A 25-ft ladder is leaning against a house when its base starts to side way. By the time the base is 24ft from the house, the base is moving away at the rate of 7ft/sec. (a) What is the rate of change of the height of the top of the ladder? (b) At what rate is the area of the traingle formed by the ladder, wall, and ground changing then? (c) At what rate is the angle between the ladder and the ground changing then?

Q: A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A: Length of ladder is l= 10ft X=8 ft, dx/dt= 18ft/sec From the fig l =[ x2 + y2 ]0.5= 10 a) from…

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

A: Given, A ladder 10 ft long rests against a vertical wall. Let x be the distance between the bottom…

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A: .

Q: A 10​-ftladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: A 13-foot ladder is leaning against a house when its base starts to slide away. By the time the…

A:

Q: Find the rate at which the surface area of the water changes when the water is 10 ft high if the…

A:

Q: 1. A 15-meter ladder is resting against a vertical wall. If the bottom of the ladder is being pushed…

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

Q: A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: A young Batman stands 30 ft. away from a hot air balloon that rests on the ground. He has tied a…

A: Let A be the base (horizontal distance between batman and balloon).Let B be the height of balloon…

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

A:

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…

A:

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A:

Q: 19. A 6 foot ladder is sliding down a vertical wall at a rate of 1 foot per second. What is the rate…

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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 small rocket is launched straight up in the air at a speed of 4ft/sec. A camera on the ground, 10…

A: Consider the given information. At any time t, rocket is at C tanθ=ACAB=AC10

Q: A balloon is rising vertically over a point A on the ground at the rate of 15 ft/sec. A point B on…

A: Let the distance of the balloon from point B be denoted as p. The balloon, points A and B form 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 kite flies at a constant height of 30 meters above the ground in a wind that blows it horizontally…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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

A:

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

A:

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

A: Let ladder AB, l=15 m, Ladder is pushed horizontally at the rate of 1.5 m/s, ⇒dydt=1.5 We need to…

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A: Area of square = a2 Where a is length of side of square.

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

A: Given: length of ladder, L=13 ft distance from base, x = 12 ft dxdt=5 ft/sec

Q: A ladder 3.9 m long is placed in a vertical plane which is at right angle to the vertical wall, the…

A: Given :                     The height of the ladder = 3.9m                     Let x…

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

A:

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: 2.) A ladder 5 feet long rests against a vertical wall. If the bottom of the ladder (on level…

A: A ladder is 5 feet long. The speed at which the ladder slides away from the wall is 1 foot per…

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…

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Q: If a ladder of length 20ft which is leaning against a vertical wall has its upper end sliding down…

A: Given : Length of the ladder = 20 ft

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Q: A conical cistern of height 5 ft and 7 ft across the top is being filled at a rate of 5 ft3/s while…

A: A conical cistern is given whose height is 5 ft and diameter at the top is 7 ft. A conical cistern…

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:

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A: Given A woman 5ft tall walks at a rate of 7ft/sec toward a street light that is 12ft above the…

Q: An airplane is flying on a horizontal path at the height of 3,800 feet. At what rate is the distance…

A: We need to find rate of distance changing.   ddθ(cscθ)=-csc(θ)cot(θ)

Q: A ladder 10 ft long leans against a vertical wall. If the bottomof the ladder slides away from the…

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

Q: Water is pouring into a conical vessel 15 cm deep and having a radius of 3.5 cm across the top. If…

A: Given the water is pouring into a conical vessel of 15 cm deep and the radius of 3.5 cm across the…

Q: A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

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A: Given length of the ladder  x=7 and  and base is moving at the rate of 72 ft/sec i.e.

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Q: g.) A ladder 14 ft long is leaning against a fence 8 ft high with the upper end projecting over the…

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.