If z =t cost, y =tsint, z=t, then x² + y² = t² cos²t+t² sin² t = t² = z², so the curve lies on the cone z² = x² + y². Since z = t, the curve is a spiral on this cone.

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A: The given integral is ∫74-x2dx

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A: I have explained everything with in the solution. Please go through that.

Q: P

A: Given,               Max.(Z)=10x+10ysubject to constraint,               5x+9y≥90…

Q: // a?dA where R {(x, y) | 16z² + 36y² < 576} Find

A: first we find limits of integration, than

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A: Let the co-ordinate of the intersection point be (x, y).  Then (x, y) lies both on the parabola and…

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A: Given,          ∫01∫x1y3+1dydx

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A: P( A given B) = P( A and B ) / P(B)  P = favorable(n) / total(N) Total ( N= 36 )

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Q: 35. Solve this auxiliary DE y"" – y" – 4y = 0,when x = 4, y = 0

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Q: 3 1-x Find [, [* (x³ + y)dydx

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Q: 2. Z=f(x,y)= Zx- 2xy+y" %3D h-Xン)1 2x<yミ4,05x<2 Find absolute max and min Draw a a graph

A: We will manipulate the constrained inequalities to form the function f(x,y) and from that we will…

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A: Here we have to find the value of the given integration.

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A: The given function is: f(x)=19x+9

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A: it is given that     d2xdt2=tet         (1)where x(0)=x'(0)=0integrate both side to equation (1)…

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Q: Evaluate [ T 1-x² x² + y² dydx.

A: Given: The integral is ∫022∫x1-x2x2+y2dydx. The aim is to evaluate the given integral. Concept:  The…

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A: Given: The given integral is ∫03∫021+x-12+4y2dydx. Integrate the integral with respect to y.…

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A: We are given an integral. Our aim is to evaluate the integral ∫04∫x21y3+1dydx.

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A: We have to first prove i2 = (-1).

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A: 3-D plot Contour Plot fx,y=x+yfx,y=x+yx≥0, y≥0x-y-x+y-x-yx≥0, y&lt;0x&lt;0, y≥0x&lt;0. y&lt;0

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A: A detailed solution is given below

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A: