A ladder 10 feet long is leaning against a wall, with the foot of the ladder 8 feet away from the wall. If the foot of the ladder is being pulled away from the wall at 3 feet per second, how fast is the top of the ladder sliding down the wall?

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

A:

Q: A red truck moving 100 km/h overtakes a 1.5 km long train moving in the same direction on a track…

A:

Q: A cross-country runner jogs at a rate of 15 feet per second. If she runs 300 feet from A to B, 450…

A: Speed of the runner is 15 feet per second. Total distance travelled is, Distance from A to…

Q: An airliner passes over an airport at noon traveling 520 mi/hr due east. At 1:00 p.m., another…

A: Given: An airliner passes over an airport at noon traveling 520 mi/hr due east. At 1:00 p.m.,…

Q: A rabbit is traveling at a pace of 250 meters per hour. How fast is the rabbit  traveling in…

A: Given:    Distance = 250 meter per hour

Q: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

A: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

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: The current in a typical Mississippi River shipping route flows at a rate of 4 mph. In order for a…

A: Let the speed of barge in still water be x miles per hour. Given the speed of river is 4 miles per…

Q: An airliner passes over an airport at noon traveling 510 mi / hr due east. At 1:00 p.m., another…

A:

Q: A plane is flying at a constant altitude of 1 mile and a speed of 400 mph toward an observer on the…

A: The plane is flying at a constant altitude of 1 mile. Let x be the horizontal distance and y be the…

Q: A 13-foot ladder is placed against a wall. If the top of the ladder is sliding down the wall at 3…

A:

Q: The top of a ladder 30 meters long leans against a vertical wall, and the lower end rests on a level…

A: Let the height of wall corresponding to the ladder lean at any instant be denoted as h. Let the…

Q: Two cars that started at the same point are driving away from each other. The first car is driving…

A: Given,          Two cars that started at the same point are driving away from each other. The first…

Q: It takes an ant farm 3 days to consume of an apple. At that rate, in how many days will the ant farm…

A: An ant farm takes 3 days to consume ½ of an apple. → An ant farm consume ½ of an apple in 3 days

Q: A ship moving 8 mph sails north for 30 minutes then turns east. If a searchlight at the point of…

A:

Q: An aircraft is flying horizontally at a speed of 600 km/h. How fast is the distance between the…

A:

Q: The White River flows at a rate of 4 km/h. In order for a boat to travel 76.8 km upriver and then…

A: Let x be the speed of water still in water. Then, Upstream speed is x-4 and downstream speed is x+4.…

Q: A man 6 feet tall walks at a rate of 5 feet per second away from the light that is 15 feet above the…

A: Consider the given:

Q: A light hangs 15 feet directly above a straight walk on which a man 6 feet tall is walking. How fast…

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Q: An airplane at an altitude of 35,000 feet begins descending at a rate of 2,000 feet per minute. How…

A:

Q: A spotlight on the ground shines on a wall of a building 20 feet away. If a man 6ft tall walks from…

A:

Q: The top of a 22 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate…

A:

Q: Two boats leave a dock at the same time. One boat travels south at 30 mi>hr and the other travels…

A: Find the rate of change the distance between the boats.

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: A ball is dropped from the top of a building 400 ft high.How long does it take to reach the ground?…

A:

Q: An automobile uses gasoline at a rate of 12 kilometres per litre and has a 65 litre tank. How far…

A:

Q: A jet plane traveling at 600 mph overtakes a propeller-driven plane which has had a 2 hour head…

A:

Q: A plane is flying at a constant altitude of 1 mile and a speed of 400 mph toward an observer on the…

A:

Q: The length of a rectangle is increasing at the rate of 2 feet per second, while the width is…

A: Let length = x feet and width = y feet  Given that dx/dt= 2 and dy/dt= 1

Q: The base of a 13 foot ladder that is leaning against a wall begins to slide away from the wa When…

A: It is given that, length of the ladder x = 13 feet,  The distance between the foot of the ladder and…

Q: A van is 5km due north of a bus at 2:00PM. If the van is traveling northward at the rate of 60 kph…

A:

Q: There are 100 bacteria cells in a dish now, but in 5 hours there will be 147 cells. At what rate do…

A: There are 100 bacteria at initial time t=0. In 5 hours that is when t=5, there will be 147 cells. In…

Q: A girl starting at 11 A.M., travels east at 4 km/hr while a boy, starting at noon from the same…

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Q: A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are…

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Q: Two cars start moving from the same point. One travels south at 64 mi/h and the other travels west…

A:

Q: Two cyclists, 90 mi apart, start riding toward each other at the same time. One cycles twice as fast…

A: Given that, the distance between two cyclists is 90 mi, and one cycles twice as fast as the other…

Q: Two railroad tracts are perpendicular with each other. At 12:00PM, there is a train on each track…

A:

Q: Two cars start moving from the same point. One travels south at 64 mi/h and the other travels west…

A:

Q: A jet plane traveling at 570 mph overtakes a propeller-driven plane that has had a 2 h head start.…

A: Let x miles from the starting point does the jet overtake the propeller-driven plane.  We will use…

Q: A boat moves at a rate of 13 mph in still water. If the river's current flows at a rate of 3mph, how…

A: given that: A boat moves at a rate of 13 mph in still water. the river's current flows at a rate of…

Q: A worker bee flies of a mile in of an hour. At this rate, how far can the bee fly in 1 hour?

A: given that a worker bee flies 58 of a mile in 116  of an hour find out how far the bee can fly in an…

Q: The radius of the tires of a car is 18 inches, and they are revolving at the rate of 673 revolutions…

A: To find the circumference of the tyre.

Q: The top of a 18 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate…

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Q: A man 6 ft. tall is walking towards a building at the rate of 4 ft./sec. If there is a light on the…

A:

Q: How much work is done lifting a 20-pound object from the ground to the top of a 50-foot building if…

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Q: A man, running 3 meters per second in an open field, runs east for 30 seconds, then turns north.  If…

A: Since the man ran 3m/s east for 90 sec so he is 90 m from the searchlight. Consider the diagram…

Q: Two cars start moving from the same point. One travels south at 56 mi/h and the other travels west…

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Q: A life raft, set adrift from a sinking ship 150 miles offshore, travels directly toward a Coast…

A: Time , distance and speed is related using a formula time=distancespeed .At the same time , both the…

Q: A man flies a small airplane from Fargo to Bismarck, North Dakota- a distance of 180 mi. Because he…

A:

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.