Find the instantaneous rate of change of y =- at x = a

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: 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 helicopter is rising vertically from the ground at a constant rate of 4.5 meters per second. When…

A:

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

A: To find the rate of change we have to find dy/dx

Q: Estimate the instantaneous rate of change of y(x) 4 at the %3D x+ 1 point x = - 2

A:

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: A fighter plane 2000 km away is spotted by a gunner in the ground. If it maintains its altitude at…

A: Pythagoras theorem: In a right angle triangle, Hypotenuse2=Base2+Perpendicular2 Differentiation…

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: Is the rate of change of a cube's volume linearly proportional to the rate of change of its side?

A: Rate of change of volume of cube

Q: If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ…

A:

Q: Find the average rate of change of f(x)=x² – 5x from: x, =-1 to x, = 3

A: We will find the average rate of change of the function.  We know,  the average rate of change =…

Q: Find the instantaneous rate of change of y with respect to x at x=2 of the function y = 2x³ + 4 %3D

A: To Find: The instantaneous rate of change of the function y=2x3+4 at x=4. Given: The function is…

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

A:

Q: 2. Estimate the instantaneous rate of change of y = at x = 1. Show your work. 2x-3x+1

A:

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: 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 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 piston is seated at the top of a cylindrical chamber with radius 5 cm when it starts moving into…

A: Let h be the distance between the piston and base of the chamber.

Q: A 200-liter tank initially full of water develops a leak at the bottom. Given that 10% of the water…

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: What is the instantaneous rate of change of f(x) = V +2-3 at %3D x = -2?

A:

Q: How fast is the circumference of a circle changing if the radius is changing at the rate of 3 mm/s?

A: Solution

Q: An object is thrown vertically upward from a point 32 feet above the ground with an initial velocity…

A:

Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

A: First we will find value of y from given equation And differentiate wrt to t

Q: estimate the instantaneous rate of change at the point indicated

A: To find the instantaneous rate of change we will find y'(x) We use the power rule

Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

A:

Q: A spherical balloon is inflated with gas at the rateof 800 cubic centimeters per minute. (b) Explain…

A: To find the rate of change of the radius, differentiate the volume of the sphere, V=43πr2 with…

Q: One ship is approaching port from the north at 10 miles per hour and is presently 3 miles north of…

A:

Q: The hour hand of a clock is 4 inches long and the minute hand is 6 inches long. At the moment the…

A: The hour hand of clock is 4 inches long and the minute hand is 6 inches long. At that time angle…

Q: The derivative f'(a) represents the instantaneous rate of change of y = f (x) with respect to x when…

A: Given that we need to check  behaviour of  the statement " The derivative f'(a) represents the…

Q: The volume of a cube decreases at a rate of 0.3 3ft/min. What is the rate of change of the side…

A: Let the length of each side of the cube be a ft. Find the volume of the cube. Differentiate the…

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: The surface area of a cube is increasing at a rate of 15 square meters per hour. At a certain…

A:

Q: As an orange grows, the rate of change of the radius r of the orange is inversely proportional to…

A: Given query is to find differential equation.

Q: A triangle has a base that is decreasing at a rate of 11 cm/s with the height being held constant.…

A:

Q: Find the rate of change of the ice circle's area towards the start of spring if the initial radius…

A:

Q: At what rate is the height of the water rising at the instant the tank is half full?

A: To find the rate at water rising

Q: What is the instantaneous rate of change of y=y=−2x^2+2x at x=0 ?

A:

Q: . Use a similar procedure to estimate the instantaneous rate of change of y = 3" at r = 0. Show your…

A:

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is…

A:

Q: Air is being pumped into a spherical balloon such that its radius increases at a rate of .50 in/min.…

A: r= 3 in dr = 0.5 in/min

Q: Let m(x) be the slope of the tangent line to the curve y = 2x° – 6x² + 3x at the point (x, y). Find…

A: We have to find instantaneous rate of change of m(x) at point (2,-2)

Q: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

A: Let b and h be the base and height of the trianglegiven rate at which base is decreasing, dbdt=4cm/s…

Q: A hot air balloon is 120 ft. above the ground when a motorcycle (travleing in a straight line on a…

A: Given that, A hot air balloon is 120 ft. above the ground when a motorcycle (traveling in a straight…

Q: One ship approaching a port from the east. Traveling west at 15 miles per hour, and presently 3…

A: Solved below.

Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

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

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. F(x,…

A: SOLUTION-

Q: DETERMINE THE INSTANTANEOUS RATE OF CHANGE OF THE FUNCTION AT X=1 sin (2³) 1 + √t - f(x) = x3 dt

A:

Exponential Growth Model

The relation that represents an exponential function is: