Find the area of the region bounded by the graphs of the given equations. y=x+12, y=x² The area is (Type an integer or a simplified fraction.)

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A: Given that

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A: Consider the function

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Q: K Find the area of the region bounded by the graphs of the given equations. y=x² +6, y=x², x= -3,x=2…

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A: Given,

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A: The given function is

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A: (a) given, if

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Q: 8. Graph the = function. 7 if x < 2 3 ₁ifx= 2 2х=3 if *72 piecewise 2x-3

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A: We will find the displacement.

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A: Consider the function

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Q: 3. A weight of 20 pounds stretches a spring 1/3 foot. The weight on the spring is then placed into a…

A: The given weight is w=20 poundsSpeing stretches  foot.The damping constant is The mass is given…

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Q: (8) Find the value of c guaranteed by the Mean Value Theorem for f(x) = 2/²/²/1 I [3, 5]. (A) 1+ 2√2…

A: Since you have asked multiple questions in a single request so we will be answering only first…

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A: The given geometric series is

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A: Sin(2A) = 2sin(A) cos(A) Cos(2A) = cos2(A) - sin2(A)Tan(2A) =

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Q: If g(x) = x + y², and R= [0, 1] × [0, 2], compute the value of SSR 9(x, y)dA. -23/6 19/6 11/3 22/3…

A: The given function , and the region .The objective is to find the value of the integral .

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A: We find a) The equation of the plane passing through the points (1, 0, 0), (0, 3, 0), and (0,0,4).b)…

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A: The given LPP,Maximize Subject to the constraints,The objective is to find the maximum value of the…