change of the area of a circle with respect to its radius is equal to the…

A: Our Aim is to show that the rate of change of area of a circle with respectto its radius is equal…

Q: 17. If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is…

A: Given: The radius of the sphere is increasing at the constant rate of 3 inches per second. To find:…

Q: A circle has an initial radius of 50 ft. when the radius begins decreasing at the rate of 3 ft/min.…

A: Area of a circle is given byDifferentiating the function of area with respect to time:

Q: Suppose that liquid is to be cleared of sediment by allowing it to drain through a conical filter…

A: Given,

Q: A cube's volume increases at a rate of 108 ft3/min. At what rate is the cube's edge length changing…

A:

Q: The lengths of the edges of a cube are increasing at a rate of 8 ft/min. At what rate is the surface…

A:

Q: 11. At what rate is the volume of the cube changing if the edge is 8 cm and is changing at 4 cm/s?

A: As we know that; The expression for the volume of the cube with the edge length ''a'' is: v=a3…

Q: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

A: Given: S the surface area of the cube, x the length of the cube and the length x of the cube…

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A:

Q: 4. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A:

Q: 7. A vertical cylinder is leaking water at a rate of 1 ft'/sec. If the cylinder has a height of 10…

A: To find the rate of change of height of water changing

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 5 ​ft/min.…

A: Given information:

Q: 3. The area of a circular inkblot starts from zero and grows at a constant rate of 4n cm/minute.…

A: Use the derivative and formula for area of circle.

Q: 1. When a circular plate of metal is heated in an oven its radius increases at a rate of 0.01…

A:

Q: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

A: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

Q: The original 24 m edge length x of a cube decreases at the rate of 4 m/min. a. What rate does the…

A: Here, We need to find a) The rate at which cube's surface area change when x=5 m b) The rate at…

Q: 2. The height and volume of a right circular cone change at the rates of 1 cm/s and -2 cm^3/s,…

A: Let's find.

Q: 2. The volume and radius of a right circular cylinder change at the rates of 1 cm^3/s and -2 cm/s,…

A: Given : Radius = 2cm, height = 1 cm Rate of change of radius is 2 cm/s and rate of change of volume…

Q: A bacterial cell is spherical in shape. If the radius of the cell is increasing at the rate of 0.01…

A: Given , Bacterial cell is in spherical shape.Let radius be 'r' μm . ∴ Volume of cell, v v = 43π…

Q: 1. The area of a circle decreases at a rate of 3 feet square a. If the circle starts at a radius of…

A: Since you have asked multiple questions in a single request we would be answering only the first…