Question 12 The side of an equilateral triangle is increasing at the rate of 2 cm/sec. The rate at which area increases when the side is 10 cm is (A 10/3 cm?/ sec (В) 3 ст?/ sес B 10 cm2/ sec D D 2/3 cm2/sec 10 cm² / sec 3 E

Q: QUESTION 1 The radius of semicircle is increasing at the rate of 0.8 cm/s, calculate the rate of…

A:

Q: Question 15 time (sec) 0 1 2 velocity (ft/sec) 11 19 20 12 3 1 8 feet

A:

Q: Question 3 How much work is required to pump all the water from a right circular cylindrical tank,…

A:

Q: A voltage V across a resistance R generates a current I = V/R. If a constant voltage of 6 volts is…

A: I=VR here V is constant and that is V=6 I=6R take the derivative with respect to t  dIdt=ddt6R…

Q: A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away…

A: According to the Pythagoras theorem:

Q: Question 18 ▼ Two cars are moving towards an intersection. One car is 150 meters north of the…

A: To solve this problem, we have to establish a geometric relationship between the cars and using…

Q: QUESTION 6 A ladder 10 m long leans against a wall in a building. When the lower end of the ladder…

A: A ladder 10m long leans against a wall in a building.when the lower end of the ladder is pulled away…

Q: Question 20 A ball is propelled straight up with an initial velocity of 250 feet/sec in a vacuum…

A: Given, intial velocity of ball=250 feet/sec

Q: Example A light is on the top of a 12 ft tall pole and a 5ft 6in tall person is walking away from…

A: (a) distance of tip of shadow frompole = AE = xp+xsrate of change = ddt(xp+xs)=dxpdt+dxsdt= 2+13079=…

Q: 4. A 13-ft ladder is leaning against a house when its base is 12 ft from the house, the base is…

A: To find the solutions of given statements

Q: 1. A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the…

A:

Q: 10​-ft ladder is leaning against a house when its base starts to slide away. By the time the base is…

A: a)   What is the rate of change of the height of the top of the​ ladder?     Let x be the base…

Q: 13. A 13 foot sliding ladder is leaning against a house when its base starts to slide away. By the…

A: We are given diagram as

Q: Example A light is on the top of a 12 ft tall pole and a Sft 6in tall person is walking away from…

A: Consider the provided question, The pole and the person are shown in the figure below;

Q: QUESTION 10 How fast is the area of a circle changing when the radius is 10 cm. if the radius is…

A:

Q: QUESTION 5 Figure 1 shows a right triangle with base 6 cm. If x is decreasing at the rate of 2 cm/s,…

A:

Q: Can you help me step by step?

A: The given situation can be picturized as follows.

Q: QUESTION 5 A conical water tank has a radius of 5 cm at the top and 20 cm high as shown in Figure 1.…

A:

Q: Question 2 2.1 A spotight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the…

A: The problems involves the differentiation to find the respective values. Differentiation is defined…

Q: Question #5 C11: "Related Rates." A man starts walking south at 5 ft/s from a point P. Thirty minute…

A: Man moves at 5ft /sec along S direction. Woman moves 4ft/sec along N direction.

Q: QUESTION 1 You want to spray a fertilrer at 425 L/ha at a ground speed of 6 km/t, using regular flat…

A:

Q: A 13-foot ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: QUESTION 9 If the radius of a circle decreases at a rate of 3 ft/s, what can you say about the rate…

A:

Q: 1. A biker is 50 meters away from a pole. The biker starts to ride south parallel to the pole at a…

A: Solution is given below:

Q: Question 1 A circular pipe with a 5.6 in diameter is conducting air at 12,500 A standard day at 6.5…

A:

Q: QUESTION 21 A ball is thrown vertically upwards with a velocity of 48 ft/s from the top of a…

A:

Q: Question 2 A balloon is rising vertically over a point A on the ground at the rate of 15 feet per…

A: Using differentiation

Q: QUESTION 5 A spherical balloon is being inflated at a rate of 8cm3/s. Find the rate of change of the…

A: Explained below

Q: Question 19 the radius r of a sphere is increasing at the uniform rate of 0.3 inches per second. At…

A:

Q: Question 12 : A spherical snowball is melting in such a way that its diameter is decreasing at rate…

A: We know the volume of a sphere is V=43πr3, where r is the radius. Given that,  Diameter, d=18 cm…

Q: QUESTION 1 It is given that the radius of the semicircle increases at the rate of 0.5 cms¹ when…

A:

Q: A balloon is a rising vertically over a point A on the ground at the rate of 15 ft/sec. A point B on…

A: Let the balloon's distance from A be h and the distance from B be x. Say at any time t, the length x…

Q: Which of the following is not true? A ladder 25 feet long is leaning against the wall of a house.…

A:

Q: B. The dimensions of a rectangular solid at a given instant (to) are (a = 13 cm), (b = 9 cm) and (c…

A:

Q: Question 14 An engineering student is experimenting on a cylindrical can with a fixed rate of 8…

A: Topic:-  application of derivatives

Q: Problem 2. You are pumping air into a spherical balloon at a constant rate of 5 cm' /s. Recall that…

A:

Q: Question 2 Sand is being dropped into a conical pile in such a way that the base radius of the pile…

A: Let's find.

Q: QUESTION 10 The volume of a sphere is given by V=(4/3)nr³. The rate of change of the volume as the…

A:

Q: QUESTION 16 The radius rof a right circular cylinder with a fixed height of 48 inches is increasing.…

A: It is given that a radius and height of a cylinder are 3 feet and 48 inches respectively.

Q: QUESTION 12 A ball is thrown vertically upwards with a velocity of 48 ft/s from the top of a…

A: Taking upward direction is positive; u=48ft/s.

Q: QUESTION 2 The height, h, of a cylinder is two times its radius, r. If the radius of the cylinder is…

A:

Q: A conical vessel 12 cm deep and with a radius of 6 cm at the top, is being filled with water. If the…

A: Let's find.

Q: Question 16 A balloon is a rising vertically over a point A on the ground at the rate of 15 ft/sec.…

A: Given:  A balloon is a rising vertically over a point A on the ground at the rate of 15 ft/sec. A…

Q: The upper end of the ladder 5 m long leans against a vertical wall. Suppose the foot of the ladder…

A: Given ladder length =5m And let x is the distance from the bottom of ladder to the wall y  is the…

Q: (a) A 5-ft ladder is leaning against a house when the base starts to slide away. by the time the…

A: First we use Pythagoras theorem and then we calculate dA/dt and solve it .

Q: Question 17 From the edge of a cliff, 128 feet high, a man throws a stone vertically upward with a…

A: Solve the given problem.

Q: Question 16 : An inverted pyramid is being filled with water at a constant rate of 25 cubic…

A: This is a problem related to derivative of the volume of the square base pyramid. Please follow the…