The altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/minute while the area of the triangle is increasing at a rate of 2.5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 8.5 centimetres and the area is 81 square centimetres?

Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

A: Given  Speed of first car =48 mi/h towards south Speed of second car =20 mi/h towards west

Q: As illustrated in the figure, a car is traveling along one road, away from the intersection, at 10…

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

A:

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

A:

Q: A ladder 25 feet is leaning against a wall. If the foot of the ladder is being pulled away from the…

A: To determine the rate at which the ladder is sliding. Given: Ladder is 25 feet long dx/dt = 14…

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: A man 6 feet tall walks at a rate of 4 feet per second away from a light that is 15 feet above the…

A: Please see the explanation below

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

A: Let height of triangle = h Base = b Then, we are given that:

Q: A 5-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away…

A: To find the rate of change of area of the triangle formed .

Q: A car accelerates constantly from speed 0 m/s to 60 m/s in 30 seconds, remains at this speed for 20…

A: First step is to write down all the data that we have.

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

A: Here we use the formula of area of triangle. First we differentiate area with respect to time and…

Q: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

A: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

Q: Two cars start moving from the same point. One travels south at 32 mi/h and the other travels west…

A:

Q: Each side of a square is increasing at a rate of 5 cm/s. At what rate is the area of the square…

A: Let,

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: 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: If the volume of a different sphere is increasing at a rate of 24 cubic inches per minutes and the…

A:

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

A:

Q: If one earthquake has a magnitude of 5 on the Richter scale and a second earthquake has a magnitude…

A: We have to determine the relationship between the intensities of the two earthquakes .

Q: The height of a triangle is increasing at a rate of 4 cm/s while the area of the triangle is…

A: Let the height, base and area of a triangle be 'h', 'b' and 'A' Given, dhdt=4 cm/sdAdt=56 cm2/s

Q: The pressure exerted by a certain Iiquid at 0 given point varies directly as the depth of the point…

A: Given pressure of liquid at a point is directly proportional to the depth of the surface at the…

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: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A: Given that increasing altitude of the triangle dh=2cm/min The increasing area of the triangle dA =…

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: The altitude (or height) of a triangle is increasing at a rate of 2.5cm/min while the area of the…

A: It is known that, the area of the triangle with the base b and altitude a is

Q: Two airplanes are flying in the air at the same height. Airplane A is flying east at 494 mi/h and…

A: Point A represents position of airplane A. Point B represents position of airplane B.Point C…

Q: At what rate is the distance between Jack and Jill changing if Jack is 3 miles from the bakery and…

A: Given:         To determine:

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

A:

Q: The radius r of a sphere is increasing at a rate of 4 inches per minute.

A:

Q: The fixed sides of an isosceles triangle are of length 6 cm. (See the figure.) If the sides slide…

A: Given: The fixed sides of an isosceles triangle are of length 6 cm and the sides slide outward at a…

Q: The length of the horizontal leg of a right triangle is increasing at a rate of 3 ft/sec, and the…

A: Given A right triangle  horizontal leg = 7ft vertical leg = 1ft

Q: If the base h of a triangle is increasing at a rate of 3 inches per minute while its height h is…

A: Area of a triangle of base b and height h is given as, A=12bh The derivative of area with respect to…

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

A:

Q: A cup of coffee cools at rate proportional to the difference between the constant room temperature…

A:

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: 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 duck is 6 feet north and 8 feet east of a buoy. He is swimming due east at a rate of 3ft/sec. How…

A: Consider the value of x=3ft/sec. A duck is 6 feet north and 8 feet east of a boy. We have to find…

Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A: Formula of area of triangle 12bhWhere b is the base and h is the altitude Chain rule (uv)'= u'v+uv'

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

A:

Q: The height of a triangle is increasing at a rate of 2 [cm/min] and its area at a rate of 2 [cm²/…

A: It is given that height of triangle is increasing with a rate 2 cm/min and area with a rate 2…

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: 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: A hot air ballon is 170 ft above the ground when a motorcycle (traveling in a straight line on a…

A: The image made from available details in the question

Q: Two cars start moving from the same point. One travels south at 16 mi/h and the other travels west…

A: A goes to south at 16 mi/h, so dA/dt= 16  After 3 hours A will be 16*3=48 mi away from the origin.…