In ARST, SV bisects y ZRST. Find the coordinates of point T in terms of a. S (a, a) 2a T?, ?) V (2, 0) R (a, 0)

Q: In what plane does the curve r(t) = t i + t2 k lie?

A: r(t) = t i + t2 k We need to find the plane of the curve located in?

Q: Find the midpoint M of CD M = (, ) X1+X2 Y1 %3D 21 C = (-2,-10) D = (-6,0) M = ([ ? ], [ ]) Enter…

A: Explanation of the answer is as follows

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Q: The distance from a point S(xo,yo, Zo) to a plane M: ax + by + cz + d = 0 is given by |n · PS| d In|…

A: From a point S(x0,y0,z0) to the plane M = ax+by+cz+d=0 Let S1=x1,y1z1 be any point in the given…

Q: Q7. What angle does the line of intersection of the plane O make with the nonnegative 2x + y - z = 0…

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Q: XZWY is a rhombus with diagonals XW and ZY intersecting at point M. Given YMX = 3p + 6, solve for…

A: diagonals of rhombus makes right angle at ntersection point

Q: Y is the midpoint of XZ and V is the midpoint of WZ. If VY = 32, what is WX? WX Submit

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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: For what positive value of c is the acute angle between the plane containing the points A(0,0,1),…

A: The equation of the plane passing through the three non-colinear points x1,y1,z1, x2,y2,z2, and…

Q: Find the points on the cone z = x+y' that are closest to the point (-2,3,0) 22

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Q: Fin He ara at tHe surface af the portion oF Hae Plane 2= 5-2X -9y

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Q: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

Q: Determine the location of a point (x, y, z) that satisfies the condition  ∣y∣ ≤ 3

A: If ∣y∣ ≤ 3 the point lies with in 3 units from xz plane on left side if y < 3 , or within 3 units…

Q: Use Green's Theorem to evaluate (V1+r) dr+2ry dy, where C is the triangle with vertices (0, 0),…

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Q: When the plane x = 3 passes through the surface x² + y? + 2? = 64, the curve that forms from…

A: Given, the plane x = 3 passes through the surface x2 + y2 + z2 = 64 . The intersection of plane x =…

Q: Which is the fourth point on plane TSW? T. U O Y

A: A plane is a 2-dimensional surface. It can have an infinite number of points. A plane is composed of…

Q: Evaluate e fxds, v ds, where C is a. the straight line segment x=t, y = from (0,0) to (8,4) 2' b.…

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Q: Let f (z) = 33O = Q A = 10and B= 10 + 10iet C be the contour composed of the line segments OAand…

A: The given problem is to evaluate the complex integral of the given function over the given semi…

Q: Use Eq. (7) to find the point P nearest to Q = (2, 1, 2) on the planex + y + z = 1.

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Q: Explain.

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Q: The midpoint of AB is M(0, –4). If the coordinates of A are (2, –1), what are the coordinates of B?…

A: Given- The midpoint of ABis M0,-4. To Find- The coordinate of point B, if the coodinate of the point…

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 points on the cone z = x +y? that are closest to the point (3,-2,0)

A: Solve the following

Q: Use Stoke 's Theorem to evaluate [ . dr, where v = y²i + xyj + xzk, and c is the bounding curve of…

A: We have to solve the given problem by using stokes theorem.

Q: ARST is reflected across a line so that T'has coordinates (1, 3). What are the Coordinates of S'? R…

A: Given: R=-4,4S=0,-2T=-3,-1

Q: Which is the fourth point on plane TSW? S T U Y O Y O W

A: we have, As we can see that a cuboid is given and their vertex are assigned by some letters. Always…

Q: Show that the minimum distance from the origin to a point on the plane ax + by + cz = d is |d| Ja? +…

A: Given :               ax + by + cz = d         We know that minimum distance (p) of a point x1,y1,z1…

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Q: Find an equation for the projection of the curve on yz plane. O y + z? = 3 O y? + z? = 4 O y? + z? =…

A: For projection in yz plane equation must be in terms of y and z only. Here x=t y=3 cos t z=3 sin t

Q: Find the point lying on the intersection of the plane x + y +z = 0 and the sphere x2 + y? + z? = 25…

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Q: Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N(8, 0).

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Q: Based on the trapezoid shown in the standard (x, y) coordinate plane above, what is the midpoint of…

A: From the graph, it is clear that B is at (-1,2) and D is at (5,-2) Now, the midpoint formula gives…

Q: Let R be the triangle in the xy-plane with vertices (0,0),(0, 1),(1,0). Find C[n(2 – x – y) dA.

A: Given vertices of triangle now we have to find the area as shown below

Q: Find the points on the cone z 22 = x2 + y? that are closest to the point (-3,1,0)

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Q: coordinates

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Q: Find the projection in the ry plane of the curve of intersection of the surfaces 2z2 = r? + y? and…

A: Let's find.

Q: If a? + b² + c² =1, then the distance from P (x0, y0, z0) to the plane ax + by + cz = 0 is |. |.…

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Q: Consider the projection from the origin of the straight line y + x = 2 on a straight line y + 2x =…

A: Graph formed by

Q: Show that the point (x0 , y0) closest to the origin on the line ax+ by =c has coordinates

A: Distance between x0, y0 and origin (0, 0) is, D=x0-02+y0-02D=x02+y02D2=x02+y02f=x02+y02…

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: Find the points on the cone z = x° + y° that are closest to the point (1,-1,0) %3D +1

A: Given,

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Q: Prove that the perpendicular distance from the point P(xo, Yo, 20) to the plane with equation ar +…

A: Here we use the distance formula between two points.

Q: Let C be the curve of intersection of the parabolic cylinder x? = 2y, and the surface 3z = xy. Find…

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Q: The distance from a point S(xo, Yo, Zo) to a plane M: ax + by + cz + d = 0 is given by |n PS| d =…

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Q: Calculate both sides of Green's Theorem when F = [-x²y, xy²] and y positively oriented circle x? +…

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Q: Let h VI and y: 8 For what value(s) of h, is y in the plane generated by vị and v2?

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Q: Let fiz) = x2 + iy? where x and y are the real and imaginary parts, respectively of z and C is a…

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