1) When oil was spilled out in the middle of a lake, it spread out on the surface of the water in a circular pattern. The radius of the circular pattern increased at a rate of 6 feet per minute. ( ?(?) = 6? ??/??? ) A. How fast was the area of the circular pattern increasing per minute? Construct the composite function to show how the area was increasing each minute. ( ?(?) = ??2 ??2/??? ). B. Find the radius of the circular pattern of oil 90 seconds after the oil starts to spread. C. Find the area of the circular pattern of oil 3 minutes after the oil starts to spread

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: A 17-foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away…

A: We have to find the rate at which  ladder is sliding down.

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.03 cm/ min.…

A:

Q: The height of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is…

A:

Q: A man starts walking north at 2 feet per second from a point P. A minute later a woman starts…

A:

Q: In an isosceles right triangle, the hypotenuse is increasing at a rate of 0.1 ft/s. When the area of…

A:

Q: 2. A boat is pulled into a dock by a rope with one end attached to the front of the boat and the…

A: Consider the figure given below, A is the front end of the boat, B is the location of the dock, and…

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

A:

Q: 1. A spotlight on the ground shines on a wall 12 meters away. If a person 2 meters tall walks from…

A: Given: A spotlight on the ground shines on a wall 12 meters away. A person 2 meters tall walks from…

Q: 7. A 6-ft tall man is walking away from a 15-ft tall street lamp at the rate of 5 ft/sec. How fast…

A: Given : A 6 ft tall man and a 15 ft tall street lamp and rate is 5 ft/sec

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

A:

Q: The radius of the circle is increasing at a rate of 1 meter per hour and the sides of the square are…

A: Solution is here

Q: 2. A boat is being pulled into a dock by a rope attached to it and passing through a pulley on the…

A:

Q: A 10-foot ladder is standing vertically against the side of a building. To show you a related rates…

A: We can solve as follows

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

A: Let h be the altitude, b be the base and A be the area of the triangle at any time t. Given that,…

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

A:

Q: a) When a gold plate is heated in order to melt it, initially its area increases at the rate of 67…

A:

Q: 4. A spotlight is on the ground 20 feet away from a wall and a 6-ft tall person is walking towards…

A: Spot light and the wall is at the distance 20 ft.  Person height is 6 ft. He is walking towards the…

Q: The radius of a circle is increasing at the rate of 0.7 cm/s.whats is the rate of increase of its…

A:

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

A: Let the base of triangle be denoted by b Let the altitude be denoted by a  So, area of triangle…

Q: A plane flies horizontally at an altitude of 4 km and passes directly over a tracking telescope on…

A: Given: A plane flies horizontally at an altitude of 4 km and passes directly over a tracking…

Q: A 50-ft ladder is placed against a large building. The base of the ladder is resting on an oil…

A:

Q: 2. A 16-foot ladder rests against a vertical wall. The bottom of the ladder begins sliding at a rate…

A:

Q: (1 point) A stone dropped into a still pond sends out a circular ripple whose radius increases at a…

A:

Q: The radius of a circle is increasing at the rate of 0.7 cm/sec.what is the rate of increase of its…

A: The radius of a circle is increasing at the rate drdt= 0.7 cm/sec r = radius of the circle

Q: 2) A person is standing 350 feet away from a model rocket that is fired straight up into the air at…

A:

Q: The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the…

A: Given that , h=48 inch r1=3 feet , r2=5 feet find average rate of change in volume.

Q: The area of a circle increases at a rate of 4 cm2 / s. a. How fast is the radius changing when the…

A: I have given an answer in step 2.

Q: Suppose that a 12 feet long ladder is leaning against a vertical wall of a house. If the top end of…

A: Given:   Adj (x) = 10 feet    Hyp = 12 feet  dy/dt = 2

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

A:

Q: 1. The area of a triangle is increasing at a rate of 2 as the altitude increases at a rate of 1. How…

A:

Q: 8. A 25-ft ladder is placed against a building resting on a banana peel. The base of the ladder is…

A:

Q: A ladder 13 ft long is leaning against a wall. The bottom of the ladder is being pulled away from…

A:

Q: In a right triangle the hypotenuse is increasing at a rate of 0.1 ft/s. When the area of the…

A:

Q: Suppose we know that the radius of a circle is increasing at a rate of 8 feet each second (Fig. 1),…

A:

Q: A boat is being pulled toward a dock as shown in the figure to the right. If the rope is being…

A:

Q: 1. Two airplanes left airports which are 960 km apart and flew towards each other. One plane flew 32…

A: This is a question of distance and velocity. Based on the general formula of distance and velocity…

Q: A rod is sliding down the side of a wall such that the height is decreasing at a rate of 5 inches…

A:

Q: 1. A man is standing on a horizontal ground 30 ft away from a hot air balloon. After a moment, the…

A:

Q: he measure of the angle subtended at

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

Q: (6) A person 2 meters tall walks directly away from a streetlight that is 8 meters above the ground.…

A: At first we draw the diagram  AC  is the street light, DE is the person. Let distance between…

Q: The altitude of a triangle is increasing at a rate of 1 cmminwhile the area of the triangle is…

A: Givendhdt=1cm/mindAdt=2cm2/minA=100cm2h=10cm

Q: A 10-foot ladder is standing vertically against the side of a building. To show you a related rates…

A:

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.05 cm /…

A: Area =πr² Find dA/dt when r=56 cm

Q: 5. A stone dropped in a pond sends out a circular ripple whose radius in- creases at a constant rate…

A:

Q: The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the…

A:

Q: A triangle's base is increasing at the rate of 2 inches/sec, its height at 5 inches/sec. At what…

A: Increasing rate of base, dbdt=2 inches/sec. Increasing rate of height, dhdt=5 inches/sec. Area of…

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

A: Let altitude = h  Area= A Base=B Given dh/dt= 1 , dA/dt=2  We have to find dB/dt at h=10 and A=110…

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

A: Given that the altitude of a triangle is increasing at a rate of 3 centimeter/ mimute.⇒dhdt=3…

Q: A 25-foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away…

A: topic - application of derivatives