According to Newton's law of cooling/warming, the rate at which the temperature of a body changes is proportional to the difference between the temperature of a body and the temperature of the surrounding medium or the ambient temperature. Formulate the Newton's law of cooling/warming.

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e-9x. (Use ...

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Q: 28. Show that D = 0 for f(x, y) =x + (x- y) and that the function has no relative extrema.

A: Given: fx,y=x3+x-y2 To calculate the critical points, ∂f∂x=0 ; ∂f∂y=0

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Q: Let f(x)= -6x^4+8x^3+72x^2 a) The values of x for which f has a horizontal tangent line are x=

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A: Given:- A rectangle is growing such that the length of a rectangle is 5t + 4 and its height is t4 , ...

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A: Since the student has posted many sub-parts of the question and does not mention any specific part, ...

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A: solution

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Q: Save your solution for this problem to answer the other problem connected to this. Consider the curv...

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Q: Twenty students like both the first (Set A) and second (Set B) techniques in solving a mathematical ...

A: We will find the solution in the following step.

Q: Convert 7383 to a numeral in base 4. 7383 = D %3D 14

A: Topic:- algebra

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A: Here we have to find the instantaneous rate of change of f(x) = √8x+9 at x=1.

Q: 2- y = prove that (sin x) = cos x %3D dx

A: Topic:- derivatives

Q: 17 O. 32 B Find the measure of each side indicated. Round to the nearest tenth. 5) 6) 43 6. 57 43° C...

A: Topic:- Geometry

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A: Given first order differential equation is solved by using integrating factor.

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Q: Consider the curve satisfying y" = 6x and is tangent to the line y = 5– 3x at x = 1. What is y' (2)?...

A: Given: y''=6xand tangent to the line y=5-3x at x=1To find y'(2)=?  

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Q: Find the following using the table below. 1 3 4 f(r) 1 4 3

A: Given that:                      

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A: Given that:                      

Q: Evaluate the integral by interpreting it in terms of areas: (3 – 5æ) dæ =

A: To evaluate the given integral by interpreting it in terms of areas.∫04 3-5x dx

Q: Let f(x)= -6x^4+8x^3+72x^2 a) lim x-> +inf f(x) b) lim x-> -inf f(x)

A: Here, the given function is: f(x)=-6x4+8x3+72x2 Here, note that the leading coefficient is negative.

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A: Follow the procedure given below.

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Q: 21 Censtruction A winch at the sp of a 12-uter ildng pae of the same kength to a vertical position. ...

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A: Topic:- application of derivatives

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Q: Solve the following initial value problem and present its particular solution: y" + y' + 0.25y = 0, ...

A: The given initial value problem is: y''+y'+0.25y=0 ;         y(0)=3,    y'(0)=-3.5

Q: sec® tan Od® coso A) tane В sece sec?0

A: topic - indefinite integral

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Q: Problem 2: (2y cos a + sin x) dæ sin a dy when a = , y = 1

A: