Sand falls from a conveyor belt at a rate of 10 m° / min onto the top of a conical pile. The height of the pile is always three-eighths of the base diameter. How fast are the height and the radius changing when the pile is 2 m high?

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

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Q: A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of…

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Q: 16 foot ladder is leaning against a wall. If the top of the ladder slides down the wall at a rate of…

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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 5 foot girl is walking toward a 20-foot lamppost at the rate of 6 feet per second. How fast is the…

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Q: A kite 160 feet above the ground moves in a direction parallel to the ground at the rate of 5 feet…

A: Let, x= the horizontal distance of the kite y=the length of the string Given that dx/dt=5 ft/sec  We…

Q: A kite 100 feet above the ground moves horizontally at a speed of 10ft/s. At what rate is the angle…

A: Let the horizontal distance be x. From the given data of question: And the diagram is:

Q: A ladder 15 ft long leans against a vertical wall. If the top slides down at the rate of 2 ft per…

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Q: The top of a 10 ft ladder slides down a vertical wall at a rate of 1 ft/sec. How fast is the…

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Q: street light is at the top of a 24 ft pole. A 5 ft tall girl walks along a straight path away from…

A: SOLUTION-

Q: A kite 30 m above the ground moves horizontally at a speed of 10 m/min. At what rate is the angle…

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Q: A 15-meter ladder is resting against a vertical wall. if the bottom of the ladder is being pushed…

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Q: A spherical balloon is inflated with gas at a rate of 10 cubic metres per minute. How fast is the…

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Q: What constant acceleration is required to increase the speed of a car from 20 mi/h to 45 mi/h in 5…

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

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Q: A 6-ft-diameter cylindrical tank is filled with water to a height of 10 ft. It is drained such that…

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

A: →cosθ = BaseHypotenuse→sinθ = 1-cos2θ→dcosθdθ = -sinθ

Q: A snowball is melting at a rate of 2.4ft^3 hr^-1 – if the snowball remains a sphere throughout the…

A: given: A snowball is melting at a rate of 2.4ft3/hr. that implies dVdt=-2.4ft3/hr where V is the…

Q: Sand falls from a conveyor belt at a rate of 10 m^3/min and accumulate in a conical pile with the…

A: Use derivative concept

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

A:

Q: A ladder is 20 feet long leaning against the wall of a house, forming a right triangle. The base of…

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Q: An object is thrown vertically upward from a point 32 feet above the ground with an initial velocity…

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Q: A flying kite is 100 m above the ground, moving in a horizontal direction at a rate of 10 m/s. How…

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

A: A ladder with 10 ft resting on a wall is shown in below figure.

Q: A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of…

A:

Q: A 15 foot ladder is leaning against a wall when its bottom starts to slide away. By the time the…

A: Please refer to the diagram on the white board. l= Length of the ladder = 15 ftx = lcosϴAt the…

Q: A conical reservoir is losing water at the rate of 12 cubic feet per minute. If the radius is % the…

A: Let the height of the conical reservoir be h. Then the radius will be = h/4 Therefore we get the…

Q: A Ferris wheel with a radius of 13m is rotating at a rate of one revolution every 2 minutes. How…

A: Given thatRadius of the Ferris wheel is 13 mThe time period of the Ferries wheel is 2 min To find…

Q: A ladder 20 feet long is leaning against an embankment inclined 60 degrees to the horizontal. if the…

A: The ladder is leaning against an embankment inclined 60 degrees to the horizontal has length 20…

Q: ow fast is the radius changing when the diameter of the balloon is 50 cm?

A: Given: A spherical balloon is inflated at a rate of 1000 cm3 /sec . Diameter of the balloon = 50 cm

Q: A radar-tracking dish located 2400 meters from the base of a spaceship's launching pad is always…

A: Find your answer below

Q: A cone with an altitude of 50 cm has its base radius changing at the rate of one millimeter per…

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Q: What constant acceleration is required to increase the speedof a car from 30 mih to 50 mih in 5 s?

A: Given: u=30 mihour, v=50 mihour, t=5 second for finding acceleration, first we convert given…

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 13-ft ladder is leaning against a house when itsbase starts to slide away. By the time thebase is…

A: If a ladder is leaning against a wall and when its base starts to slide away it makes a triangle…

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 100ft  above the ground moves horizontally at a speed of 8ft/s  At what rate is the angle…

A: Let x= horizontal distance L= length of string,  Then a rough sketch of the problem is as follows:

Q: A 20-foot ladder is resting against a wall. The base is being pulled away from the wall at a rate of…

A:

Q: A water tank is in the form of a right circular cone with vertex down, 12 ft. deep and 6 feet across…

A: Given: height, h=12 ft., radius, r=62=3 ft., and dVdt=10 ft3/minTo find, The rate at which the water…

Q: A comet loses material when it gets close to the Sun at a rate of 100 cubic meters per minute.…

A: Given Comet is a sphere Its radius is 200 meters Let V be the volume of the comet then r be the…

Q: A man walks along a straight path at a speed of 4ft/s. A searchlight is located on the ground 30…

A: Given data is : dxdt=4 ft/sec To find the Rate of the searchlight is rotating

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

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Q: A conical cup is 4 cm across and 6 cm deep. Water leaks out of the bottom at the rate of 2 cm3 /sec.…

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Q: pouring

A: We will find the rate of change of height.

Q: A gas line-driven lawnmower has a blade that extends out 1 foot from its center. The tip of the…

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Q: A light is placed on the ground 30 ft from a building. A man 6 ft tall walks from the light toward…

A: This question is based on application of derivative.

Q: A ladder 20 ft long is leaning against an embankment inclined 60° to the horizontal. If the bottom…

A: Let x= distance of ladder from the embankment, y= vertical height. Given: dxdt=-1 ft/sec To find:…

Q: . A kite 100 ft above the ground moves horizontally at aspeed of 8 fts. At what rate is the angle…

A: At what rate is the angle between the stringand the horizontal decreasing when 200 ft of string has…

Q: A ladder 9 ft long rests agains a vertical wall. If the bottom of the ladder slides away from the…

A: Let the distance between base B of the wall and bottom of the ladder C, BC= x feet  And the angle…

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

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.