QuestiuI 3. A lighthouse is on a small island 3 km away from the nearest point P on a straight shoreline, and its light makes 4 revolutions per minute. At what rate is the beam of light moving along the shoreline when it is 1 km away from P?

Q: 3. A man 6 ft tall walks along a straight path away from a lamp post 15 ft high at the rate of 2…

A:

Q: (8) A baseball diamond has the shape of a square with sides of 75 feet long. A player running from…

A:

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

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

Q: 1. A 25 feet long ladder is leaning against a wall and sliding toward the floor. If the foot of the…

A:

Q: 1. A 17 feet ladder is leaning against a wall. If the bottom of the ladder is pulled along the…

A: Given : dx/dt = 5 y = 8 Now we find the dy/dt = ?

Q: A picture 40cm high is placed on a wall with its base 30cm above the level of the eye of an…

A: Shown below

Q: 20. A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the…

A: Given : A kite is 100 ft above the ground moves horizontally at a speed of  8 ft/s. To find : At…

Q: 7. A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base…

A:

Q: Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west…

A:

Q: the altitude of a triangle increases at a rate of 1 cm/min while its area increases at a rate of 3…

A:

Q: 2. A fighter plane 2,000 km away is spotted by a gunner in the ground. If it maintains its altitude…

A:

Q: 2. A ladder 10 meters long is leaning against a wall. If the bottom of the ladder is being pushed…

A: Given, A ladder 10 m long is leaning against a wall. Bottom of the ladder is being pushed…

Q: 19. A 6 foot ladder is sliding down a vertical wall at a rate of 1 foot per second. What is the rate…

A:

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

A: Consider the given information and draw the diagram: Let y be the length of the rope from the dock…

Q: a fisherman on a wharf 1.2 meters above the level of still water is pulling a rope tied to a boat at…

A: topic - application of derivatives

Q: 7. A 6ft tall human is walking away from a 20ft lamppost. Given that the length of the shadow of the…

A: Let the distance of the person from the bottom of the light post be x. Let the length of the shadow…

Q: A man 2 meters tall walks at a rate of 1.2 meters per second away from a light that is 5 meters…

A: dy/dt = rate of moving of tip of shadow dp/dt = rate of change in length of shadow

Q: 4. A man is walking beside a 30-m street lamp. After walking 25 m away from the street lamp, he sunk…

A: As per our guidelines we can solve only one question at a time. Please repost unsolved question…

Q: A metallic ball with a diameter of 12 cm is covered with a layer of ice, so if the ice begins to…

A:

Q: 9. A man 5 n tall is walking toward a building at the rate of 3 A/sec. If there is a light on the…

A:

Q: A man of height  1.9  meters walks away from a 5-meter lamppost at a speed of  2.1  m/s. Find the…

A: Let distance of the man from the pole=x   Let the length of the shadow =y…

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: Area of triangle= 12b hb= baseh=height

Q: The altitude of a triangle is increasing at a rate of 3 cm/min while the area of the triangle is…

A: Given that  The altitude of a triangle is increasing at a rate of 3 cm/min The area of the triangle…

Q: 2. A 15 foot ladder is resting against the wall. The bottom is initially 10 feet away from the wall…

A:

Q: 17. A man of height 1.8 m walks away from a 5-m lamppost at a speed of 1.2 m/s (Figure 9). Find the…

A:

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: Solution: Given that  A=160cm2 ,h=10cm and dA/dt= 2cm2/min  ,dh/dt=1cm/min

Q: A balloon is 30 meters above the ground when a car, running at 40 kph, passes directly below it. It…

A: Given,         A balloon is 30m above the ground when a car, running at 40kph passes directly below…

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

A:

Q: 1. Sand being dumped from a funnel forms a conical pile whose height is always one￾third the…

A:

Q: 19. A spot light is on the ground 6 meters away from a wall and a 1.8-meter tall person is walking…

A:

Q: A 25 ft ladder is leaning against a vertical wall. 25 ft At what rate (with respect to time) is the…

A:

Q: 2. A light shines on top of a lamppost 30 feet above the ground. A woman 5 feet tall walks away from…

A: Let X be the distance of man from lamppost .

Q: 5. A man 1.9 meters tall is walking away from 6,7-meter-tall lamp post at the rate of 170 cm/s. a.…

A:

Q: udent is walk

A: Here it is given that,  A student is walking towards the foot of a flagpole 20 meters high at the…

Q: C. Two cars start moving from the same point. One travels east at 55mi/h and the other travels south…

A: We use Pythagoras theorem

Q: At time t = 0, Car A passes through an intersection and goes east at a speed of 40 feet per second.…

A:

Q: 3) A camera is located on the ground 3000 ft from the spot where a rocket takes off. If the rocket…

A:

Q: 5. A 6-ft man walks away from a 15-ft lamppost at a speed of 3 ft/s. Find the rate at which his…

A:

Q: A weather balloon is rising vertically at the rate of 2 m/sec. An observer is standing on the ground…

A: The diagram of the given question will be as follows Given: dydt=2 m/s To find: dxdt

Q: A dock is 6 feet above water. Suppose you stand on the edge of the dock and pull a rope attached to…

A:

Q: 4. Water flowing in a conical tank 20 ft deep and 10 ft across the top at the rate of 15 cu. ft/…

A:

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A:

Q: 3. A woman walks along a straight path at a speed of 2 m/s. A light is located on the ground 100…

A: Consider the given: Let x be the distance from the man to the point on the path closet to the search…

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

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

A: The lighthouse is moving at 5 revolutions per minute, therefore: dθdt=5×2π1dθdt=10πrad/min A…

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: given that the area of a triangle(A)=140cm2 altitude(h)=20cm dh/dt=1cm/min dA/dt=2cm2/min let the…

Q: A lighthouse is on a small island 4 km from the nearest point P on a straight shoreline. Its beacon…

A: Given: lighthouse is situated on a small island 4 km from point P   number of revolutions= 1…

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: Topic = application of derivative

Q: 5. A ladder 20 ft long leans against a vertical building. If the top of the ladder slides down at a…

A: Given query is to find the speed at which bottom of the ladder is sliding.

Q: Ship A is 70 km west of ship B and is sailing south at the rate of 25 kph. Ship B is sailing north…

A: At t = 0 { initial position } , distance between ships.Let the distance between ship A and ship B be…

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.