1.8 Let D = (V, E) be a digraph with q edges. Show that E id(v) = od(v) = q. vĒV vEV

Q: 3 Which transformation turns the pre-image ABCD into the image A'B'C'D'? 2 o 10 11 12

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Q: Evaluate | 36e dz, where C is the polygonal path consisting of the line segments from z = Oto z =…

A:

Q: This graph shows the number of calories burned while riding a stationary bike. 100 80 60 L 40 20 4…

A: the meaning of the point (8,32) is: in 8  minutes, the number of calories burnt is 32.

Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: 8. Determine the dot product of u = [7,-4.1] and v = [3.-2.2].

A: Dot product is also known as the scalar product.

Q: Find 2 x²z ds, where C' is the line segment from (0,-3,-4) to (5,-2,-5). C

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Q: Evaluate Ja xdx + ydy + zdz where C is the line segment from (3, 4, 1) to (4, 5, — 1).

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Q: 9. 11 Let a1 = -6 a2 -4 |, and a3 = 11 -3 -4 The set {a1, a2, a3} will span R° unless h =

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Q: 9. AEFG has the vertices E(2, 6), F(8, 6), and g(6, 2). Find the orthocenter.

A: Let H be the Orthocenter of triangle EFG  So, (slope of HE) •(slope of GF) =-1

Q: What is the ALGEBRAIC RULE for REFLECTION over the line y = x? (х, у) —

A: This question is related to reflection of coordinates, We will solve it using given information.

Q: marked on the plane, any three of which were not collinear. These points determined 36 straight…

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Q: 4. Let A Sketch the collection of points Ar for i in the unit square.

A: Let A=1101. Sketch collection of points Ax¯ for x¯ in the unit square. Matrices maps a polygon to a…

Q: 12. Triangle STU with verlices S-1,-6), 70.-3), and U3,-4): S': U': T'

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Q: Let a = (-3, 0, 4) and 6 = (0,4,-4). Find the projection of 5 onto ā. proj₁ = 25

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Q: Let P(6, – 2, 2) and Q(0, 0, 0) be two points in R³. Find the distance between P and Q. - PQ

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Q: 16. Show whether point N lies on or outside the line AB N=(2,1.5,3), B (0,1,2), A (4,2,4) N=(2,2,5)…

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Q: Family OF lines parring through (0, -4)

A: Given that family of lines passing through (0,-4). To find differential equation based on above…

Q: Let u = and v = . Now, w = is a linear combination of i and v. That is, w = aju + azv. Determine…

A: Answer:

Q: 9. Let X Bin(4,.30), compute a. P(X=0) b. P(X= 1) C. P(X= 4)

A: Given that  Success of probability p=0.3 , q=1-p=0.7 Number of trials n=4 X~binomial (n,p)…

Q: 2. Find the siope of a ine witi tie given points (-Z, -9), (ū, -5), (Z, -i), (4, 3)

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Q: 4.3.15 Generate i.i.d. X1, X2, ..., X, distributed N(-4, 3) with n large (take n = 10° if possible).…

A: Consider the given information:Consider the i.i.d variables X1, X2, X3 distributed with mean -4…

Q: Find proj,u and scal,u by inspection without using formulas.

A: Given the graph

Q: Q2) Find the least -5quaras line y=fca) = Ax +B for the following data 2 2. -1 2. 3.

A:

Q: 8. If W = and V =, compute W x V.

A: To compute w*V from the given vectors.