A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 6 ft ftom the house, the base is moving away at the rate of 16 ft/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 triangle 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 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: b. find Find the rate of the volume of a sphere with respect to its diameter D when the diameter is…

A:

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

A: .

Q: A baseball diamond is a square with sides of 90 feet. Home Base 90 ft 90 ft. 1st Base 3rd Base 90…

A: Given that  a baseball diamond is a square with side of 90 feet. A batter at home base hits the ball…

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: 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 Conical Cup is 4cm across and 6cm deel. Water leaks cut of the bottom of the cup cit a rate of…

A: Consider the given information. The diameter of the cup is 4 cm. r=d2=42=2 cm The height is 6 cm.…

Q: A 13 ft ladder is leaning against a house. The ladder slides down the wall at a rate of 3ft/min. a)…

A: We have to use differentiation to solve the problem

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

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 conical tank with an upper radius of 4 m and a height of 5 m drains into a cylindrical tank with a…

A:

Q: The Cleveland City Cable Railway had a 14-foot-diameter pulley to drive the cable. In order to keep…

A:

Q: A baseball diamond is a square with sides of 90 feet. Home Base 90 ft. 90 ft. Ist Base 3rd Base 90…

A: Let us assume that, the position of the batter is B.  3rd base = A Home base = O OB=x AB=y Halfway…

Q: 1. A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the…

A:

Q: If the rate of change of the side length of an equilateral triangle is 2br / sec, what is the rate…

A: Please rate and feel free to ask any query about any part of the question.  I have used applications…

Q: a) Water runs into a conical tank at the rate of 9 ft^3/min. The tank stands point down & has a…

A: Since multiple questions are asked, we will solve the first question for you. To get the solutions…

Q: A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward…

A:

Q: The clepsydra, or water clock, was a device that the ancient Egyptians, Greeks, Romans, and Chinese…

A: The water dripping out of the cylindrical container is modelled by a differential equation.…

Q: An object is launched at an angle of 50 degrees from the horizon at an initial velocity of 500 ft…

A: Given data: Formula used :

Q: A ladder 13 feet long is leaning against the wall. If the base of the ladder is pushed toward the…

A:

Q: On a day  when the wind is blowing toward the south at 3 m/s, a runner jogs west at 1.9 m/s.what is…

A: Let V1 be the velocity of the air and V2 be the velocity of the runner, then the relative velocity…

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

A:

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

A:

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

A: Rate of change

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

A: Let x be the distance between the base of the wall and the bottom of the ladder. And let θ be the…

Q: A shot putter threw an 8 Ib 13 oz shot 62 ft, 2 in. Assuming the shot putter launched the shot at a…

A: answer is in next step

Q: Find the rate of change of area of the circle with respect to its radius, in ft2/ft, when the radius…

A: We have to find the rate of change of area of the circle with respect to its radius in ft2/ft. Also…

Q: A winch is on top of a pole that is 25 ft high and it is using a rope to pull object A. The rope is…

A: Let the distance of the object from the wall is x. the length of the rope is L and the length of the…

Q: . A 13-ft ladder is leaning against a house when its base is 12 ft from the house, the base is…

A:

Q: A street light is at the top of a 29 ft pole. A 6 ft tall girl walks along a straight path away from…

A:

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

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

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

A: Consider h is the height, and b is the base, ladder's length be 'L' apply the Pythagoras theorem,…

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

A: Using triangle find angle then find the rate of change of angle

Q: The radius of a sphere increases at a rate of 4m/sec. Find the rate at which the surface area…

A: Surface area of sphere is S= 4πr^2. And rate of change means derivatives.

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

A:

Q: 15. Water is being poured at the rate of 150 cm³/s into an inverted cone with a diameter of 3 meters…

A:

Q: A street light is at the top of a 20 ft pole. A 5 ft tall girl walks along a straight path away from…

A:

Q: A kite, 120 ft above the ground, is moving horizontally at a rate of 10 ft/sec. At what rate is the…

A:

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A:

Q: A 15 feet long ladder is leaning against the wall. The bottom of the ladder is sliding away from the…

A:

Q: A street light is at the top of a 26 ft pole. A 5 ft tall girl walks along a straight path away from…

A: Given:

Q: The volume V=r° of a spherical balloon changes with the radius. a. At what rate (ft°/ft) does the…

A: Consider the given equation: V=43πr3 Where V is the volume and r is the radius. Differentiating the…

Q: A 13-ft ladder is leaning against a house when its base starts to slide away (see accompanying…

A: Let the distance of the base from the wall is x ftAnd the top of the ladder is y ft high. Then x and…

Q: 1. A 13-ft ladder is leaning against a house when its base is being pushed towards the wall. By the…

A:

Q: 2. A woman standing on a cliff is watching a motor boat through a telescope as the boat approaches…

A:

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.