A square of side length s is inscribed in a circle of radius r.(a) Write the area A of the square as a function of the radius r ofthe circle.  (b) Find the (instantaneous) rate of change of the area A withrespect to the radius r of the circle. (c) Evaluate the rate of change of A at r = 1 and r = 8. (d) If r is measured in inches and A is measured in squareinches, what units would be appropriate for dA/dr?

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Q: 3. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a…

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Q: 2) Find the average rate of change of the function f (x) = -3x-1 from x = a to x a + h.

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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: A triangle base is increasing at a rate of 4 cm/s and its height is decreasing at a rate of 1 cm/s…

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Q: How do you solve?

A: Given, Side of square= x x(t)= 3t+1 Therefore, Area= (3t+1)*(3t+1) A(t)= 9t²+6t+1

Q: What is the rate of change of y with respect to rfor this function?

A: Given,           The table represents some points on the graph of a linear function.

Q: Find the instantaneous rate of change of 7. y = (x + 1)*(x – 3) at a = 1.

A:

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

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Q: Find the average rate of change of f from 0 to π /6 . f(x)=sec(2x)

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Q: The concentration C (in mg/cc) of a particular drug in a person's bloodstream is related to the time…

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Q: 2. A tank with a shape of a cone is 20 feet deep and has a diameter of 10 feet at the top. Water is…

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Q: 11. What is the instantaneous rate of change of f (x) = at x = 2? %3D %3D Sown ight ore the low ng…

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Q: tan(Cx) Va6+2 find the rate of change of P with respect to x, where C is a Given that P = constant.

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Q: 2. The radius and lateral area of a right circular cylinder change at the rates of 1 cm/s and -2…

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Q: 15) The volume of a sphere is increasing at a rate of 6 cm³/sec. Find the rate of change of its 4T…

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Q: b. One airplane is approaching an airport from the north at 206 km/hr. A second airplane approaches…

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Q: Suppose the area A of a particular rectangle increases at a rate of 2 cm^2/sec and the width w of…

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Q: estimate the instantaneous rate of change at the point indicated. f (x) = e^x ; x = 0

A: To find the instantaneous rate of change at x=0 we need f'(0) So we find f'(x)

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A: The given function is,

Q: 2. The height and volume of a right circular cone change at the rates of 1 cm/s and -2 cm^3/s,…

A: Let's find.

Q: 2. The volume and radius of a right circular cylinder change at the rates of 1 cm^3/s and -2 cm/s,…

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Q: Prove that the relative rate of change 1/f(x)is negative that of f(x). Give a general formula for…

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Q: Find the average rate of change of ​f(x)=3x^2+3 a. From 1 to 3 b. From 3 to 5 c. From 1 to 4

A: Consider the given function.

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Q: 13. (a) Find the average rate of change of the area of a circle with respect to its radius r as r…

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Q: Consider an isosceles triangle of base 16 inches and edges z, and assume that z is a function of…

A: Base of triangle = 16in  Edges = z in

Q: A pendulum of length 10 cm has swung so is radian measure of the angle formed by the pendulum and a…

A: Follow the procedure given below.

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.