5 Find the valume of the Sotids abtaind by-revelving the Yegion in the firstquadrand boundby the Curves about theYasxis Y=2=x² and Y X2

Q: By using Green's theorem evaluate £ (Ary – y") dr + (** + 3ry) dy where C is a closed curve starting…

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Q: 3) Find the exact length of the curve: x = y = In(1+t); 0<t<2.

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Q: And the Vorume of the solid gererated by rovolung the reglon boundid by the given ines't (urves…

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Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y-xy= 0 2y+5x+x-x'y² =…

A: Find your answer below

Q: 8. Show that the one parameter family of curves y² = 4k(k + x) (k E R) are self orthog- onal.

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Q: Suppose the closed curve C in R? starts at the point (-1,1), goes along the parabola y = x2 to the…

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Q: rea under the curve y = 2x – x² from x = 1 to x = 2 with n = 4 %3D tonglon

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Q: . Find the length of the curve defined by R(t) = (3t+1, 4t3/2, 4-3+2) from the point (1,0, 4) to…

A: Note : The length L of a curve r(t)→=(x(t) , y(t)  ,z(t) )  from t=a  , t=b is given by…

Q: 2 32 |for 1st<3. length of the curve c(t) =| In t,-t"

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Q: 10. Evaluate the integral cz(z-1) where C is a simple closed curve in the positive direction that…

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Q: Evaluate the line integral 32xy ds, where C is the portion of the parabola y = x² from (-1,1) to…

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Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

Q: 4. Graph the surface 1 = y² + z² – by first sketching at least three cross sections in each of the…

A: Graph the surface by using a 3D graphing calculator like desmos. Three cross sections in xy plane…

Q: find the to the the tang horizontal. X-volves at which the _9x+2 Y = ex curve ent

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Q: Find the exact sülution fur ylz Xtzy

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Q: 17) Find the area of te senface genereted by revolving the curve X=3¢, y= 2f about fue x-qxis on tue…

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Q: For a χ2-curve with 19 degrees of freedom, find the χ2-value that has area a. 0.025 to its right. b.…

A: a) Degrees of freedom is 19 The chi-square value that has area 0.025 to its right is given below:…

Q: 8how that the square of the leng point on the curve by = (x + a)° , length of the subnormal at that

A: Subnormal and Sub tangent: Allow y=f(x) to be the differentiable curve at point P. Let the tangent…

Q: 4. Graph the surface 1 = y² + z² by first sketching at least three cross sections in each of the 4…

A: We have to graph the surface 1=y2+z2-x24 by sketching at least three cross-sections in each of the…

Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

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Q: 3.) Consider the fllowing tewe surtaces. 2=2xy,82-sy -82= -13 a) Show that the surkaces intersect at…

A: Given: Two surfaces z=2xy2 and 8x2-5y2-8z=-13. The surfaces intersect at point (a, b, c) if both the…

Q: 1.13 Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

A: The given function is x4dx+xydy By green's theorem, the integral becomes, ∫06∫06∂M∂y-∂N∂xdxdy where…

Q: Prove that the following curves are intersecting with a right angle: 5y-2x+ y -x²y =0 2y+5x+ x* –…

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Q: 9. Evaluate the line integral / (2x – 3y) ds; where C is the line segment from (-1,0) to (0, 1)…

A: 9.

Q: Consider the region bounded by the Xxy curves J 3-2x, and y=3, %3D

A: Calculating the area of the region bounded by the curves

Q: 9 Find the length of the curve x = on 3sys5. %3D 27' 4y The length of the curve x = 9 - on 3sys 5 is…

A: We have to find arc length of give curve.

Q: 7.Find the maximum and minimum distances from (0,0) to the curve 5x2+6xy+5y2=8

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Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral 2|(xdx…

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Q: Use the Green's Theorem to evaluate the line integral 2xydx + x² – y² dy where C is the curve…

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Q: By using Green's theorem evaluate £ (Ary – y) dr + (** + 3ry) dy where C is a closed curve starting…

A: Green's theorem in a plane: If D is a region inclosed by a closed curve C then ∮C u dx+v dy=∫∫D…

Q: 1. Compute (1/zy, 1/(z + y))- dr along the curve (t, t2). 1<ts4

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Q: 3. Discuss how to evaluate f () dz , where C is a simple closed curve C=10 enclosing the origin.

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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

Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y²-x²y = 0 2y +…

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Q: 11 Calculate the line integral f Gy)ds for the given junc rion and path xiyl=xy KHt)=<3+,2t=-37 for

A: r(t)=&lt;3t,2t-3&gt;=&lt;0,-3&gt;+t&lt;3,2&gt; x(t)=3t  and y(t)=2t-3 ds=32+22dt=13dt 0≤t≤1

Q: 6 - Find the length of the curve y = (x)7 from the x = 0 to x = 4. a) O 8/27(10^(3/2)+2) b) O…

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Q: The area bounded by the curve y = 6z and the lines a = 5 and z= 8 above the T aris is 234.00 square…

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Q: 3. Given the closed curve defined by y = vx in the first quarter up to 1000 = x (area production),…

A: FIND: a) how many unit squares it contains b) number of squares needed in the cover

Q: 6. Find the area and centroidal distances of the curve that lies between the equations y-4-x^2 and…

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Q: Consider Gollow Sx2 of Eunluate y when y to Find y Evalnate of when 11 Write Mhe etios to the Write…

A: Now when x = 1, Now differentiating given equation with respect to x, we get Now when x = 1,

Q: Find the Võlumé of thé šólid generated by revolving the shaded region about the given axi About the…

A: Explanation: If we rotate the shaded region about the x-axis, we will get the cone shape. Height of…

Q: 1) The plane of 2 = x*+y² X+y+2 = 12 and %3D inter sect along d para boloid Find the curve. lowest…

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Q: .11 Compute (1/ry, 1/(x + y)) · dr along the curve (2t, 5t), 1 < t < 4.

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Q: Use Green's theorem to find the k number that satisfies (k + 3) ∫C((k/2)*(x^k)*(y^2))dx + ((yx^(k +…

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Q: Obtain the dirfferential equation of the family of plain curves given 1. All circles passing…

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Q: gjwnich of the following ye-3x =4 nd line is the grea of the region between 3A-24=11 ? Curve

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Q: 5. Show that the following orthogonal families of curves: are x² + y² : = ax, x² + y? = by

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Q: THE DiffieRENITAL ECLATDOM WITH INITIAL conoirDON. dy- XSENX こ dx 3.2

A: Given query is to find the solution of the differential equation.

Q: The area under the curve y = 3z bounded by the linesI = 3 and z= 7 above the z- azis is O 174.00…

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