The area of a circle is increasing at a rate of 80n square feet per second. How fast is the radius changing when the radius is 10 feet?

Q: A5 feet 6 inches tall man is walking away from a lamppost at a rate of 2 ft/sec. If the lamppost is…

A: We have, A 5 feet 6 inches (5.5 feet) tall man is walking away from the lamppost of height 12 feet…

Q: The sides of a square are increasing at the rate of 2 inches per minute. How fast is the Area…

A: Given The side of square is increasing at rate of 2inches per minute.  The area of a square with…

Q: Wheat is poured through a chute at the rate of 10 ft/min and falls in a canonical pile whose bottom…

A:

Q: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

A: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

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

A:

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

A: Here we find rate of shadow lengthening.

Q: Each side of a square is 6 ft and is increasing at a rate of 2 ft per second. How fast is the area…

A: By differentiating equation of area of square with respect to time and substituting the value of…

Q: A 5 foot girl is walking toward a 20- foot lamppost at the rate of 6 feet per second. How fast is…

A:

Q: ick is increasing at a rate of 3 meters per minute. How quickly is the area changing when the oil…

A:

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

A:

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

A:

Q: An aircraft is flying horizontally at a speed of 600 km/h. How fast is the distance between the…

A:

Q: A helicopter flies parallel to the ground at an altitude of 1/2 kilometer and at a speed of 2…

A:

Q: If the diagonal of a cube is increasing at a rate of 3 cubic inches per minute, how fast (in…

A: We will find the rate of increase of side of cube.

Q: A man 7 ft tall walks at a speed of 5 ft/sec toward a street lamp which is 15 ft above the ground.…

A:

Q: How fast is the area of the circle of the ripples expanding at the instant that the radius of the…

A:

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

A: Given:- A 17 feet ladder is leaning against a wall. if the bottom of the ladder is pulled along the…

Q: A spotlight on the ground is shining on a wall 24m away. If a woman 2m tall walks from the spotlight…

A: Here we use the application of derivative

Q: A spotlight on the ground shines on a wall of a building 20 feet away. If a man 6ft tall walks from…

A:

Q: Two people start from the same point. One walks east at 2 km/h and the other walks northeast at 3…

A:

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

A: Let, a be the spotlight and “ed” be the wall on which the spotlight shines.Therefore, “ad” is the…

Q: A man 6 ft tall walks along a level sidewalk away from a lamppost. On the post is a street light 18…

A:

Q: The volume of a cube is increasing at 24 cubic inches per minute. What is the rate of change of its…

A: volume of cube = side3 V= volume  x= side dVdt=24 in3/minutedxdt=? at x=2

Q: Elton John is standing 3 kilometers from a launchpad when a rocket blasts off. The rocket rises…

A: Differentiation of a variable is the rate of change of the variable. Differentiation of a function…

Q: The base of a triangle begins to increase at a rate of 2 inches per minute while the height remains…

A: Consider the following variables, b=base of the triangleh=height of the triangleA=area of the…

Q: A rock dropped into a pond causes a circular wave of ripples whose radius increases at 4 inches per…

A: The new area of the circle is, A=π602=11304 The radius changes at 4 inches per second. Consider the…

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

A:

Q: A fire has started in an open field and is spreading in the form of a circle, with its radius…

A:

Q: If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is the…

A: Given dr/dt = 3

Q: A man 6-ft tall walks with a speed of 5 ft./sec. away from a street light that is a top of a 24-ft…

A:

Q: A spotlight on the ground is shining on a wall 24m away. If a woman 2m tall walks from the spotlight…

A:

Q: A rectangle has one side of 10 cm. How fast is the area of the rectangle changing at the instant…

A: Given that: Let the one side of rectangle is (a) = 10 cm and the other side of rectangle is (b)= 18…

Q: A ladder 20 feet long rests against a vertical wall. If the bottom of the ladder slides away from…

A:

Q: A 6-ft tall man is walking towards a 15-ft tall street lamp at the rate of 9 ft/sec. How fast is his…

A:

Q: A bacteria culture contains 1500 bacteria and doubles every half hour. What is the size of the…

A: Given that: Given that: A bacteria culture contains 1500 bacteria and doubles every half hour.…

Q: Sand flows out of an hourglass at a rate of 4 cubic inches per second and forms a conical pile. How…

A: Write the expression for volume of cone take the derivative with respect to time t than put the all…

Q: A 30-foot ladder is leaned up against a 2-story building with 8-foot floors. The bottom of the…

A: Consider the diagram below with marked information: Speed of change in base is 6 feet per second.

Q: The length of a rectangle is decreasing at the rate of 1 feet per second, but the area remains…

A: Let x and y ( in feet ) be the length and width of rectangle and A ( in ft2) be the area of…

Q: If the area of a square is increasing by 10 square inches per minute, how quickly is the length of…

A: Let us consider x inches be the side of the square. Area = x2. We are given that the area of the…

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

A:

Q: A man 6 ft. tall is walking towards a building at the rate of 4 ft./sec. If there is a light on the…

A:

Q: A man 6 feet tall walks at a rate of 2 feet per second away from a light pole that is 16 feet high.…

A: From the figure substitute value of BE, AE, AD and AC in equation (1)

Q: A kite travels upwards at 30 mph, while a kid runs away at 6mph. What rate is the distance between…

A:

Q: A revolving beacon is situated 3600 feet off a straight shore. If the beacon turns at 2 revolutions…

A:

Q: The radius of a sphere, initially zero, increases at the rate of 4 feet per second. Find how fast…

A: Solution :Given  the adius of a sphere, initially zero, increases at the rate of 4 feet per…

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.…

Q: The side of a square sheet is increasing at rate of 4 cm per minute ,At what rate is the area…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.