Related Rates: A child holding a balloon is walking at a rate of 5 ft/sec. The child lets go of the balloon and continues to walk. The balloon rises at a rate of 2 ft/sec. After 4 seconds, how fast is the balloon moving away from the child?

Q: A car is merging onto a freeway (beginning at rest), accelerating at a constant rate of 12ft/sec How…

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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…

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Q: A ladder 25 feet long is leaning against a barn. It is sliding down the barn at a rate of 3 ft/sec.…

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Q: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its…

A: Refer to the figure shown below: [Note that we have to consider the depth of 5 ft to solve the…

Q: 1. A 25 feet long ladder is leaning against a wall and sliding toward the floor. If the foot of the…

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Q: Sketch the situation If necessary and use related rates to solve. Kvita A 14 ft ladder is leaning…

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Q: Stephanie is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder…

A: Given dx/dt = 3 ft / sec Lentgh of ladder = 13 ft

Q: A balloon is released from the ground 60 meters from an observer. The balloon rises directly upward…

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Q: A square changes its area at a rate of 300 units^2/s. If a circle is always inscribed in this…

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Q: A man 6 feet tall walks at a rate of 4 feet per second away from a light that is 15 feet above the…

A: A man 6 feet tall walks at a rate of 4 feet per second away from a light that is 15 feet above the…

Q: 3. A light at eye level stands 20 ft from a house and 15 ft from the path leading from the house to…

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Q: A ladder 13 feet long is leaning against a house. The base of the ladder is pulled away from a wall…

A: Let,      x: The distance of the base of the ladder from the wall      y: The height of the ladder…

Q: A ladder is leaning against a wall. The ladder is 5 feet long. The top of ladder slides down the…

A: Let the horizontal distance be x and the vertical distance be y . According to the given problem we…

Q: A spherical balloon is inflated with gas at a rate of 14 cubic feet per minute. How fast is the…

A: Use volume of sphere to evaluate

Q: A 25-foot ladder is leaning against a house. The base of the ladder is pulled away from the house at…

A: Given information- Length of the ladder = 25 foot Base of the ladder is moving away with the rate =…

Q: 1. A 10 ft ladder is leaning a gainst a wall. If the top of the ladder slides down the wall at a…

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Q: 10. A boy is flying a kite on a string. The kite is 120 ft above the ground and the wind is blowing…

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Q: 2. A boat is being pulled into a dock by a rope attached to it and passing through a pulley on the…

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Q: baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with…

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Q: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its…

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Q: Example A light is on the top of a 12 ft tall pole and a Sft 6in tall person is walking away from…

A: Consider the provided question, The pole and the person are shown in the figure below;

Q: leaning

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Q: A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away…

A: Given that, A ladder 25 feet long is leaning against the wall of a house. The base of the wall is…

Q: A ladder 20 feet long is placed against a wall. The foot of the ladder begins to slide away from the…

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Q: A ladder 25 feet long is leaning against a wall of a house. The base of the ladder is pulled away…

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Q: 6. A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1…

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Q: 9. A man 6 ft tall walks away from a lamp post 16 ft high at the rate of 5 mi/hr. How fast does the…

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Q: A sailboat is sitting at rest near its dock. A rope attached to the bow of the boat is drawn in over…

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Q: 1. Merle is six feet tall. He is standing under a light that is hanging 15ft above the ground. As he…

A: according to our guidelines we can answer only first question and rest can be reposted.

Q: A 13-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

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Q: 1. Sand being dumped from a funnel forms a conical pile whose height is always one￾third the…

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Q: A child flies a kite at a height of 50 ft, the wind carrying the kite horizontally away from the…

A: Given that  A child flies a kite at a height of 50ft , the wind carrying the kite horizontally away…

Q: A ladder 15 feet long is leaning against a vertical wall. The top of the ladder slides down the wall…

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Q: A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away…

A: We will apply derivative to find rate of change Rate of change in y w.r.t. x is given by dy/dx

Q: Water is flowing into a conical reservoir 20 ft. deep and 10 ft. across the top, at the rate of 15…

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Q: 5. A ladder 25 feet long leans against a vertical wall. The bottom of the ladder slides away from…

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Q: A spherical balloon is inflated with gas at a rate of 14 cubic feet per minute. How fast is the…

A: Given, A spherical balloon is inflated with gas at a rate of 14 cubic feet per minute.

Q: The altitude of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is…

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Q: A 13-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

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Q: conical reservoir 50 ft deep and 200 ft across the top is falling at the rate of 0.002 ft/hr. How…

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Q: A ladder 25 feet long is leaning against a wall of a house. The base of the ladder is pulled away…

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Q: olve a Related 12 foot ladder is leaning against a wal. If the top of the ladder slides down the…

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Q: A ladder 13 ft long is leaning against a wall. The bottom of the ladder is being pulled away from…

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Q: A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec. How…

A: Given; A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec.

Q: A balloon is rising at a constant speed 4 m/s. A boy is cycling along a straight road at a speed of…

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

A: To determine the rate at which the ladder is moving.

Q: a girl flies a kite at a height of 300ft. the wind carrying the kite horizontally away from her at a…

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Q: 5. A ladder 20 ft long leans against a vertical building. If the top of the ladder slides down at a…

A: Given query is to find the speed at which bottom of the ladder is sliding.

Q: The base of a 45-foot ladder is being pulled away from a wall at a rate of 6 feet per second. How…

A: Use Pythagoras theorem

Q: A 25-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

A: As per given by the question, There are given that 25 foot ladders is leaning against a vertical…