. Show that the plane minus the origin with the usual topology, that is R² − {(0,0)}, is homeomorphic to S¹ × R.

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Given, through the point (4, 2, -5) and perpendicular to the plane…

Q: 9. Find the equations of the planes that are parallel to 2.x - 2y + z = 5 such that the distance…

A: We will solve the problem.

Q: Let C be the positively oriented closed plane curve consisting of the line segment from (-3,0) to…

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Q: Determine the intersection if any between the line L₁: [x, y, z] = [3, 2, − 5] + r[0, 1, 4] and the…

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Q: The plane with equation:

A: Given, the plane with equation:                        r→=(1, 2, 3)+m(1, 2, 5)+n(1, -1, 3)…

Q: Find the value of k so that the line [x, y, z] = [2, -2, 0] + t[3, 5, k] is parallel to the plane 4x…

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Q: Find the plane through P = (4, −1, 9) containing the line r(t) =〈1, 4, −3〉+ t〈2, 1, 1〉.

A: The plane contains the line r(t)=1, 4, -3+ t2, 1, 1, so a vector in the plane is 2, 1, 1. The line…

Q: 3. Determine the intersection (if any) of the following planes. Show your work clearly ₁: 2x + 3y z…

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Q: 2. Find the plane that is orthogonal to the line : +1 = 431 = z and contains the point where l…

A: line parallel to the vector  V=⟨a,b,c⟩ passing through the point (x1,y1,z1) is given by the…

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: Is a subset of the plane {(x1, x2); x1 > 0, x1x2 ≥ 1} convex? Justify.

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Q: Find a plane containing the lines x = 3+ 21 x =1- 21 y = 4– 31 and y = 7+41 where -o <t<00, z =1-31.…

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Q: Find the derivative using the methods of Example 6 in the text. y = x8x y =

A: Consider the equation y=x8x We have to find the derivative of y=x8x Taking logarithmic both the…

Q: If the line L: X = 3 + 2t , Y= 2t , Z=t intersects the plane X+ 3y Z -4 in a point P. The…

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Q: Find the point at which the line (4, –1, 4) + t(4, 2, 3) intersects the plane 4x 5y + z = 88.

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Q: Michelle draws a restangle with a length of 6 cm. She draws a second rectangle with a length of 11…

A: Michelle draw 1st rectangle of length =6 cm 2nd rectangle=6+5=11cm And so on, she keep drawing more…

Q: Let L, be the line through the points (1,2,6) and (2,4,8). And let L2 be the line of intersection of…

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Q: ) fnd the equ. f Plane that Contains the two line S: X-1=3+ 6=そ X-リ=Z-4 and Passes through origin?…

A: Given problem:- find the equation of Plane that contains the two lines x - 1 = y + 6 = z ,    x= y =…

Q: 12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is…

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