stone dropped into a pond sends out a circular ripple whose radius increases at a constant rate of 4ft per second. After 12 seconds, how rapidly is the area enclosed by the ripple increasing?

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. What is the…

A:

Q: A ladder 10 feet long is resting against a wall. If the bottom of the ladder is sliding away from…

A: Let the base be x  And the perpendicular be y and length of ladder=10 feet   dxdt=1 feet/sec…

Q: A ladder 10 meters long rests on horizontal ground and leans against a vertical wall. The foot of…

A:

Q: a 17 foot tall ladder is leaning against a vertical wall and its base is on level ground. The top of…

A: We have to find at what rate is the top of the ladder sliding down the wall when it is 8 feet above…

Q: A 13-foot ladder is resting against a wall and the bottom is initially 10 feet away from the wall.…

A: To find- rate at which its top moving up the wall.

Q: A submarine started at the surface of the ocean and began diving -15 kilometers per minute towards…

A: Given: Diving speed of submarine, s = 15 km/min, and time of diving, t = 48 min

Q: A small balloon is released at a point 60 feet away from an observer, who is on level ground. If the…

A:

Q: A balloon leaves the ground 18m from an observer and rises vertically at 1.25 m/s. How fast is the…

A:

Q: A hand-tossed pizza crust starts off as a ball of dough with a volume of 400πcm^3. First, the cook…

A:

Q: The length of a rectangle is increasing at arate of 5 cm per second and its width is decreasing at a…

A:

Q: The length of a rectangle is increasing at a rate of 5 cm per second and its width is decreasing at…

A: Given: Rate of increase in length of a rectangle, dldt=5 cm/s Rate of decrease in width of a…

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A: Given that, Let length of the ractangle is L and the width is W and area is A. Then according to the…

Q: All edges of a cube are expanding at a rate of 6 cm per second. How fast is the volume changing when…

A:

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A:

Q: All edges of a cube are expanding at a rate of 7 cm per second. How fast is the surface area…

A: All edges of a cube are expanding at a rate of 7 cm per second. How fast is the surface area…

Q: A stone dropped into a still pond on a calm day sends out a circular ripple. If the radius increases…

A:

Q: A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min.…

A: Rate of change

Q: The sides of a cube are increasing at a rate of 1cm/s. How fast is the diagonal of the cube changing…

A: Explanation: Given that,  The sides of a cube are increasing at a rate of 1cm/s. The objective is to…

Q: Water is flowing into a cylindrical tank at the rate of 2 m^3/min. If the radius of the tank is 0.5…

A: Water is flowing into a cylindrical tank at the rate of 2 m3/min.If the radius of the tank is 0.5 m,…

Q: A 15-foot teddy bear is leaning against a shelf. The top hand of the teddy bear is sliding down the…

A: Let horizontal distance= x ft , vertical distance= y ft Relation between x and y is: Given that…

Q: A plate in the shape of an equilateral triangle expands with time. The length of a side increases at…

A: Given that the length of side increases at a constant rate of 2 cm/h find out at what rate is the…

Q: cylindrical tank with radius 5m is being filled with water at a rate of 3m3/min. How fast is the…

A:

Q: The length of a rectangle is increasing at a rate of 5 cm per second and its width is decreasing at…

A: Let x be the length, y be the width and A be the area of the rectangle. Then we get, A = xy The rate…

Q: All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the surface…

A: All edges of a cube are expanding at a rate of 2 centimeters per second.

Q: A perfectly spherical balloon is losing volume at a rate of 3 in3 per sec. How fast is the balloon’s…

A:

Q: The radius of the circle is increasing at a rate of 1 meter per minute and the sides of the square…

A:

Q: The radius of a right circular cone is increasing at a rate of 5 inches per second and its height is…

A:

Q: The area of a rectangle remains 30 cm2. One side of the rectangle is expanding at a rate of 1 cm/s.…

A:

Q: Each side of a square is increasing at the rate of 8 cm/sec. At what rate is the area of the square…

A: Solution :let, side of square=xArea of square=Adxdt= 8 cm/secA= 36 sq. cmA=x2    Area of square=side…

Q: 2) A person is standing 350 feet away from a model rocket that is fired straight up into the air at…

A:

Q: A population of yeast cells can double in 6 hours. Assume an initial population of 4,000 cells. What…

A:

Q: An artist paints a portrait on a circular canvas and encloses it in a circular metal frame. At a…

A: Let the radius of the circular canvas be r.   The area of the canvas will be given by: A=πr2   Also,…

Q: The length of the rectangle is decreasing at a rate of 5 cm per second, and its width is increasing…

A:

Q: a spherical snowball is melting in such a way that its surface area decrease at the rate of…

A:

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. what is the…

A:

Q: The length of a rectangle is decreasing at the rate of 5 cm/s and its width is increasing at the…

A: Area of a rectangle = length× width Rate of change with respect to time is D/Dt

Q: A ladder 12 meters long rests against a wall. The foot of the ladder is pulled away from the wall at…

A: According to the question we have the diagram

Q: vulcanizing shop has a trapezoidal drum that is 5 meters long, 1.5 meter wide at the top, 1 meter…

A: Solution of the problem as follows

Q: The length of the rectangle is decreasing at a rate of 5 cm per second, and its width is increasing…

A:

Q: As a balloon in the shape of a sphere is being blown up. the volume is increasing at the rate of 4…

A: Given that, Rate of increase of volume, dV/dt = 4 cu.in per sec Value of radius, r = 1 inch

Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 5 meters per…

A: Let r be the radius of circle ands be the length of the side of squareGiven: drdt=-5 and ds/dt=5Let…

Q: An apple pie with an initial temperature of 170 -C is removed from the oven and left to cool in a…

A:

Q: A pole that is 74 feet long is leaning against a brick wall. The bottom of the pole is getting…

A: This question is related to rate of change, we will solve it using given information.

Q: Water is flowing out of a cylindrical storage tank at a rate of 2 m3/min . If the tank has a radius…

A:

Q: (a) Water flows from a storage tank at a rate of 900 – 6t liters per minute. Find the amount of…

A: This question is related to calculus . solve in step 2.

Q: A 5m long ladder has its upper end leaning against a vertical wall and lower end on a perfectly…

A: To determine the rate at which the ladder is moving down in cm/sec when the lower end is 3 m away…

Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A:

Q: A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant…

A: a) Let 'r' be the radius

Q: All edges of a cube are expanding at a rate of 6 centimeters per second. (a) How fast is the surface…

A:

Q: Helium is pumped into a spherical balloon at a constant rate of 3 cubic feet per second. How fast is…

A: