Find the instantaneous rate of change Of the function at the Speciried value of X flx)=X?-2; X -3

Q: assume that an airplane is flying toward you at a constant height, h miles, and at a speed dx/dt.…

A: assume that an airplane is flying toward you at a constant height, h miles, and at a speed dx/dt.…

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 3 ft/min.…

A: The given data is: Initial radius ri=50 ft Radius is decreasing at the rate of drdt=3ft/min To find…

Q: the velocity of a particle is the rate of change in the position function over time true or false

A: We have to check

Q: A balloon is 20 m horizontally away from an observer. At an instant, the balloon rises vertically at…

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Q: A point on the graph of y = is moving along the curve in such a way that its x-coordinate is…

A: Given graph- y=1x Rate of increase of x-coordinate,dxdt= 6 units per second y-coordinate = 5 Then,…

Q: The radius of a spherical balloon is decreasing at a rate of in/sec.

A: Radius of balloon = r = 4 inchesDecreasing rate of balloon = drdt = -2πinches/secondVolume of…

Q: The volume of a sphere is increasing at a rate of 4 cm3/sec. Find the rate of change of its surface…

A: We will use derivative as rate of change

Q: A cube is heated in such a way that the volume increases at a rate of 1 mm/s. The rate of change of…

A: A cube is heated in way that volume increases at the rate of 1mm/s. the side of the cube is 7mm…

Q: Let y=sqrt(2x). Find the rate of change of y with respect to x at x=4.

A: Answer is 1/(2√2).

Q: A hot-air balloon is 140 ft above the ground when a motorcycle (traveling in a straight line on a…

A: Given the height in which the hot air balloon placed above the ground is 140 ft. Velocity of the…

Q: A spherical snowball is melting in such a way that its volume is decreasing at a rate of 2 cm / min.…

A: Given-  dVdt=-2cm3/min (negative sign indicates that it is decreasing). To find- The rate of radius…

Q: A 15-meter ladder is resting against a vertical wall. if the bottom of the ladder is being pushed…

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Q: A ladder of length 3 meters is placed on a wall, with the distance from the wall x and the height of…

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Q: The edge of an expanding cube is changing at the rate of 2.3 cm/s at the instant its edge is 18.3 cm…

A:

Q: 3. A 20 ft ladder is leaning against a wall and begins to slide. How fast is the top of the ladder…

A: A 20ft ladder is leaning against a wall and begins slide.The ladder is 12ft away from the wall and…

Q: A spherical snowball melts at a rate proportional to its surface area. Show that that rate of change…

A: It is given that, the spherical snowball melts at a rate proportional to it’s surface area. This can…

Q: 7. A 6ft tall human is walking away from a 20ft lamppost. Given that the length of the shadow of the…

A: Let the distance of the person from the bottom of the light post be x. Let the length of the shadow…

Q: What is the rate of change of y = In x at x = 10?

A: Explanation: Given that,  y=lnx   Concept Used: To find the rate of change we will find the…

Q: A spherical balloon is being deflated at a rate of 80 cm3/min. At what rate is the radius decreasing…

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Q: A spherical balloon is being inflated at the rate of 12m3 /min. If the radius of the balloon is 6m,…

A:

Q: A man of height  1.9  meters walks away from a 5-meter lamppost at a speed of  2.1  m/s. Find the…

A: Let distance of the man from the pole=x   Let the length of the shadow =y…

Q: A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off…

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Q: A man of height 1.8 m walks away from a 5-m lamppost at the speed of 1.2 m/s. Find the rate at which…

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Q: An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If the oil was…

A: Given that  An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If…

Q: A triangle has an area that is increasing at a rate of 555 square feet per minute with the height…

A:

Q: If I am blowing up a balloon at a rate of 3 cubic feet per minute, what is the rate of change of the…

A: Since, it is given that a person is blowing up a balloon at a rate of 3 cubic feet per minute, then…

Q: A weather balloon is rising vertically at the rate of 10 ft/s. An observer is standing on the ground…

A: Given:A weather balloon is rising vertically at the rate of 10 ft/s. An observer is standing on the…

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

Q: Water is discharged from an inverted cone-shaped tank with a height of 12 meters and a radius of 6…

A: Given: The height of the inverted cone-shaped tank, h = 12m. Also, its radius, r = 6m. From the…

Q: A square with side x, is changing with time where x(t) =3t + 1. What is the formula for the rate of…

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Q: A designer develops a cylindrical box with a fixed height of 15 cm. Calculate the instantaneous rate…

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Q: A cylinder is leaking water but you are unable to determine at what rate. The cylinder has a height…

A: Given, Radius is 2m, height is 2m. Height is decreasing at 10 cm/min when height is 1m.

Q: Let 7=sin ( y+. *). Find the rate of change of z with respect to x at the point (2, 1) with y held…

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Q: A 100-ft long cable of diameter 4 in. is subsequently submerged in seawater. Due to corrosion, the…

A: Given that diameter is 4 inches and height is 100 feet. And rate of decrease in area is 750 in2yr.…

Q: A circle has an initial radius of 50 ft. when the radius begins decreasing at the rate of 3 ft/min.…

A: Area of a circle is given byDifferentiating the function of area with respect to time:

Q: 5. A 6-ft man walks away from a 15-ft lamppost at a speed of 3 ft/s. Find the rate at which his…

A:

Q: A weather balloon is rising vertically at the rate of 2 m/sec. An observer is standing on the ground…

A: The diagram of the given question will be as follows Given: dydt=2 m/s To find: dxdt

Q: A man of height 1.9 meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate…

A: Given Data: The height of the man is: h=1.9 m The height of the lamppost is: H=5 m The increasing…

Q: a spherical balloon is filled with gas at a rate of 300 mm3/sec. Find the rate at which the surface…

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Q: A funnel in the shape of an inverted cone is 30 cm deep and has a diameter across the top of 20 cm.…

A: Geometry

Q: A kite 100ft  above the ground moves horizontally at a speed of 8ft/s  At what rate is the angle…

A: Let x= horizontal distance L= length of string,  Then a rough sketch of the problem is as follows:

Q: The side of a square is increasing at the rate of 0.2 cm/sec . Find the rate of increase of the…

A: we know that the perimeter of the square is with side x is                        P=4x…

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 5 ​ft/min.…

A: Given information:

Q: A hot-air balloon is rising vertically at a rate of 5 meters/sec. An observer stands 300 meters from…

A: The figure below can be compared with the observer and balloon Let C be the position of observer…

Q: A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec. How…

A: Given,            A balloon leaving the ground 60 ft from an observer rises vertically at the rate…

Q: A weather balloon is rising vertically at the rate of 10ft/s. An observer is standing on the ground…

A: Given: -

Q: Find the rate of change. Volume V of a cylinder with respect to radius if the height is equal to the…

A:

Q: . A kite 100 ft above the ground moves horizontally at aspeed of 8 fts. At what rate is the angle…

A: At what rate is the angle between the stringand the horizontal decreasing when 200 ft of string has…

Q: The surface area of a cube with sides of length x is given by S = 6x2 . Find the rate of change of…

A: