If 6 J of work is needed to stretch a spring from 12 cm to 14 cm and another 10 J is needed to stretch it from 14 cm to 16 cm, what is the natural length (in cm) of the spring?

Q: Show that the functions are linearly dependent on the real number line: y1 = 17; y2 = 3cos2x; y3 =…

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Q: Determine the inverse Laplace transform: F(s) = 4/s2 - 5/(s + 1)

A: To determine the inverse Laplace transform.

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Q: For a standard normal distribution, find: P(-1.29 Z-1.07)

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Q: Given s(t) = 5t+20, where s(t) is in miles and t is in hours, find each of the following. a) v(t) b)…

A: Given s(t) = 5t + 20, where s(t) is in miles and t is in hours, find each of the following.a) v(t)b)…

Q: Find the area of the region enclosed by y=4.75x and x = 9 - y². 2 on 5 6 7 00 a Use horizontal…

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Q: 2. Use Calculus to find all local extrema of the function g(x)=x√3-x.

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Q: 7. u = (2, 2), v = (2, −2) 8. u = (2,-2), v = (−2, 2)

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Q: Suppose f(x, y) = x² + y² - 8x and D is the closed triangular region with vertices (8,0), (0,8), and…

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Q: Use the quadratic formula to solve the equation. Give two forms for each solution: an expression…

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Q: 2.21 A mathematical model describing the state of a learner y(t) at time t while learning a specific…

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Q: The following integral is an improper integral. ( Explain why it is improper, (b) determine whether…

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Q: Find the derivative of the function. y = (tan-¹(7x))² y' =

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Q: Use partial fraction decomposition to find the following integral -da 24-1

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A: given function

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Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

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Q: Consider the following. {-x³ +3, -x² + 4x, x≤0 x > 0 Find the critical numbers. (Hint: Check for…

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Q: Find the derivative b. y= sec^-1(2x+1) c. y=x^e^x

A: I have appended the formula used in the solution procedure.

Q: If what does the following integral equal? 4 19 q(s)ds = [ q(s)ds = 13 and La q(s)ds = 10.7

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Q: List the first five terms of the sequence. an 1 + an a1 a2 аз a4 a5 || = = = a₁ = 6₁ an+1 =

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Q: Consider the following. A = Convert the iterated integral to polar coordinates. A B S^L. ( Jo Jo B =…

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Q: Z₁ cos# = 2 V₁ 1 V +(x-2- sin e Z₁ cos Z₁ X + V₂ V₂ cos 9) +1/+ Z₁ 1 V. cose V 2 -sin 0 +

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Q: Graph the function hoo-x-30 0x30 30x50 0.5x-65 i x>50 Choose the correct graph below OA 1530456075…

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Q: find maximum rate of change of f(x,y)=x sin(y) @ the point (2,0)

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Q: b.Let f(x)=x²-3x² -1, x ≥ 2. Find the value of af dx at x = -1.

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Q: Suppose R is the shaded region in the figure. As an iterated integral in polar coordinates, A = B =…

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Q: (Order your answers so the x-coordinates are in order from least to greatest.) f has ---Select---…

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Q: Consider the following differential equation to be solved by the method of unde y" + 2y = -18x²e2x…

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Q: Find the linear g(x) z approximation of the function given below at a = 0. g(x) = √1+x

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Q: 18. Find dy/dx by implicit differentiation.

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Q: Solve 2(cos2x)y' + ysin(2x) = 4cos4x 0 =< x < pi/2

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Q: 3. Consider the circle as a vector-valued function r(t) = cos(t)i + sin(t)j. Calculate limt→+∞ r(t)…

A: Find the limit