Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 5 pounds compresses a 15-inch spring a total of 3 inches. How much work is done in compressing the spring 9 inches? in-Ib

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Q: Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi+ yj – zk. %3D - V · (F × G) = %3D

A: To solve the following problem

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Q: 2) Find and of the following equation then simplify whenever possible. dx x = 1+ Sin t y = Cos? t

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Q: 0.09 ) 12t At the end of t years, the future value of an investment of $37,500 in an account that…

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A: We need to find integral.

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Q: mal places as needed.)

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Q: D If the Taylor series expansion for f (x) is given by f(x) = Eo- (x- 2)*, then f(4) (2) = %3D

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Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

A: This is a problem related to derivative of the function. For calculating the unit if derivative…

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Q: Find y': y = /5+ 2x – x² - 1-x O y = V5+2x-a2 1 O y = 2/5+2x-a2 7-2x O y = 2/5+2x-a²2 O y = /2 – 2x

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Q: Consider a wood beam (see figure) carrying a uniform load of 20.5 kN/m (which includes the weight of…

A: answer is in next step

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A: Differrtiate with respect to t

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Q: For the function y=JHx +1 + Find: a) The equation of the tang ent liné at X = 2 b) The equation of…

A: Given,            y=4x+1+2xTo find : a The equation of the tangent line at x=2.                b The…

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Q: 2) Center: (11, 16) Radius: 1 4) Center: (-4, 0) Radius: 7 6) Center: (-7, -12) Radius: 3 8) Center:…

A: The Equation of a circle : (x - h)2 + (y - k)2 = r2 Where, r = Radius of the circle (h,k) = Center…

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A: The given equation is: r(x,y)=(7-2t)i+10tj⇒x=7-2t    y=0+10t

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Q: L xe* xe2x dx хе

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Q: Find the directional derivative of f(x, y) = sin(x + 2y) at the point (-2, -3) in the direction 0 =…

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Q: Find the first three nonzero terms in Maclaurin Series for each function

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Q: 3. If dt , find g'(2). 5. g(x) =

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Q: Verify Green's Theorem by evaluating both integrals dA Əx ay, or the given path. C: boundary of the…

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Q: ||r'(t) x r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = 8 cos(8t)i+8 sin(8t)j+ 5tk…

A: The given formula is: κt=r't×r''tr't3 And rt=8cos8ti+8sin8tj+5tk

Q: The graph of f(x) is shown (see figure). f(x) %3D Vx2 +7 Net draw o scale (a) Find the following…

A: Solution: f(x)=9xx2+7

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Q: 5.) Matching : Match the terms at the right with the best term on the left that matches it. Secant…

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Q: Find curl (4z i+ 5x j+ 8y k). curl(4z i+ 5x j+ 8y k) = ( )i +( i j+( i )k

A: To Find : curl(4z i + 5x j +8y k)   Note that : If F=〈P,Q,R〉 is a vector field in ℝ3, and Px,Qy, and…

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Q: emplicit differuntintion to find an Use equaton of 44 tangent line to yle graph of ve equation given…

A: The given equation,       arcsin4x+arcsin3y=π2,  28,26

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Q: What is the second derivative of f(x) 2x-3 2 x+1 10 (x+1)* 10 3 (x+1)° -10x+10 (x+1)* 10x-10 (x+1)*

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Q: The sales function for a product is given by S(x) 124 + 37.8x? – 0.6x, wherex represents thousands…

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Q: Use the following information to answer the question below. lim f(x) = 3 lim f(x) = ∞ lim f(x) = -3…

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Q: Find the area of the following region bounded by the graph of f(x) = (x - 5) and the x-axis between…

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