3. A light at eye level stands 20 ft from a house and 15 ft from the path leading from the house to the street. A man walks along the path at 6 ft per sec. How fast does his shadow move along the wall when he is 5 ft from the house?

Q: A trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at…

A:

Q: 5. A kite 100 feet above the ground is being blown away from the person holding its string in a…

A: So, here x2+1002=s2...(1) Given dxdt=10 Now, at s=200, from (1):…

Q: (b) If its' owner uses 3 pipes of radius 4cm, with water flowing at a rate of 30cm/s, how long will…

A: (a) Area of circuler face= pi*r2  =pi*102 = 314 cm2.                    (pi=3.14)

Q: Assuming your car can slow at a constant rate of 15 ft/sec2, how much distance will your car cover…

A:

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 kite is 40 ft. high with 50 ft. of cord out. If the kite moves horizontally at 5 mi. per hr.…

A: Draw the position of kite as shown below.

Q: 1. A ladder 8 m long is leaning against a wall. If the bottom of the ladder is pulled horizontally…

A: We will draw figure and use differentiation  to find rate of change . Note . Only one question…

Q: At what rate is water pouring into a rectangular bathtub with base 65 fť if the water level rises at…

A: According to the given information it is required to calculate the rate at which water is pouring…

Q: A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks toward the pole with a…

A:

Q: Car A is traveling west at 50 mi/h and Car B is traveling north at 60 mi/h. Both are headed for the…

A: In first question we find out dz/dt .and in 2nd question first we put dy/dx=0 for extreme values.and…

Q: A boat is being pulled with a rope towards a dock that is 10 ft above the water, as shown in the…

A: Let the distance of the boat= x ft y=length of the rope.  So,  given that dy/dt= 1.5 ft/min We have…

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

A: In the figure, x is the distance of pole from the man at the ground level. s is the length of the…

Q: A rope is attached to a boat at water level, and a man on the dock is pulling on the d) rope at the…

A: Draw a schematic diagram of given figure.

Q: A lamp post 3 m high is 6 m from a wall. A man 2 m tall is walking directly from the post toward the…

A:

Q: A train, starting at noon, travels north at 40 ml per hr. Another train, starting from the same…

A:

Q: A man 6 ft tall walks along a level sidewalk away from a lamppost. On the post is a street light 18…

A:

Q: 9. A man 6 ft tall walks away from a lamp post 16 ft high at the rate of 5 mi/hr. How fast does the…

A:

Q: A person stands at the end of a pier 8 ft above the water and pulls in a rope attached to a buoy. If…

A:

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

A: Given  Height of the man =6ft  A street light is mounted at the top of a 15-ft-tall pole Let the…

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

A:

Q: 17. A boat is being pulled toward a dock as shown in the figure. If the rope is being pulled in at 3…

A: Follow the procedure given below.

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 trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at…

A: We have to find how fast is the water level rising when the water is 6 inches deep.

Q: 4. A basketball player is 7 feet tall walking away from a light that is 28 feet above the ground at…

A:

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

A: Please refer the attached image for complete solution. THANK YOU !

Q: You watch at a horizontal distance of 40 ft as a hot air balloon rises straight in the air at 10…

A:

Q: A light hangs 15ft above a horizontal path and a man 6ft tall is walking away at 5 ft/sec. i) How…

A: Given problem:- A light hangs 15ft above a horizontal path and a man 6ft tall is walking away at 5…

Q: A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away from her at…

A: Given A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away from…

Q: 2. A steel girder 27 feet long is to be moved on rollers along a passageway 8 feet in width and into…

A: Given: A steel girder 27 feet long is to be moved on rollers along a passageway 8 feet in width and…

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: We sketch the situation roughly  Let us assume x=the distance of the boat from the dock y=the…

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 ladder 7 m long is leaning against a wall. If the bottom of the ladder is pushed horizontally…

A:

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

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

Q: A baseball diamond has the shape of a square with sides 90 ft long, as shown. A player is running…

A: A baseball diamond has the shape of a square with sides 90 feet long. A player running from second…

Q: A trough is 12 ft long and its ends have the shape of isosceles triangles that are 2 ft across at…

A: Given data:   The length of the trough is L=12 ft. The side of the isosceles triangle is b=2 ft. The…

Q: At noon,ship a is 130 km west of ship b.Ship a is sailing east at 25 km/h and ship b is sailing…

A:

Q: 4. A steel girder 27 ft long is to be moved on rollers along a passageway 8 ft in width and into a…

A:

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 boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: The dock is 1m higher than the bow of the boat. Pulled rate of the rope of 1.4m/s To calculate the…

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

A:

Q: A trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at…

A:

Q: 29. A kite 100 feet above the ground is being blown away from the person holding its string. It…

A: Solution Let initially  kite was at position A while person holding Kite was at position O such that…

Q: A trough is 14 ft long and its ends have the shape of isosceles triangles that are 2 ft across at…

A: It is required to find the rate at which water level is rising in the given trough whose sides are…

Q: 5. must the ball be launched to land 450 ft from the base of the building? A golf ball is hit in a…

A:

Q: You are videotaping a race from a stand 132 ft from the track, following a car that is moving at 180…

A: To  Determine: How fast will your camera angle u be changing when the car is right in front of you?…

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

A:

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

A:

Q: A kite is 30 ft. high and is moving horizontally at a rate of 10 ft./min. At what rate is the string…

A: Calculate the rate in the following way:-

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

A:

Q: A streetlight is at the top of a 10 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A: