Q4:a) Which of the following is a planar gaph? and what the chromatic number x(G) of each graph? 1) Cn 2) K5 3) K33 4) KA

Q: Let f(x) = STA 0, if if xe Q or x = 0 m x = in lowest term' n . Compute for ff.

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Q: Give an example of a differentiable function g: R → R such that f is strictly ncreasing on R but g'…

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Q: Q4. Paul took some money to buy some bags. Each bag cost the same price. If he bought 7 bags, he…

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Q: 2. Let AM₁ (R) be given. (a) If AA=0, prove that A-0₁. Does this hold if A € M₁(C)? (b) Suppose that…

A: This is the problem of Linear Algebra and Linear Transformation.

Q: from Example 10.18. Using Runge-Kutta method of fourth order, solve for y at x = 1.2, 1.4 dy 2xy +…

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Q: Use Fermat's Little Theorem to compute 51990 mod 7.

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Q: constants. ple 9.2. From y₁ = A2" + B(− 3)", derive a difference equation by eliminating the

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Q: 3. Find the maximum and minimum values of |-| on |z| ≤ 1 (where a with lal < 1 is fixed) 1

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A: The tangent is the line that just touches the function at a single point. In this problem, the…

Q: 3.2. The least squares solution of smallest norm of th in m x n matrix, is given by

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Q: . Determine the volume of the solid obtained by rotating the region bounded by y= x - x^3, x = 0, x…

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Q: at an average rate of 30% within a squar r of pla th w gordon

A: Average rate per square meter Agro Chemicals  Non-Agro 10000 cm2 10% 30%     Rectangular…

Q: use Cauchy's residue theorem, where appropriate, to evaluate the given integral along the indicated…

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Q: Example 9.10. Solve y2 - 4y = n² + n - 1.

A: Please find step by step answer below:

Q: Txample 8.9. Find the maximum and minimum value of y from the following data : =2 0 1 2 4 2 - 0.25 0…

A: Solution

Q: Determine the convolution of the following signals using z-transform: 1,(0)-(-)-(4-1). 20)-[1-()*1.0…

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Q: A field of characteristic p *0 such that each element of the field is the ph power of some member of…

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Q: - - * x - م - و : (of : (x) } cu

A: This is a question from the series and sequence.

Q: The task is to identify the solution of the given system linear Ordinary Differential Equations. Use…

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Q: 2°) Write the volume integral of the solid bounded by 2 = √ x² + y²² and 2= √√2-x²-y²¹, in a)…

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Q: Example 10.12. Solve the following by Euler's modified method dy = log (x + y), y (0) = 2 dx. at x =…

A: Solution: Given, y'=log(x+y) y(0)=2 Applying Modified Euler method: f(x,y)=log(x+y)…

Q: 1. Prove that the following functions are quasi-concave: (i) f(x, y) = xy¹, x > 0, y> 0; (ii)…

A: Given: fx,y To find: Quasi-concave function

Q: A string of length 15 cm is stretched between two points as shown in Figure 1. A point P on the…

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Q: ? For the sequence 2, 8, 32, ...; Write the formula for the general term and use it to find ts

A: To find the general term and 8th term  of the given sequence :-

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Q: Suppose that f and g are both continuous functions. Also f, ge [a, b] and b that f f = fg. Prove…

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Q: 3) Using mathematical induction, show that for all integers P(n): n ≥ 8, n can be written as a sum…

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Q: first 4 terms of the Taylor series for : f(x)=sin лx near a=0.5

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Q: et K be an extension of a field F. If a and b in K are alg ma ±b, ab and (b+0) are algebric over F…

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Q: H) A class contains 10 students, 6 boys and 4 girls. We need to pick 3 students to represent the…

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Q: 3. Find the maximum and minimum values of z-a 1 āz on |z| ≤ 1 (where a with |a| < 1 is fixed)

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Q: Let K be a field extension field F and let a € K be algebric over F.

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Q: n 18. Let H be a subgroup of all automorphisms of a field K. Then the fixed field d of K.

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Q: d) Given a and r = -5, calculate S6. 2 e) Given tn = 3tn-1+2 and t4 = (-2), find ts.

A: Solution

Q: Which of the following sequeces in GP will have common ratio 3, where n is an Integer? a) gn = 2n2…

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Q: (B) Give an example for a commutative ring with identity.

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Q: Use Simpson's Rule to evaluate the following. n = 10 3 1 dx -3 1+x²

A: Simpson's 13 rule: ∫abydx=h3(y0+4(y1+y3+y5+...++yn-1)+2(y2+y4+y6+...+yn-2)+yn), where h=b-aN and N…

Q: Other Math Explain why good knowledge in Astronomy is important for fields like Accounting,…

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Q: Prove 10^47+67 is not a prime(use Fermat's). Thank you :)

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Q: em of Let f: G→ H be a group homomorphism. Then, Im f The kernel of f, we write Ker f, is Ker f = {g…

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Q: An open box with a volume of 128 cm3 can be made by cutting a square of the same size from each…

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Q: Thinking-OPTIONAL-Do you want me to mark this question? 7. If f(x) = mx²-x+2 and g(x)=3x² +nx-4, and…

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Q: 3:Use Gamma & Beta properties to evaluate : f (In x)³ dx

A: The gamma function is Γ(z)=∫0∞e-ttz-1dṭ The Gamma function is a non-integer generalization of the…

Q: 1.Tony is 6 years older than Jonathan. Six years ago, she was twice as old as he. How old is Tony?…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 3. Let f [2,3] → {1,3} be a continuous function such that the equation f(x) - x = 0 has a solution a…

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Q: Consider the division of two polynomials: f(x)=(x-c). The result of the synthetic division process…

A: Part (a) We have the coefficients of the dividend are 1  -2   -13   -1  -48 So, the dividend is:…

Q: Find the number of roots of the equation z^4+4z-1=0 in the annulus 1/3<|z|<2.

A: Rouche's Theorem : If f(z) and g(z) are two analytic functions within and on a simple closed curve C…

Q: The simultaneous linear equations mx + 7y= 12 and 7x+my = m have a unique solution only for A. m = 7…

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