A lighthouse, L, is on an island 4 mi away from the closest point, P, on the beach. If the lighthouse light rotates clockwise at a constant rate of 19 revolutions/min, how fast (in mi/min) does the beam of light move across the beach 2 mi away from the closest point on the beach?

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

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: Each side of a square is 6 ft and is increasing at a rate of 2 ft per second. How fast is the area…

A: By differentiating equation of area of square with respect to time and substituting the value of…

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

A: To find: The rate at which the angle between the ladder and the ground  is changing

Q: Each side of a square is increasing at a rate of 6 cm/s. At what is the area of the square…

A: Given that, Area of square is  25cm2    Area A = x2 Where x is the side length. The area of square…

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

A:

Q: What constant acceleration is required to increase the speed of a car from 20 mi/h to 45 mi/h in 5…

A:

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: Two buses are driving along parallel freeways that are 5mi apart, one heading east and the other…

A:

Q: At noon Person A is 15 km east of person b. person A is walking west at 3km/h, and person b is…

A: initially A and B apart 15 km apart that  person A moves towards west at rate (da/dt) = 3 km/hr…

Q: A 7,453 newton car is initially at rest. How much force (in Newton) is required to move the car by…

A:

Q: A 17 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A: Given, length of ladder = 17 ft But given that ladder is leaning against a wall ⇒  the ladder and…

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: A 8,511 newton car is initially at rest. How much force (in Newton) is required to move the car by…

A: 2

Q: A lighthouse, L, is on an island 6 mi away from the closest point, P, on the beach. If the…

A:

Q: A kite 100 ft above the ground moves horizontally at aspeed of 8 ft/s. At what rate is the angle…

A:

Q: A lighthouse is located on a small island 3km away from the nearest point P on a straight shoreline…

A:

Q: 3. A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above…

A:

Q: A certain clock has an hour hand of length 4 in and a minute hand of length 5 in. In inches per…

A: Using law of cosines the distance between tips when the hands are at angle of θ is:…

Q: A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline…

A: Given a lighthouse which is located on a small island 3 km away from the nearest point P

Q: A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline…

A: Let y be the distance of lighthouse from nearest point on the shoreline and at time t, the beam…

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

A:

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

A:

Q: A lighthouse, L, is on an island 8 mi away from the closest point, P, on the beach. If the…

A: Given: A lighthouse rotates clockwise at a constant rate of 17 revolutions/min.

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

A:

Q: A 17 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A:

Q: 7. A revolving beacon is situated 3600 feet off a straight shore. If the beacon turns at 2…

A: Note: According to our expert guidelines only first individual question is to be answered kindly…

Q: A rope is attached to the bow of a sailboat coming in for the evening. Assume that the rope is drawn…

A: Given: The rope is drawn in over a pulley 5 feet higher than the bow at the rate of 2 feet per…

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

A: Diagram of the given question will be as following x is the distance of the man from pole y is the…

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 computerized spin balance machine rotates a 25-inch-diameter tire at 480 revolutions per minute.…

A:

Q: A man 6 feet tall walks at a rate of 3 feet per second away from a light that is 15 feet above the…

A:

Q: A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline…

A:

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: A man 6 feet tall walks at a rate of 7 feet per second away from a light that is 15 feet above the…

A: Let OA= height of light      CD= height of man      BC= length of shadow…

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: How fast is the tip of her shadow moving?

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: was an earthquake in South America with magnitude 4.3 that caused only minor damage. How many times…

A:

Q: An observer who is 3km from a launchpad watches a rocket that is rising vertically. At a certain…

A: Rate of change

Q: Each side of a square is increasing at a rate of 7 cm/s. At what rate is the area of the square…

A: If the area of a square, A, is x2 units , then the length of its side is x unit .

Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.  How fast does the tip of…

A: Given that, A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.

Q: On the planet Gzyx, a ball dropped from a height of 20 ft hits the ground in 2 s. If a ball is…

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 car braked with a constant deceleration of 16 ft/s2, producing skid marks measuring 50 ft before…

A:

Q: A revolving beacon is situated 3600 feet off a straight shore. If the beacon turns at 2 revolutions…

A:

Q: A lighthouse is located on a small island 3 km away fromthe nearest point P on a straight shoreline…

A:

Q: The base x of the right triangle in the figure increases at a rate of 6 cm/s, while the height remai

A: In this question we will use basic of calculus i.e application of differentiation. We will first…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.