1)A man 7 ft tall walks at a speed of 5 ft/sec toward a street lamp which is 15 ft above the ground. How fast is the length of the man's shadow decreasing?

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: Can the distance traveled by a particle ever be less than its displacement? When are they equal?

A: No, the magnitude of the displacement is always less than or equal to the distance traveled.

Q: A baseball is thrown straight downward with an initial speed of 40 ft/s from the top of the…

A: Let t be the time taken by the ball to reach the ground and the velocity of the ball is v. Now, the…

Q: A rod of length 2m is connected at its ends to perpendicular sliders so that moving one end also…

A: Let y m be the height of the slider and x m be the foot of the rod away from the slider. Then,  by…

Q: A researcher is interested in how frequently Starbucks coffee shops locate close to other coffee…

A: Given: n =  48.0x = 12.0 one third of Starbucks outlets are located in close proximity to another…

Q: In order to kill a bird 20m up in the air, a boy uses his catapult to shoot a pebble vertically…

A: given that  bird is at h=20m up in the air. a boy uses his catapult to shoot a pebble vertically…

Q: 2. A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

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Q: A train 220 m long is running with a speed of 59 kmph . In what time wil it pass a man who is…

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Q: Starting with a 60​-foot-long stone​ wall, a farmer would like to construct a rectangular enclosure…

A:

Q: The rectangular tank shown here, with its top atground level, is used to catch runoff water. Assume…

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Q: Starting with a 200-foot long stone wall, a farmer would like to construct a rectangular enclosure…

A:

Q: Starting with a 180-foot-long stone wall, a farmer would like to construct a rectangular enclosure…

A: topic - application of derivatives

Q: A straight wire 50cm long is bent into the shape of an L.  What is the shortest possible distance…

A: Suppose the wire bent into the shape of  L  be the right triangle ∆PQR with QR=x cm,  PQ=50-x cm By…

Q: 21. In basebalI, a batter stands 2 feet from home plate as a pitch is thrown with a velocity of 130…

A: Answer is mentioned below

Q: The rectangular tank shown here, with its top atground level, is used to catch runoff water. Assume…

A:

Q: pherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min. At…

A: The radius of the balloon decreases at the rate of =15 cm/min let radius of balloon =r then…

Q: Suppose a cyclist was using a 150-millimeter-diameter chainring and an80-millimeter- diameter…

A: Given: Let, dc  and rc denotes the diameter and radius of Chainring respectively and ds  and  rs…

Q: 13. A baseball is batted at a height of 1 m above the ground and reaches a maximu height of 33 m at…

A: Given that height=1m Maximum height=33m Horizontal distance=4m

Q: A flexible tube of length 4 m is bent into an L-shape. Where shouldthe bend be made to minimize the…

A: A flexible tube of length 4m is bent into an L-shape. Let x,y be the length of sides of L-shape.…

Q: A ball is thrown from a height of 6ft at an angle of 60 degrees with the horizontal. If the ball…

A: Initial Speed in horizontal directionux= v cos 600initial speed in vertical directionuy = v sin…

Q: Starting with a 160-foot-long stone wall, a farmer would like to construct a rectangular enclosure…

A:

Q: A snail slid 7 cm down a stalk and climbed 5 cm back up. Hlow far was the snail below its original…

A: Given : A snail moves 7 cm down then moves 5 cm up.

Q: What is the maximum area of a rectangle inscribed in a right triangle with legs of length 3 and 4 as…

A: Given: Formula used: The area of a rectangle is length * width.

Q: A 75 kg box is pushed off of a 120 m tall building with an initial horizontal speed of 15 m/s. How…

A: We have to first sketch the given situation.

Q: A ball returns two-thirds of its preceding height on each bounce.  If the ball is dropped…

A: Here, the ball is dropped from a height of 6 m., it will rebound to a height of 23rd of initial…

Q: = Boosi 28

A:

Q: A fence 20 feet tall runs parallel to a tall building at a distance of 5 f diagram

A: Given, a fence 20 feet tall runs parallel to a tall building at a distance of 5 it from the building…

Q: A simple pendulum, consisting of a mass of 8.237 kg, is attached to the end of a 2.68 m length of…

A: To calculate the speed of the mass (in m/s) at the bottom of the swing. Given that: Mass = 8.237 kg…

Q: When a rocket is 3 kilometers high, it is moving vertically upward at a speed of 400 kilometers per…

A: Let the height of the rocket be h and the angle of elevation from the observer’s eye is x.

Q: A man, 1.59 m tall is walking on a horizontal street at 2.5 kph away from a vertical street light,…

A:

Q: The ends of a trough, 8 ft in length, are isosceles triangles with height 2ft and base 4ft. Water is…

A: Rate of change

Q: Two cars start moving from the same point. One travelssouth at 60 mih and the other travels west at…

A:

Q: A rubber ball is made to fall from a height of 70 feet and is observed to rebound 3/4 of the…

A: The sum, S, of the infinite geometric series, a+ar+ar2+ar3+⋯ is defined as S=a1-r. Here a is 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: When a rocket is 3 kilometers high, it is moving vertically upward at a speed of 400 kilometers per…

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Q: a. How fast is the top of the ladder sliding down the wall when the base of the ladder is 12 feet…

A: It is given that the length of ladder is 13 foot which acts as the hypotenuse of the right angled…

Q: A car braked with a constant deceleration of 16 fts 2 , producing skid marks measuring 200 ft…

A: Given, deceleration a(t) = 16 ft/sec2. s(0) = 0 ft and s(T) = 200 ft and v(T) = 0. Where T is the…

Q: The volume of a cube is increasing at a rate of 64 in ³/sec. At what rate is the length of each edge…

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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…

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Q: The volume of a cube is increasing at a rate of 68 in3/sec. At what rate is the length of each edge…

A: Given Volume of cube increasing at a rate of 68 in3/ secTo the rate of change of length of each edge…

Q: A conical water tank with vertex down has a radius of 13 feet at the top and is 28 feet high. If…

A: Let V be the volume of the water and d be the depth of the water. Then, the volume is given by,…

Q: Starting with a 40-foot-long stone wall, a farmer would like to construct a rectangular enclosure by…

A: Length of the stone wall is 40 foot. Rectangular enclosure fencing is 280 feet after addition. The…

Q: A stone is dropped into a quiet lake and waves move in the form of circles at a speed of 4 cm/ sec.…

A: Please see the answer in Step 2.

Q: Suppose you filla conical paper cup with a height of 6" with water. If all the water is then poured…

A: Given, height of cone= 6 inches

Q: 2. A single-lane street 10ft wide goes through a semicircular tunnel with radius 9ft. How high is…

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Q: Suppose that you just completed a nonstop bicycle trip of 5.5 km. You know that each wheel of your…

A: Given Data: The distance covered by the bicycle is: d=5.5 km=5500 m The radius of the wheels of a…

Q: Find how fast the area of a triangle increases as the length of the base of the triangle increases…

A: