1. A 20 ft ladder is leaning against the wall. The bottom of the ladder is pulled along the level ground at 2 ft/sec. How fast is the top of the ladder moving down the wall when the foot of the ladder is 4 ft from the wall?

Q: 3. A light is hung 15 ft above a straight horizontal path. If a man 2 ft tall is walking away from…

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Q: Assuming your car can slow at a constant rate of 15 ft/sec2, how much distance will your car cover…

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Q: Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section…

A: The situation is as shown below: Consider a small differential element of water at a height of h…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Given: Length of a ladder which rests against a vertical wall is 10 ft. Let the distance between…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: To find: The rate at which the angle between the ladder and the ground  is changing

Q: 1. A ladder 8 m long is leaning against a wall. If the bottom of the ladder is pulled horizontally…

A: We will draw figure and use differentiation  to find rate of change . Note . Only one question…

Q: At what rate is water pouring into a rectangular bathtub with base 65 fť if the water level rises at…

A: According to the given information it is required to calculate the rate at which water is pouring…

Q: 2) Water is pouring into an inverted cone at the rate of 8 cubic me- ters per minute. If the height…

A: Given that Height of cone h=12 m radius of its base r=6 m rate of pouring water into cone dVdt=8 m3

Q: A light is at the top of a 16 ft pole. A man 6 ft tall walks away from the pole at a rate of 5ftsec…

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Q: A 40-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 7…

A: Find the rate of the top of ladder sliding down.

Q: . A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking…

A: We make diagram of the situation .

Q: A man starts walking north at 4 fts from a point . Fiveminutes later a woman starts walking south…

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Q: A light is hung 15 ft above a straight horizontal path. if a man 6 ft tall is walking away from the…

A: Solution :x=distance from lights=length of shadowlet,height of light,D=15 ftheight of…

Q: a) Water is flowing into a leaky cistern at the rate of 31.4 cu ft./min. The cistern is a right…

A: Given that  The water is flowing into a leaky cistern at the rate of 31.4 cu ft./min ⇒dVdt=31.4…

Q: A ladder 20 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

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Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

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Q: 6) A 13 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate…

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Q: A 15-foot ladder is leaning against a mango tree. If the top of the ladder is sliding down the tree…

A: We need to find rate of bottom of ladder moving.

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

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Q: A person stands at the end of a pier 8 ft above the water and pulls in a rope attached to a buoy. If…

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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: A boat is pulled toward a dock by means of a rope wound on a drum that is located 3 ft above the bow…

A: a rough sketch of the problem will be as follows:

Q: 2) A 5-ft ladder, leaning against a wall, slips so that its base moves away from the wall at a rate…

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Q: 4. A basketball player is 7 feet tall walking away from a light that is 28 feet above the ground at…

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Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: Given : The pulley is 1 m higher than the bow The rate at which rope is pulled dydt=-1m/s and x=8.…

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: We sketch the situation roughly  Let us assume x=the distance of the boat from the dock y=the…

Q: A ladder 7 m long is leaning against a wall. If the bottom of the ladder is pushed horizontally…

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Q: 5. A baseball diamond has the shape of a square with sides 90 ft long. A player 60 ft from second…

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Q: A 50 ft ladder is placed against a wall, as shown below. The base of the ladder is slipping away…

A: Let the horizontal distance of the ladder is = x ft Vertical distance = y ft So, Given that:…

Q: A kite, at a height of 60 ft. is moving horizontally at a rate of 5ft/sec. away from the boy who…

A: From the given information, draw a picture.

Q: A 13-ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A:

Q: 4. A street light is at the top of a 16 ft pole. A 6 ft tall woman walks along a straight path away…

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Q: A boat that arrives at a dock 20 ft above water level is being pulled in by a fisherman using a rope…

A: To find: The speed of the boat approaching the dock when the total length of rope out is 50 feet.…

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: Let A= Pulley , B= Boat Given that AC=1  Let, x= distance of the boat from the dock. y=length of the…

Q: A 35-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 8…

A: Let BC = x = distance from the base of wall to bottom of the ladderAB = y = distance from the base…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: To determine the rate of change of angle between the ladder and the ground.

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: The dock is 1m higher than the bow of the boat. Pulled rate of the rope of 1.4m/s To calculate the…

Q: A 17 ft ladder is leaning against a wall. If the bottom of the ladder is pulled along the ground…

A: x2+y2=172=289Differentiate with respect to 't'2xdxdy+2ydydt=0   xdxdt+ydydt=0

Q: a kite at a height of 60 ft is moving horizontally at a rate of 5 ft/sec away from the boy who flies…

A: Let boy is at the point A, and when 100 ft cord is released the kite is at the point C, which is…

Q: A kite, at a height of 60ft.is moving horizontally at rate of 5ft./sec away from the boy who flies…

A: In right angle triangle ,According to the Pythagoras theorem , H2 = P2 + B2 Where H is horizontal ,…

Q: A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At which rate is the angle…

A: Given,  Consider the height of the lite from the ground is 100 ft. The speed is dxdt=8 ft/s. To find…

Q: a. How fast is the top of the ladder sliding down the wall when the base of the ladder is 12 feet…

A: It is given that the length of ladder is 13 foot which acts as the hypotenuse of the right angled…

Q: A 20-foot ladder is leaning against a vertical wall. Suppose the base of the ladder slides away from…

A:

Q: a kite 100 ft ft above the ground moves horizontally at a speed of14ft/s. at what rate is the…

A: If you like the solution then please give it a thumbs up..... The Answer is:     Result = - 0.035…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Given:-  Ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away…

Q: A 15-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 3…

A:

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: A boat is pulled toward a pier by means of a taut cable. If the boat is 20 ft below the level of the…

A:

Q: A kite is 30 ft. high and is moving horizontally at a rate of 10 ft./min. At what rate is the string…

A: Calculate the rate in the following way:-

Q: A 20-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 6…

A: Let x= horizontal distance y=vertical distance Given that dx/dt=6 ft/sec and x=16 ft At x=16 we find…