When a guitar string is plucked, it vibrates with a frequency of F = 200√T, where F is measured in vibrations per second and the tension T is measured in pounds. Find the rates of change of the frequency when (a) T = 4 pounds and (b) T = 9 poun

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Q: The radius r of a sphere is increasing at a rate of 6 inches per minute. (a) Find the rate of change…

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Q: Find the rate of change. Cube root 3√x with respect to x when x = 1, 8, 27

A: Consider the given: fx=x3ddxfx=ddxx3ddxfx=ddxx13ddxfx=13x13-1ddxfx=13x23

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Q: A rectangle has width w inches and height h inches, where the width is twice the height. Both w and…

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Q: James is pumping air into a spherical balloon at a rate of : бст3 What is the rate of change of the…

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Q: What is the rate of change of f (t) at t = 7.5?

A: The rate of change is calculated using differentiation. The derivative of f(t) at t=7.5 gives the…

Q: The radius r of a sphere is increasing at a rate of 6 inches per minute. (a)  Find the rate of…

A: Given:The radius r of a sphere is increasing at a rate of 6 inches per minute.

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Q: A​ hot-air balloon is 190 ftabove the ground when a motorcycle​ (traveling in a straight line on a…

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Q: Find the rate of change of area of the square in m/s with respect to its side when the sides, s, is…

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Q: What is the average rate of 5. If f (t) = -3t + 7t, describes the movement of a whale in meters.…

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Q: The sides of an equilateral triangle are increasing at the rate of 3cm/min. Find: a.)the rate of…

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Q: The radius of a spherical balloon is decreasing at a rate of 2 - in/sec. Which of the following is…

A: As we know that the expression for the volume of the sphere: v=43πr3 Where; ''r'' is the radius of…

Q: For a certain animal, the surface area S of the body is related to the body's weight W according toS…

A: The surface area S of the body is related to the body's weight W according to S is:

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A: Let L be the length of the rectangle and W be the width of the rectangle. then we have ,…

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A: Given  At time t  the radius of a sphere is 'r'

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A: Now differentiating with respect to x, we get

Q: need help

A: Consider the figure below. Let x be the distance between the man and the pole and y be the distance…

Q: Water leaks from a tank at a rate of 2 + 5t liters/hour (L/h), where t is the number of hours after…

A: Given, water leaks from a tank at a rate of 2 + 5t liters/hour (L/h), where t is the number of hours…

Q: the top of a 25 foot ladder is sliding down a vertical wall at a constant rate of 3 feet per minute.…

A: Given  c=25 ft b= 7ft dbdt=3 ft/minute dcdt=0

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Q: find the rate of change. Speed of sound v (in m/s) with respect to air temperature T (in kelvins),…

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A: Application of derivative

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Q: 7. If f (t) = -t + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

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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…

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A: Given: The surface area of the cube : S=6x2 To find : Rate of change of surface area with respect to…

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A: Consider the provided question, Drawn a figure according to the given question,

Q: The number N of bacteria in a culture after t days is modeled by 3 N = 500 1 (1? + 2)2 Find the rate…

A: N=5001-3t2+22

Q: The radius r of a sphere is increasing at a rate of 4 inches per minute.

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Q: from the edge of a cliff into described by the function ht rate of change in the height - 4.9t² +…

A: Formula average height change=(h(b)-h(a))/(b-a) Where a=4second b=5second

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A: Area of square =(side)2

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A: Given: A square with side x. changing with time is given as, xt=4t-2. The objective is to find the…

Q: If V(t) is the volume of water in a reservoir at time t (seconds), v(t) is the rate of change,  then…

A: Rate Change: Rate change is defined as the change in one quantity with respect to any other quantity…

Q: The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x2 units,    (40 ≤ x ≤ 60) where x…

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A: We have to find displacement

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Q: The radius r of a sphere is increasing at a rate of 8 inches per minute. Find the rate of change of…

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Q: It started raining at 10:15 am, and by 12:10 pm the barrel had 7 inches of water in it. What was…

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Q: The height of a triangle is increasing at a rate of 2 [cm/min] and its area at a rate of 2 [cm²/…

A: It is given that height of triangle is increasing with a rate 2 cm/min and area with a rate 2…

Q: The rate of change of the population of a certain town is given by R(t) = 50e0.05t, where t is the…

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Q: The length of a rectangle is increasing at a rate of 9 in./s, while its width is decreasing at 2…

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Q: The radius of a sphere is decreasing at a rate of 2 cm/sec. At the instant when the radius of the…

A: Given that Radius of the sphere is decreasing at a rate of 2 cm/sec. drdt=-2 cm/sec, where r is…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.