As a hardworking student, plagued by too much homework, you spend all night doing math homework. By 6am, you imagine yourself to be a region bounded by Y = 7x? As you grow more and more tired, the world begins to spin around you. However, according to Newton, there is no difference between the world spinning around you, and you spinning around the world. Unfortunately, you are so tired that you think the world is the x-axis. What is the volume of the solid you (the region) create by spinning about the x-axis?

Q: Find the value(s) of c such that the area of the region bounded by the parabolae y=x2-c2 and y=c2-x2…

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A: Consider the given integral. I=∮c-y2dx+xydy The green theorem is defined as, ∮cPdx+Qdy=∬R∂Q∂y−∂P∂x…

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A: Given: Equation of curve:                                    r(t)=t i +(6t-t2) k Equation of…

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A: Use double integral

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A: Explanation of the solution is given below...

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Q: Find the value(s) of c such that the area of the region bounded by the parabolae y=x^2 - c^2 and…

A: Given: The given parabolas are y=x2-c2 and y=c2-x2. Determine the points of intersection.…

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Q: Consider the hyperbolic PDE shown below = 4- at? For a value of At=0.1, what are the values of Ax…

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Q: (2) Find the Ualue of the constant m while the Curl of Foaoy,z) = (mxy- 2) Ĉ +cm-2)x)+(1-m)x2° Â is…

A: Please see the answer in step 2

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A: Given:

Q: Figure 4.6 shows the curves y = Vx, x= 9, y = 0, and a rectangle with its sides parallel to the axes…

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Q: number 44 and it says use example 4 so i attached that as well

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Q: 2. Find the area of the smaller loop of the curve r = = 3( 1- 2cose)

A: We will solve the following

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A: We need to find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k

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A: Given curve is y=e-8x, x≥0 is rotated about x axis.

Q: At what points does the curve r(t) = ti + (6t – t2)k intersect the paraboloid z = x2 + y2? (If an…

A: knlk

Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle e…

A: The answer is given below:

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A: Definition used -                            Length of subtangent =ydxdy

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A: Given: r→t=ti^+2t-t2k^ and z=x2+y2

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A: Consider the given two spheres x-42+y-12+z2=27 and x-132+y-102+z+92=a are externally tangent to each…