Given that point T on the unit circle with center at (0, 0) has coordinates ( 4, 12 ), find the value asked for below. T(6,) (0,0)

Q: A circle has its center at (3,-2) is tangent to the line 3x+4y-26=0. Compute the point of tangency…

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Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: Find the equation of the tangent plane to the following surface at the given point. 4y cos (3ar 2)…

A: Given equation of surface and point is

Q: Find the coordinates of the point(s) on the curve y = Va + 3 that are closest to the point (8, 0). O…

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Q: 6) Graph the points z = x+ iy that satisfy the given conditions:- a) z-1= 2 b) z+ 1= 1 (ans. : on…

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

Q: Find a parameterization for the line segment joining points (0,3) and (12,0) using the angle 0 in…

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Q: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

Q: 1. Consider the curve C given by y = 5 + 2x3/2, 0 < x <1. (a) Find the length of the curve C.

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Q: Find the exact length of the curve. = 플Vy (y-3), 4sys 16 3

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Q: 4 Find a. the equations of the tangents to the circle x'+y +4x-2y-24 0 at the points where the…

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Q: Find the point(s) of intersection of the curves p = 6 /3 and r = 12 sin 0. OA. 63,3 OB. 6,- 27 6, 3…

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Q: Find the length of the arc of the curve from point P to point Q. x2 = (y − 8)3,  P(1, 9),  Q(8, 12)

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Q: Find the length (in units) of the curve y =    16 − x2between x = 0 and x = 2.

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Q: 4 Find a. the equations of the tangents to the circle x + y +4x - 2y - 24 = 0 at the points where…

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Q: If the distance from P(1, 0) to the point T(1 ) is x, determine the coordinates P(1,0) of the point…

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Q: (b) Eliminate the parameter to find a Cartesian equation of the curve.   for  −5 ≤ y ≤ −1

A: The parametric equation of curve are x=1-t2 y=t-3

Q: 1. Point K is located at (4. 2, 0. 3)and point Lis located at (5. 8, -0.6). What is the location of…

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Q: Find the exact length of the curve. 23/2, Osxs 6

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Q: Find the length of the arc of the curve from point P to point Q. x2 = (y − 4)3,  P(1, 5),  Q(27,…

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Q: 9. Find the point (x, y) on the line y = 2x + 3 such that the distance from (x, y) to (1, 1) is as…

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Q: 1. Find the standard form of the equation of the circle tangent to both axes at (-3,0) and (0,3).

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Q: Let F=-yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by…

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Q: 5) Find the distance between the pole and the point (r, 0) = (-1, ). %3D

A: A detailed solution is given below.

Q: If C is a circle of radius 3 centered at the point ( 3, -4 ), then evaluate £(3y – ein(=) ) dz +…

A: The integral is given by ∮C3y-esinxdx+10x-siny3+ydy Where, C is a circle of radius 3 centered at the…

Q: 5. In the standard (x, y) coordinate plane, the midpoint of LM is at (4, –4) and L is at (1,3). What…

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Q: Find the tangent plane to the equation z = 6e" -20 at the point (4, 8, 6)

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Q: 6. Prove (by plot) the equation (x²+y²=16) is the circle in 2D , and cylindrical in 3D.

A: We will answer the first question since we don't answer multiple questions at a time. Please…

Q: Let C be the curve.

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Q: If C is a circle of radius 9 centered at the point ( -5, 5 ), then evaluate $ (2y – esin ( x ) ) dæ…

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Q: A lamp is placed three units to the right of the y-axis, and a shadow is cast by the elliptical…

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Q: 7.) Find the shortest distance between (4,2) and the curve y? = 8x.

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Q: C is the part of the circle of radius 3 in the first quadrant from (3,0) to (0,3) and F = (1, -y),…

A: Given, C is part of circle of radius 3 in the first quadrant from (3,0) to (0,3) and F=[1,-y] The…

Q: Find the length of the tangent to the circle x² + y² − 2x − 3y − 1 = 0 from the point (2, 5)

A: Solution- The equation of the circle x2+y2-2x-3y-1=0 The point =2,5 length of the tangent

Q: 3. For the curve x – xy² = 8e²4, do the following | a) Verify that the point (2,0) is on this curve.

A: Given, curve x3-xy2=8e2y

Q: The equation of the tangent plane to the surfice. -yeV + = 0 at the point (0,1,1) is ar + by + cz =…

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Q: Find an equation of the curve in the xy-plane that passes through the point (2, 3) and has, at every…

A: integration

Q: Integrate counterclockwise around the unit circle (|z| = 1) and choose from the options below that…

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Q: Find the coordinates of the point/s on the curve y = 2x? which are closest to the point (9,0).

A: We have to find the closet point to the point    (9, 0)

Q: 2. Let be the part of the circle x² + y² = 9 from (-3,0) to (0, 3) in the upper left quadrant.…

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Q: Find an equation of the tangent plane to the surface at the given point. z = 8 – (3, –4, 4)

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Q: Find the equation of the osculating circle bent X=y^2-y at point (0,1) .

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Q: By means of Lagrange's formula, prove that 1 Yo = - 1 - [2 (y₁+y_₁). (Y3 - y₁) 2 -Y₁) - 2 (Y-₁-y-3)…

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Q: Find the length of the curve ƒ1x2= x3&gt;2 between x = 0 and x = 4 (as shown).

A: Given curve is fx=x32. To find the length of curve between x=0 and x=4. Solution: We know that…

Q: A curve on the ry-plane passes through the point (0, a) for some number a, and has the property that…

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Q: 1 ,3/2 y92 - y"2 between the points 3 ,1 and (6,9). 3 Find the length of the curve x=-y" 1/2

A: Given : The curve is : x=13y32-y12  We have to find the length of the given curve between the points…

Q: 4 Find a. the equations of the tangents to the circle x +y +4x-2y – 24 = 0 at the points where the…

A: Given,  (a) Equation of the circle   x2+y2+4x-2y-24 = 0  We have to find the equations of tangents…

Q: 1. Find the distance from point P to AB. Show your work. Ay C(3, 4) B(1, 2) 6 x А(-3, —2) Р(5, — 2)

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Q: find the length of the curve given x = (y/4)2 - 2 ln (y/4), 4>= y>=12.

A: The arc of length of curve is given byL = ∫y0y11+dxdy2dyhere y0=4 and y0=12 Given function…

Q: If C is a circle of radius 3 centered at the point (-4, 2 ), then evaluate £ (2y - eh (=) ) da + (6z…

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Q: If C is a circle of radius 6 centered at the point ( 3, -2 ), then evaluate 6y – esin ( z ) ) dæ +…

A: Given if C is a circle of radius 6 centered at point 3,-2 then  We have to evaluate…