. A 13-ft ladder is leaning against a house when its base is 12 ft from the house, the base is moving at the rate of 5 fi sec. (a) How fast is the top of the ladder sliding down the wall then? (b) How fast is the area of the triangle formed 13- ladder by the ladder, wall and the ground changing then? (c) At what rate is the angle e 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…

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

A: Given that, the length of the ladder is 10 ft and distance between the wall and ladder in base is 6…

Q: O. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

A:

Q: A kite is flying at a height of 40 ft. A boy is flying it so that it is moving horizontally at a…

A: Given: Kite is moving horizontally at a rate of 3 ft per sec. To determine: The rate at which the…

Q: 8.A kite at an altitude of 200 ft. moves horizontally at the rate of 20 ft/sec. At what rate is the…

A: We have to find the rate of change of angle.

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

A: .

Q: A 6 ƒt tall Batman runs (into the night) away from a 10 ft streetlamp at a rate of 1 How fast is his…

A: The diagram of the situation is shown below:

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

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

A:

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

A: Given : A kite is 100 ft above the ground moves horizontally at a speed of  8 ft/s. To find : At…

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

A:

Q: 4. A 13-ft ladder is leaning against a house when its base is 12 ft from the house, the base is…

A: To find the solutions of given statements

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

A:

Q: 11. A ladder is leaning against a wall when its base begins to slide along the floor, away from the…

A: Let the length of the ladder is L which is a fixed length. let the length of the base is y. and the…

Q: A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point.…

A:

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 10ft. long is resting against the side of a building if the foot of the ladder slips away…

A: Solved below

Q: Two sides of a triangle are 15 and 20 ft long, respectively. a) How fast is the third side…

A: Given: Two sides of triangle are 15ft and 20ft. We use cosine rule         C=a2+b2-2abcosθ     where…

Q: A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off…

A:

Q: 9. A ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides away from…

A:

Q: A large conical tank of height H being filled with water by a hose at the top of the tank at a rate…

A: given: A large conical tank of height H=9 feet and radius R=3 feet is being filled with water by a…

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

A:

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

A:

Q: A hot air balloon rising vertically is tracked by an observer located 5 km from the lift-off point.…

A: Given: x=5 km θ=π5 raddθdt=0.3 rad/min The person and the hot air balloon form a right triangle,…

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 13 m long leans against a wall. The foot of the ladder is parallel along the ground away…

A:

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

A:

Q: A spherical balloon is being inflated at a rate of 9(pi)cm^3/sec. At what rate is its radius…

A:

Q: (2) In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all…

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 hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A: Given that a hot air balloon is rising vertically is tracked by an observer located 7km from the…

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

A:

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

A:

Q: 10. A ladder 13 ft. long leans against a vertical wall. If the top slides down at 1.5 ft. per sec.,…

A: Definition used-         In a right angle triangle -…

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:

Q: 2) In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all…

A: Solution

Q: (a) A 5-ft ladder is leaning against a house when the base starts to slide away. by the time the…

A: First we use Pythagoras theorem and then we calculate dA/dt and solve it .

Q: 2. A tank of water in the shape of a square pyramid is leaking water at a constant rate of 4…

A:

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

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.