1. Answer the following questions based on the graph below: a f d e a) Find the number of verticals and Find the number of edges. B) Find the degree of each vertex. C) Represent the graph with an adjacency matrix.

Q: Assume that x ∈ Z. Consider the following: If x is odd, then 2 does not divide x. (a) Prove the…

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Q: Suppose that liquid flows into a tank at a variable rate of q(t) litre per second. It can be shown…

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Q: Q3/ Solve the following equation by (Finite Difference Method), choose (h= 0.5) d²y + 2y = 3 , y (0)…

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Q: QI) Evaluate the integral , S, dy dx using polar coordinate

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Q: Q3) Evaluate triple integral S, y(x2 - y²)dz dx dy.

A: To Evaluate: ∫01∫y1∫-y2x2x2-y2dz dx dy

Q: . i. Is 221 – 1 a prime? Give your reason. Note 21 = 3 x 7 is not prime. ii. Is 219 – 1 a prime?…

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Q: e- lim

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Q: A coin is tossed three times. Let Hand T be the head and tail shown on the side of the coin facing…

A: We have to find (C union B')

Q: 2) Use properties of circles, triangles and/or angles to find the following. (Not to scale). 120°…

A: Solution

Q: Q3/ Solve the following equation by (Finite Difference Method), choose (h= 0.5) * + 2y = 3 ,y (0) =…

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Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 5 6 Y 4 9 10 10 8 O3

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Q: 14. Briefly explain why || d || == || c || when d=axb and || a ||=1. a b d

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Q: Q1/ Estimate f (1.72) from the given data using Newton's Backward Difference Formula: 1.7 1.8 1.9…

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Q: Q1) Evaluate the integral S dy dx using polar coordinate

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Q: Find plane area inside the polar functionr 2 and outside polar function r 2 sin +0) in second…

A: Area using polar coordinates is given by  A=∫∫A r dr dθwhere x=r cos θy=r sin θ

Q: Given 4x –9y =1. Find by implicit differentiation. dx

A: Given equation is 4x2 - 9y2 = 1

Q: Find the values of a and b for the curve r'y+ay =b if the point (1,1) is on its graph and the…

A: Let us consider the given curve y=f(x) The slope of the tangent to the given curve at point (a, b)…

Q: Instructions: • Write the GIVEN with their respective symbols and units. • Do not skip the…

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Q: 2 -1 3 -1 3 If A = and B = 2 2 -1 find: ЗА - 2В A +2 (В — А) -5 (A + 2B)

A: Given matrices are A = 2-13012  and  B = -13-12-11

Q: Q4/ solve the equation by Newton -Raphson Method: F(x) = x* - 5x + 65 , start at x =2, accuracy…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: We have to find Distance.

Q: Give the VALUE only. No need to include the unit. * A chemical manufacturer sells sulfuric acid in…

A: We have Cx=100000+50x+0.0025x2 Now, the price is $100 per unit and production is of x units, then…

Q: Evaluate the triple integral zdV, where E is bounded by the cylinder y +z2 = 16 and the planes E x =…

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Q: Suppose two cylindrical tubes with the same diameter intersect at right angles. If the diameter of…

A: To find the volume of the common part between two cylindrical tubes kept at 90° .

Q: Q2/ Fit a second - order polynomial to the data in the following table: 5 6 4 2 9 7 Y 2 8 3 4 -1 8 4

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Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: Q4) Find plane area inside polar function r 2 and outside polar function r= -2sine in third quarter.

A: We know the relation between polar and cartesian coordinates system, x = rcos(θ)   ,     y =…

Q: Use the vectorized Euler method with h = 0.25 to find an approximation for the solution to the given…

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Q: Pl Use fixed -point method to find the real root of equation 3. X=6X-4 on the interval Co,)) put…

A: Solution

Q: X – 1 is to be se ethod. If the ini en the absolute ation is

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Q: If two complex numbers are (*+) 21 5 + 5/3i) and z2 = + 2i 21 then radian value of the argument of…

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Q: Q5) Find volume of body bounded by z2 + y2 + x2 = 9.

A: Given equation is x2 + y2 + z2 = 9

Q: Q2: Find the integration by applying substitution method: 7 dX (X - 1)VX- 2x - 48

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Q: ii, 20 coins are flipped each with a probability of 0.5 that it will be heads. What is the standard…

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Q: Area = 2 Area = 1. Area = 3 3 5 7 Area = 7 Graph of f' The figure above shows the graph of f', the…

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Q: у (0) %3D —2, у(0) ||

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Q: Find the Area bounded by the curves y2 = x and x = 2y – y?.

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Q: 3. For each of the following entities, say whether it is a member of P(N), and explain why or why…

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Q: Continue the two sequences of numbers below and find an equation to each of the sequences 1 2 3 4 5…

A: 1. In first. 1+1=2 2+3=5 5+4=9 9+5=14 14+6=20 20+7=27 Hence the eqution is  an=an-1+n

Q: SKet the cerve r²= 29° cOS 20

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Q: d. Z,Z3 + Z4 e. (Z1 + Z3)/(Z2 - Z4)

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Q: r1.5 (3-y dx dy using polar coordinate Q1) Evaluate the integral o

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Q: Give the VALUE only. No need to include the unit. Let s, =15r +10r +20 and s, = 5r + 40r , t 2 0, be…

A: Given positions functions are SA = 15t2 + 10t + 20SB = 5t2 + 40t

Q: Q2/ Fit a second - order polynomial to the data in the following table: 6 1 4 9 7 Y 2 8 3 4 -1 8 4

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Q: Q1) Evaluate the integral Sdy dx using polar coordinate

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Q: Find at least three examples of Golden Rectangles in your surroundings.  Provide sketches and…

A: Given below clear explanation

Q: Give example open set is compact

A: Note that, every compact set in R is closed and bounded. Example of compact open set is attached in…

Q: Q1) Evaluate the integral dy dx using polar coordinate

A: Solution

Q: Q3/ Solve the following equation by (Finite Difference Method), choose (h= 0.5) + 2y = 3 , y (0) =…

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Q: Q4) Find plane area inside polar function r = 2 and outside polar function r = -2sine in third…

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