Question 5: A balloon leaves the ground 250 m from an observer and rises at a rate of 5.0 m/s. How fast is the angle of elevation of the balloon increasing after 8.0 seconds?

Q: The bast x of the right triangie in the figure, increases at a rate of 5 cm/s, while the nei ght…

A:

Q: Question 19. A circular area of r0 is swept out as a rod of fixed length r = 1 m pivots about a…

A: Given :                     Since a circular area of 12r2θ is swept out as a rod of fixed…

Q: Question 9 A toy rocket is launched from the ground with an upward velocity of 64 ft/sec. When will…

A: Given data is : Upward velocity is 64ft/sec To find time required to hit the ground. Upward…

Q: A person stands 30 feet from point P and watches a balloon rise vertically from the point, as shown…

A:

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: A 13 ft ladder is leaning against a house. The ladder slides down the wall at a rate of 3ft/min. a)…

A: We have to use differentiation to solve the problem

Q: Question 13 :  A street light is at the top of a 11 ft tall pole. A woman 6 ft tall walks away from…

A: Given the length of street light 11 ft, woman is 6 ft tall, the woman is moving away from the pole…

Q: A spy uses a telescope to track a rocket launched vertically from a launching pad 6 km away, as in…

A: Given that

Q: A man 6 ft tall is walking at the rate of 3 ft/s toward a streetlight 18 ft high (see Figure 1). (a)…

A: By using similarity rule:

Q: - A ladder of length 17 feet is leaning against a wall. The base of the ladder is moving away from…

A: Given query is to find the rate of change of angle.

Q: Question 24 A ball is thrown vertically upwards with a velocity of 48 ft/s from the top of a…

A:

Q: Problem #10] A kite 100 ft above the ground is being blown away from the person holding its string…

A:

Q: Question 4 A ball is thrown downward wi Jot yet its height above the ground i nswered (a) Determine…

A:

Q: 1) A7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Question: 3 The volume of a cube is increasing at a rate of 15cm/min. At what rate the side of the…

A: We know that volume of cube is (side)3. That is V=x3, where x is side of a cube. Differentiate V…

Q: QUESTION 11 A 5-foot-tall person is walking towards a 7-foot-tall lamppost at a uniform rate of 2…

A:

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 11. For a certain rectangle, the length of one side is always 6 times the length of the…

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: QUESTION 15 A 5-foot-tall person is walking towards a 7-foot-tall lamppost at a uniform rate of 2…

A:

Q: QUESTION 1 Find the rate of change of the area of a square (Area is A = s if the sides are 14 cm…

A:

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

A: Given query is to find speed of the tip of man's shadow.

Q: (Question 11) It is night. The lamp in the dog park is 20 ft tall. A sweet dog is running from the…

A: The triangle is shown below. Here, H is the height of the lamp, h is the height of the dog., x is…

Q: QUESTION 8 An object is thrown vertically upward from a point 32 ft above the ground with an intial…

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: A tracking camera, located 1200 ft from the point of launching, follows a vertically ascending…

A: We need to find the rate at which balloon is rising in the air. This means we need to find dh/dt

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 6 A kite is rising vertically at a constant speed of 2 m/s from a location at ground level,…

A:

Q: QUESTION 3 A spherical balloon is being inflated at the rate of 7 cm³ /sec. Determine the rate at…

A:

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: Given data- Height of man = 6 feet. Distance of light from the ground=15 feet. Distance between man…

Q: QUESTION 4 At noon, Ship-A is 210 miles east of Ship-B. Ship-B is sailing due east at rate of 30…

A:

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 14 A 5-foot-tall person is walking towards a 7-foot-tall lamppost at a uniform rate of 2…

A:

Q: Question 25 : A street light is at the top of a 19 ft tall pole. A woman 5.5 ft tall walks away from…

A:

Q: QUESTION 6 A 5-foot-tall person is walking towards a 7-foot-tall lamppost at a uniform rate of 2…

A:

Q: Problem 5. An observer is positioned 3km away from a rocket launch pad. How fast is the distance…

A: This question can be solved using the concept of rate of change.

Q: The figure below shows a camera mounted at a point 6000 ft from the base of a rocket launching pad.…

A:

Q: Question 6 From the edge of a cliff, 128 feet high, a man throws a stone vertically upward with a…

A: I am attaching image so that you understand each and every step.

Q: A kite 100 ft above the ground moves horizontally at a speed of 6 ft/s. At what rate (in rad/s) is…

A:

Q: The legs of an isosceles triangle are increasing at the rate of 0.5 feet per minute, and the…

A: In an isosceles triangle ABC: From the given data: The legs of an isosceles triangle are increasing…

Q: Question 18 > Two cars are moving towards an intersection. One car is 170 meters north of the…

A:

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: A man 6 ft tall is walking at the rate of 3 ft/s toward a streetlight 18 ft high (see Figure 1). (a)…

A:

Q: Question 19. A circular area of 1²0 is swept out as a rod of fixed length r = 1 m pivots about a…

A: The rate of change of area with respect to the time can be calculated by differentiating the area…

Q: A man 6 feet tall walks at a rate of 8 feet per second away from a light that is 15 feet above the…

A: Part(a) We have lamp 5ft above ground . Man is 6ft tall . Man is moving at speed of 8ft/sec . To…

Q: Question 10 A man who is 5 feet tall is walking away from a lamp post that is 10 feet high. How fast…

A:

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: Question 14 An engineer is experimenting with a cylindrical can with a fixed height of 15 inches…

A: The volume of a cylinder of radius r, and height h is given by, V=πr2h

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…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.