Describe the convex hull of the set S of points in R² that satisfy the given conditions. Justify your answers. (Show that an arbitrary point p in S belongs to conv S.) a. y = 1/x and x > 1/2 b. y = sin x c. y = x/2 and x > 0 a.

Q: Let P=(−28.4,28), Q=(−24,x+4.29) and R=(−29.4−x,32) points in space. Check the alternative that…

A: The solution of above question is written in step2.

Q: P = (9,6,1) R = (9,8,5) Find the point such that R is the midpoint of PQ.

A: given R is midpoint of PQ  if two points is (x1,y1,z1) and (x2,y2,z2)then coordinates of midpoint is…

Q: Consider the points A(2, a,0), B(0,1,B),C(1,1,B) where aand Bare negative real numbers. Find a and…

A: To add or subtract, two or more vectors add or subtract the corresponding components of each vector.

Q: Let P = (0,0, 0), Q = (1, –1, –2), R = (2,1, 1). Find the area of the triangle PQR. area = Let T =…

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Q: Use a graphing utlity with wertor copa bilities to fnd Ux V U= (-1,4,1), v=(4,1,4) Shaw that uxV is…

A: Given vectors are u=-1,4,1v=4,1,4 To find their cross product.…

Q: Evaluate F. dr along the line segment C from P to Q. F = -8xi+y j; P(-2,0), Q(7,0) F• dr =

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Q: a circle is 24 cm and the distance is

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Q: Show that for all values of θ and φ, the point (a sinφcosθ, a sinφsinθ, a cosφ) lies on the sphere…

A: Show that for all values of θ and φ, the point (a sinφcosθ, a sinφsinθ, a cosφ) lies on the sphere…

Q: II1. Find all constants a for which the (smaller) angle between the planes ax + y + z =7 and x – y +…

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Q: A point starts at the location (1.5, 0) and moves counterclockwise along a circular path with a…

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Q: 2-89. If F = {3501 - 250j – 450k} N and cable AB is 9 m long, determine the x, y, z coordinates of…

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Q: Which line segment is a reflection of AB in the x-axis? D. IJ 3 GH C 1 A 4 x 1 2 G -4 -3 -2 -1 0 3…

A: Given : point for AB  : A (-1 , 1)  , B(-1 , 3)

Q: Derive the distance formula between a point S and a plane through point P. |n· PS| d = |n|

A: We have to derive the distance formula between a point S and a plane through point P.

Q: Each diagram shows a point P on the coordinate plane and its image P' under a translation T.…

A: There are three diagrams are given , we have to find translation T

Q: 5. Derive the distance formula between a point S and a plane through point P. |n PS d 3D |n|

A: Let Π be a plane passing through P with a normal vector n v is a vector parallel to n and passing…

Q: Find (x, y, z). (Let P = (8, 8, 0) and the Midpoint = (0, 2, 2).) (x, y, z) = (____________)

A: Given that the endpoints are (8, 8, 0) and (x, y, z). And the midpoint is = (0, 2, 2)

Q: Find the barycentric coordinates of p with respect to the affinely independent set of points that…

A: Given 11, 35, 06, p=23 let a=11, b=35, c=06, p=23 Now we write the points in augmented matrix form…

Q: 13. If B is the midpoint of AC, and AC= 8x- 20, find BC. 3x - 1 В

A: We will find BC as following.

Q: 1. For an angle to be in standard position, which of the following conditions MUST be satisfied? i.…

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Q: Find the area of the triangle with the given vertices. Use the fact that the area of the triangle…

A: Given The given vertices are Apply formula

Q: Ex.: Find the area of the triangle whose vertices are A(1,-1,0), B(2,1,-1) and C(-1, 1,2).

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Q: Verify . that the. functrun. u= 1+y. t.2? sais fies the thredimensianal.aplace eg. Ux. +Uyy +Uzz=o

A: Given u=1x2+y2+z2

Q: Let P = (1,2,1) and Q = (0,2,−3). What is the distance between P and Q?

A: Given: Let P = (1,2,1) and Q = (0,2,−3).

Q: B-N and u Compute the distance d from y to the line through u and the origin. Let y = d= 4 1 3 -4

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Q: Detevmine the com uergen e the isteguail -3% Xe dx

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Q: Use Green's Theorem to evaluate x dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: A contour diagram of z = f(x, y) is given in the figure. Determine whether fx, fy, fxx and fyy are…

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Q: Let A(0, 1) and B(1, 3). Find the point C such that 0 (24) (2-4) (-2,-4) O (2.5) O(-2-3) AC = 2AB.

A: given   A(0,1) B(1,3) let  C=(x,y)

Q: IV. Let s=2j+2k and t=2i+2j+hk. Find h such that the angle between s and t is Find the area of the…

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Q: curl f)•noA=? 15.°F = [y, x,z + x] around the triangle with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0)…

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