Suppose {x, y, z} is a primitive Pythagorean triple, so x2 + y2 = z2 and (x, y, z) = 1. Prove that x is odd and y is even, so z must be odd.

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Q: 6) Given the data 0.90 1.42 1.30 1.50 1.61 1.31 1.35 1.47 1.95 1.66 1.96 1.47 1.92 1.35 1.05 1.85…

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Q: 4. A graph G has 9 vertices and 21 edges. Three vertices have degree x, three have degree y, and…

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Q: 7. Use the Divergence Theorem to evaluate the integral Ends d.S JJs S for the vector field F(x, y,…

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Q: Evaluate the surface integral. 27) fs z dS, where S is the part of the S paraboloid z = x² + y² that…

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Q: Given F(x)= phảnh 3r 2ª √3+t dt. Find F'(0).

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Q: Prove (without using venn diagrams or truth tables) for arbitrary sets A and B, P(A)n P(B)=P(ANB)

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Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = 4xyi + zªj + 6yk…

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Q: At which labeled point on the graph is the slope the most negative slope? A B 30 Y с X

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Q: prove that If tangent to a curve makes a constant angle a with fixed line, then ở = ± p tan &.

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Q: Prove that Serret-Frenet formulae can be written in the from t' = dxt, n'=dxn, b' = d x b and…

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Q: Find the volume of the solid that lies within the sphere x² + y² + z² = 81, above the xy plane, and…

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Q: 1 1 4 1 2] 01 21 1 0012 -1 0 0 2 1601 D) Find the rank of the matrix 0 1 2

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Q: Suppose that x² - 2y² = 1² and y=tsin 0. Find (7). 0 (77) ¹(2), and 0

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Q: B) Compute the following limit if it exist lim iz5 z→-i z³-42z

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Q: 4. Consider the fixed-point iteration n+1 - = 1+en. Show that this iteration converges for any co €…

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Q: (4) Compute 3180 mod 13 without using a calculator.

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Q: (a) (b) With usual notations, prove that p² ] = K² [k ²² - k² t] = k ² = ² ( 1 ds k [t' +" +"] = [~"…

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Q: 1. Maximize function using dual, solve using graph and simplex (use duality theorems) π = 39x₁ +…

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Q: Prove that Serret-Frenet formulae can be written in the from t' = dxt, n' = dxn, b' = d xb and…

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Q: 152 2 10 7 -2 -10 -1 or each of the following vect ector x so that Ax-v₂- [-5] ND L

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Q: Exercise 7.2.7 Suppose A is an nxn matrix and let V be an eigenvector such that AV = V. Also suppose…

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Q: (a) For parts (i) and (ii) below, suppose that A is a 4 x 4 matrix with eigenvalues 6,-2, 1 and 3.…

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Q: For the given differential equation write a particular solution with unde- termined coefficients. Do…

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Q: Determine if each series diverges or converges.

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Q: Find zw and. Leave your answers in polar form. W z=9-9i w=√3-i

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Q: May i please request a hand written solution

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Q: Exercise 5.8.2 Let B = in R². Find CB(x). {[+][6][+])} 0 be a basis of R³ and let x = 5 -1 4 be a…

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Q: you make it more clear because I cannot understand what it is written.

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Q: Determine the minimum value of the following function: f(x ,y, z) = x2 + y2 + z2 subject to the…

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Q: Exercise 5.9.9 Write the solution set of the following system as a linear combination of vectors 0 0…

A: As per our guidelines we are supposed to answer only first question . kindly repost other part in…