1. 2p-2 = ¹+¹ (mod p) p+1 2. (1.) k = 0 (mod p), whenever k = {1, 2,. ,p-1}

Q: In its natural condition a soil sample has a mass of 2290 g and a volume of 1.15 x 10-³ m³. After…

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Q: 11. Simplify the following expressions: 11.1 z=¬¬(ave) v (πv¬0)) 11.2 z=(¬α ^ß) v (B^¬μ) V(B^H) Z=

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Q: 4. 3 log₂ 4-log3 9 + log, 64 5. (log, 25-3log, 128) + 2 log, 343 single logarithm.

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Q: Chapter 2, exercise 11.1: Let x be an element of order r of a group G and let y be an element of a…

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Q: In Exercises 9, 10, 11, and 12, show that the graph is not planar. 9.

A: A graph is not planar iff it contains k5 or k3:3 as a minor

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Q: Prove that for any graph G, y(G) ≤ 2ir(G)-1.

A: Please find the attached solution

Q: 10. Say Z₁=2+15i and z2 = 3-6i, find Z1*Z2*

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Q: ]i+ 5x sec² (xy) —- 3] + [6 y j+(6xz+2) e³x² –3]k, For F(x, y, z)=[5ysec²(xy)+6z²e³² find the curl…

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Q: a finite group and Z is its centre, then class equation of G is expressi o(G) o(G) = o(Z) + E…

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Q: C. Write down a sequence for the number of shapes/dots in each pattern. Explain how to obtain the…

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Q: Find the least squares line for data (1,1), (2,1.5),(3,3),(4,4.5),(5,5). Question. Identify the Y…

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Q: of the function f(x) =e* the value of e 0.2 2. Use the linearization at a=0 to approximate

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Q: The answer is not shown for the 2

A: Left end sum=sum of areas of the rectangles      =7X10+9.8X10+13.2X10+18.1X10+20.5X10      =68.6X10…

Q: Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the…

A: Given initial value problem is              y'=x2y-12y2     with    y0=3        Let…

Q: Find the root of the function using the following methods. c- One-Point Iteration Method

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Q: Calculate the following limits, or explain why they diverge. x² - 4 x+2x² 3x + 2 (d) lim (e) lim x 0…

A: Given : d) limx→2x2-4x2-3x+2 e) limx→∞xx To Find : The limit or explain why they diverge.

Q: a. f(t) = cos(2t). Find F(s) b. g(t) = e²t sin(3t). Find G(s) c. H(s) = 3s +1 s² - 2s + 5* Find h(t)

A: We have to find the Laplace transform and inverse Laplace transform.

Q: Set up (do not evaluate) the iterated triple integral in spherical coordinates that gives the mass…

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Q: Analyze the pattern shown. " * #*. A. Identify two expressions that represent this pattern. B.…

A: The general form of: Exponential functions: y=abx. Quadratic functions: y=ax2+bx+c. Linear…

Q: Zs. Explain why they are generators. (7.3) Let G be a group, and let H and K be subgroups of G.…

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Q: Use finite difference to determine the equation for the polynomial corresponding to the table of…

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Q: Q17B. Define the sets A, B, C, and D as shown. Find A U (B n D). A W C S C Q 3 р a g D h f B…

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Q: The area A of the region S that lies under the graph of the continuous function is the limit of the…

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Q: QUESTION 1 Consider the integral I = dz, direction. dz, where C is the circle |z| = 3 taken in the…

A: The given integral is, I=∫C1z2dz   where C is the curve z=3 taken in counter-clockwise. To Find: The…

Q: 4. Solve the following boundary value and initial value problem for wave equation Utt-c²Uzz = 0, 0 0…

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Q: How much should Kelsey have in a savings account that is earning 3.75% compounded monthly, if she…

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Q: Four partners are dividing a piece of land that each see as worth $124,000 among themselves. They…

A: Four partners are dividing a piece of land that each see as worth $1,24,000 among themselves. They…

Q: Solve the Goursat problem:    Utt − c 2Uxx = 0 u|x−ct=0 = x 2 u|x+ct=0 = x 4 . Hint: Use the…

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Q: Write out the third order Taylor poly- nomial about 0 to approximate e−0.5. (i) Show that the…

A: Introduction: The most crucial use of Taylor series is probably to estimate functions using their…

Q: Let A and B be independent events with P(A): 1 == 6 and P(B) = 1 == 5 Find P(An B) and P(A U B). ...

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Q: Prove that the inverse of any element in a group is unique

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Q: (7.4) For the group Z6, find two subgroups whose union is not a subgroup.

A: This is a problem of the Group Theory.

Q: Given the following equations, with (1,1) as initial values: f(x,y) = 3x² + 2y²-25 g(x,y) = 2x²-y-15…

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Q: Knowing that S+x x² e ²² dx. +∞ +∞ Se-¹² dx = √√2π, find x2 е

A: Given:  ∫-∞∞e-x22dx=2πTo find: ∫-∞∞x2e-x22dx

Q: 2. Using the function f(x) = 2x+cos³ (x) - sin(x) bounded by x = 4 to x = 10 Find the area using…

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Q: 81 = 7 82 = 3 For k starting at 0 and ending with 8: Sk = (k-1) gk-1 + gk-2 What is the last term,…

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Q: A bag contains 2 gold marbles, 9 silver marbles, and 25 black marbles. Someone offers to play this…

A: Given that, Number of gold marble=2 Number of silver marble =9 Number of black marble =25 Given that…

Q: (1) Let E= R, fn = X[0,1], and f = X[1,2]. Check which converse implications do not hold in Question…

A: Please find the attached image.

Q: Determine if each of the following is true or false. (a) G= 12x27-8y] is a gradient field. False…

A: Given the field, G→=12x2i→-8yj→ To check whether it is conservative, it needs to checked that for a…

Q: 1. Consider R4 with the usual dot product. a. Find a basis for the orthogonal complement of the…

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Q: 5 [] Let S be the parallelogram determined by the vectors b₁ = The area of the image of S under the…

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Q: The table represents 2054 randomly chosen people age 25 years or older in regard to educational…

A: We know that Probability= No. of favourable outcomes/                          No. of total…

Q: if sis a group of order p", then its center 24, peing a primes

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Q: Q9. Consider the following algorithm: sum = 0 For j starting at 1 and ending with 15: sum = sum +…

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Q: Show that Sn is path-connected, by constructing for any two points x, y € Sn an explicit path…

A: We shall answer first Que only asper answering guidelines. For others kindly post again by…

Q: Compute the following integral by hand, using an appropriately chosen contour integral in the…

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Q: 1. Solve the initial value problem on the real line Utt - Uzz = sin x xx U(x,0) = 0 Ut(x,0) = sin x

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