3. Explain what is wrong with the following statement: If R,T are corresponding regions in the xy and st planes, the change of coordinates * = t°, y = s leads to the formula (x+ 2y)dzdy = (t + 2s)(-31)dsdt R.

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: 8. , (2x – y) dA, where R is the region in the first quadrant enclosed by the circle x? + y² = 4 and…

A: Dear bartleby student ,According to bartleby rule Answer the first question, unless the student has…

Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

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Q: Identify and sketch the graph of the following SURFACES. x² + y² = sin²z, z = [0, π]

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Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…

A: given:

Q: 5. Find the area and centroidal distances of the curve that lies between he equations y%3D4-x^2 and…

A: The region bounded by curves y=4-x2andy=x+2 To find the area and centroidal distances.

Q: 10) The line x = -1+t,y = 2 +t,z 2t + 7 intersects the surface z = x2 + y?. Find the cosine of the…

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Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

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Q: 2. Evaluateſ. a+ (z+30:) dz along C which is the circle |z + 3i| = 3, counterclockwise. %3D (z+3i)

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Q: D A Find thepolar eavation for the cartesian curve (x²ty) - A)r-4 cos o =4x. Br°=4 cos e c)r?=4cos o…

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Q: Find the acute angle between the planes x + y = 1 and y + z = 1.

A: The acute angle between the planes x + y = 1 andy + z = 1. Use the cosine definition of the dot…

Q: 35. In the xy-plane, the circles with equations (x-3)² +y² = 11. and (x+2)² + y² = r² |3D %3D 2re…

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Q: 4 and Consider the region in the second and third quadrants between the circles x² + y² = x² + y² =…

A: Concept: cartesian coordinates can be converted into polar coordinates using trigonometric functions…

Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

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Q: Find the equation of the tangent plane to the surface z = 4 +y? at the point (2,-3, 10) Ox+ 4y- z =…

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Q: Evaluate [. 2y² + 4z² ds, where o is the first octant portion of a cone z = x² + y2 with height of…

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Q: 2: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x–2)²+(y-3)² = 4 | a) Using Green's Theorem

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Q: 8., (x + y) dA, where R is the region that lies to the left of the y-axis between the circles x? +…

A: As you have asked to answer question 8, we will answer question 8.Question 8.The given integral…

Q: 2) Consider the oriented curve C given by C = C1uC2, where C2 is obtained by intersecting the…

A: We will first parametrize the curves C1 &amp; C2 then substitute the x,y,z values into the line…

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A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: Find the acute angle between the planes 3x + y + z = 0 and x − 2y + z

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Q: b) If we are at the point (1, 2, 4) on the surface z = xy², and we move a short distance in the…

A: Please check step 2 for solution.!

Q: 12. Evaluate 3x ds where C is the parabolic are along y from P(0,0) to Q(2, 2).

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Q: A surface in R³ is defined by the equation 4z = x² + 4y².

A: Given:-                 The surface in  is given by  . Sketch the intersections (traces) of this…

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Q: 3. z = (c

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Q: r(t) = 6ti + 3/2ťj+2¢k, 0<t<1

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Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: 4. Evaluate y ds where C is the upper half of circle x² + y² = 9, traversed in the counterclockwise…

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Q: I. Find the acute angle between the given curves. 2. x'y+4a° y=8anx²=4 ay 3. x*y+4y=8Ax²y=4

A: We have to find the acute angle between the given curves: x2y+4y=8 and x2y=4

Q: 2.5 What is the distance between two parallel hyperplanes {r E R" | a"x = b1} and {r E R" | a"x =…

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Q: /| 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y?…

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Q: The region S = (x, y (x- 2) + y² < 4 is rotated about the line x = 5.

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Q: The area bounded by the curve y = 4r and the lines z = 2 and I=8 above the I- aris is O 240.00…

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Q: VI 23) Consider the region in the second quadrant between the ciréies X²+y?=4ard x?7y==25 ?-25, and…

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Q: 3. Evaluate ff, (x² + y²)³/²dA, where D is the region in the first quadrant bounded by the x-axis,…

A: Given problem:- Evaluate ∫∫D (x² + y²)3/2 dA, where D is the region in the first quadrant bounded by…

Q: 3. Use the Secant method on the circle function (x + 1)²+(y – 2)²= 16 to %3D find the intersection…

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Q: Evaluate f.y ds where C is the upper half of circle x? +y² = 9, traversed in the counterclockwise…

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Q: 6.2 Finl the Voune of the Selid enclosed by the curves y=eX, y=0 x=0,'= "about the x-axs.

A: Given: y=ex, y=0, x=0, x=1 From the given curves the bounded region is as shown below; Apply the…

Q: 5. Evaluate (y +tan x)dx+(x -2ry+y)dy, where C is the circler +y' =4 and is oriented in a positive…

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Q: What is the equation of the circle concentric with circle(x-2)2 + (y+1)2 = 5 that is tangent to the…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: b) Find the points on the curve 2 17x + 12xy + 8y“ = 100| that are farthest away from the origin…

A: Substitute x = rcosθ and y= rsinθ

Q: Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and…

A: answer is in next step. please give a like !!

Q: T 1) Reflect quadrilateral ABCD across the y-ar reflection on the coordinate plane to the right. new…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 10. Given the expression x* – 3x + 7 = y* on the interval [3,5], determine the surface of revolution…

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Q: Q2 Calculate 8- Z -dz, (4 – 2) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: х2, у3D 12 — х, х 3D 0, around line y — -2

A: the function given to us is y = x2 and the line about which it revolves is y = -2 we have to use the…