14. A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 6 ft above the bow. The rope is hauled in at the rate of 3 ft/sec. Complete parts (a) and (b) a. How fast is the boat approaching the dock when 10 ft of rope are out? ft/sec (Type an integer or a simplified fraction.) b. At what rate is the angle 0 changing at this instant? rad/sec (Type an integer or a simplified fraction.)

Q: 3. A woman in a hot air balloon drops her GoPro Hero 10 when the balloon is 175 ft above the ground…

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 helicopter takes o from a point 80 m away from an observerlocated on the ground, and rises…

A: Thus when the helicopter is 60 m above the ground the elevation angle of theobserver’s line of sight…

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

A:

Q: 01/Water poured into a conical tank through a faucet, this tank has a base radius of 5 ft and 10 ft…

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 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: Can you help me step by step?

A: Given,

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: 8. The radius of an inflating balloon in the shape of a sphere is changing at a rate of 3cm/sec. At…

A:

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

A:

Q: Can i get help with this problem step by step

A: The surface area of the cube, S = 6x2 The volume of the cube, V = x3 We have given dS/dt = 72.

Q: 4.A ladder 10ft. long is resting against the side of a building if the foot of the ladder slips away…

A: This question is based on application of Derivative.

Q: How fast is the bicycle traveling in miles per​ hour? (Hint: 5280 ft=1 mi)

A:

Q: 8. The minute hand on a watch is 4 cm long and the hour hand is 3 cm long. How fast is the distance…

A: Distance between the tips are

Q: 20. If a point R on the unit circle moves along the circle at the rate of 1 unit per second, then…

A: Given: A point R on the unit circle moves along the circle at the rate of 1 unit per second. To find…

Q: ross the top is being filled at a rate of 5 ft3/s while it was leaking by 1% of the rate it is being…

A: The height of the conical cistern ,H=5ft. The radius of the conical cistern ,R=3.5ft. The rate at…

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

A:

Q: 01/ Water poured into a conical tank through a faucet, this tank has a base radius of 5 ft and 10 ft…

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

Q: Can you help me step by step?

A: The given situation can be picturized as follows.

Q: 8. A street light hangs 24 ft. above the sidewalk. If a man 6 ft. tall walks away from the light at…

A: We can find the required as answer as below.

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

A: Consider the given information:

Q: A light is on the top of a 12 ft tall pole and a 5 ft 6 in tall person is waking away from the pole…

A: Given that:Height of the poll is 12 ft and height of the person is 5 ft 6 in or 5.5 ft.Let x and y…

Q: The radius of a circle is increasing at a constant rate of 0.2 meters per second. What is the rate…

A: At the instant when the perimeter of the circle is 20π, then p=2πr20π=2πrr=10 m

Q: and passes directly over a tracking telescope on the ground. When the angle of elevation is ?/4,…

A:

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

A:

Q: 5. A 15ft ladder is leaning against a brick wall. If the base of the ladder is being pulled from the…

A:

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

A:

Q: 17. A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the…

A: Concept of similarity along with derivative is used.q

Q: 27. A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is…

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: 2. The wheels on a racing bicycle have a radius of 10 inches. How fast is the cyclist traveling in…

A:

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

A:

Q: 12. A baseball player is running from the second based to the third base at 20 ft./s. At what rate…

A:

Q: 9. A balloon, leaving the ground 60 ft. from the observer, rises 10 ft. per sec. How fast is the…

A: 9- Given- The ballon leaving the ground 60ft. from the observer rises 10 feet per second. To find-…

Q: 14. As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the…

A: We have to find the rate at which the sand is leaking out when the height is 10 in.  Or we can say…

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: A conical vessel 12 cm deep and with a radius of 6 cm at the top, is being filled with water. If the…

A: Let's find.

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

A:

Q: 1) a car is slowing down at the rate 0.8 ft /sec², How the will the can move before it stops if its…

A:

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

A:

Q: 1. Two sides of a triangle are 15 and 20 ft long, respectively. a) How fast is the third side…

A:

Q: 11. A snowball melts so that its surface area decreases at a rate of 0.5 cm²/min. Find the rate at…

A: Here we use the concept of derivatives.