20. A 13 foot ladder leans against a vertical wall. When the ladder is pulled away from the wall at a rate of 0.5 ft/s, how fast is the top of the ladder sliding down the wall when the foot of the ladder is 5 ft away from the wall?

Q: A 13ft ladder rests against a vertical wall. If the bottom of the ladder is sliding away from the…

A:

Q: 17 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how…

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Q: (8) A baseball diamond has the shape of a square with sides of 75 feet long. A player running from…

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Q: 2. A 13-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the…

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Q: 1. Water is flowing at the rate of 2 m3/min into a tank in the form of an inverted cone having an…

A: It is given that the cone has altitude 16 m and radius 4 m. That is, hcone=16,rcone=4. Let r and h…

Q: 21. A ladder 5 m long is leaning against a vertical wall. If a person pulls the bottom of the ladder…

A: Topic:- application of derivatives

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: a)How quickly is the water leaving the barrel over the first two seconds? b)Will the water drain…

A: The solution is given below in the next step:

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: 2. A rope is attached to a boat at water level, and a man on the dock is pulling on the rope at the…

A: Draw the given situation at any time t then using Pythagoras theorem and application of derivative.…

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Differentiate volume wrt t

Q: 1. Water is poured into a conical tank 6 m across the top and 8m deep at the rate of 10 How fast is…

A: To find: The rate of water level rising when water in the tank is 5 m deep. Formula used: The volume…

Q: 11. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

A:

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

A:

Q: 2. a) A ladder 10 ft long leans against a vertical wall. If the top of the ladder slides down the…

A: Given:-  a) A ladder 10 ft long leans against a vertical wall. If the top of the ladder slides down…

Q: An 8- meter ladder is leaning against a vertical wall. If a the ladder away from the person pulls…

A: Given  Length of the ladder = 8 meter The rate at which ladder is pulled away from the wall =0.7m/s…

Q: 1. If the radius of a spherical balloon is increasing at the rate of 3 cm/s, which of the following…

A: We are only allowed to solve one question at a time so we will answer only the first question.…

Q: 2. A street lamp is 5m tall and located 6m from a brick wall. A person who is 2m tall walks away…

A:

Q: 2. A pulley 4 meters from the ground is used to lift a 100 kg block. If the rate at which the block…

A: Given: The distance between pulley and the ground s1 = 4 meter The velocity of the block getting…

Q: 3.) A conical tank is 10ft across the top and 12 ft. deep. If oil is poured into the tank at the…

A:

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given that,  At time, t=0, the amount of cane sugar in water =75kg At time, t=30minutes, the amount…

Q: A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is…

A:

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

Q: 13. A 10-meter ladder is leaning against a vertical wall with its foot on the same horizontal plane…

A:

Q: 2. A man walks across a bridge at the rate of 5 ft/s as a boat passes directly beneath him at10…

A: From the given data , Man walks across a bridge in one second AC=5 feet and boat passes in one…

Q: A liquid solution is passing thru a conical filter 2 feet deep and 4/3 feet across the top, into a…

A: We have to find the rate at which the level of the solution in the cylinder rising.

Q: 7. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

A: Given data A ladder slides a vertical wall at rate of 0.15 m/s  find the length of ladder = ?

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

A:

Q: 1. A conical paper cup 4 inches across the top and 4 inches deep is full of water. Since there is a…

A: We have been given the cone as in the figure  By the given figure we get r = 2 in. and h = 4 in. We…

Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A: This question can be solved using the concept of rate of change of physical quantities.

Q: 2. Suppose that the bottom of a conical shaped tank of water has been ruptured. At the instant when…

A:

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

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Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6oz of this…

A: The amount of mold at time 0 is m0. The amount of mold present after t hours is m. The rate of…

Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

A: Given,  A ladder slides down a vertical wall at a rate of 0.675 m/s  When the bottom of the ladder…

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

A:

Q: 1. Suppose the length of the diagonal of a square is increasing at the rate of 2 inches per second.…

A:

Q: The top of a ladder that is 5 m long slides down a vertical wall at a rate of 2 m/s. At what rate…

A: Given :Length of ledder=5m

Q: The top of a ladder slides down a vertical wall at a rate of 0.25 m/s. At the moment when the bottom…

A: Given:

Q: D. A ladder 10 feet long rests against a vertical wall. If the top of the ladder slides down at a…

A: Make a diagram according to the situation.

Q: 1. How fast is the water level rising in a rectangular fish tank whose base is 20 ft² if the tank is…

A: Give: Area of base is A=20 ft2 Rate with which tank is filling dVdt=0.5 ft3/min. Volume of a…

Q: 6. What is the rate at which the two hands of the clock are separating when the time is two o'clock…

A:

Q: 2) A kite is flying at a fixed height of 30 ft. If 50 feet of string is out already from the spool,…

A: Given- A kite is flying at a height of 30 feet, if 50 feet of string is out already from the spool…

Q: 2. A ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed towards…

A:

Q: 5) If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

A: The volume of cylinder is given by the formula V=πr2h. The given values are as follows: r=40 inches,…

Q: 6) A light is 20 meters above a straight horizontal path. If a man 1.65 meters tall is walking away…

A: Given: Height of light is 20 meter. Height of man is 1.65 meters. Rate with which man is walking is…

Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

A: Given: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when…

Q: Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved.…

A: 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left.

Q: How do you solve question 2?

A: Let x= horizontal distance y= vertical distance Given that dx/dt=1 ft/sec We have to find dy/dt at…

Q: 4. A trough filled with liquid is 2 m long and has a cross section of an isosceles trapezoid 30 cm…

A: Given: 4) Question is wrong (Some values are missed) 5) dxdt=10 ft/sec, h=100 ft, and l=125 ft