I. Prove the following assertions using a direct proof. a. If x is an odd integer, then x+5 is even. b. If x and y are both even integer, then x+y is even. If x and y are both odd integer, then x+y is even. C.

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A: The given function is fx=13log314+log3x To find: the domain of f(x) and solve the given equation.

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A: To determine whether the given statement is true or false.

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A: Given dydx = 1xy+y,   y(0)  = 1

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Q: (B) Show that for any value of the arbitrary constant C the function xy(C-.x)=1 is a solution of the…

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A: Given- Given A = 5-20-262027 and X = x1x2x3. To Show- Show that XTAX = 27, suggest that 5x12 + 6x22…

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A: As per the question we are given a 4×4 game matrix and we have to use the algebraic method to solve…

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A: Given:MaxP=10X+10Y+30ZThe constraints are300X+10Y+20Z≥30020X+10Y+20Z≥10050X+40Y+30Z≥80We have to…

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A: Given- The sales of certain products in three cities are given in the 4 by 3 matrix below. The cost…

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A: Given:  1) a) ℤ2x/x3+x+1≅ℤ2x/x3+x2+x+1 b) ℂ[x]/x2+1 is a field. c) x2+100x+2500-n2 is irreducible…

Q: Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

A: To find normal line and parallel plane we need to find normal vector to the surface / function .…

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A: Find the intersecting line L. For any random point on the line L, we can find the general distance.…

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A: We will find the equation of the required plane

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Q: 4. Prove that (a + b) ≤a+b≤ a + b for any real numbers a and b. (Hint: Use cases when a, b ≥ 0; a, b…

A: 4. To show: -a+b≤a+b≤a+b Please post the multiple question separately.Here i answered 1st question…

Q: Q1A) The vectors A = 3i+j+ 4k, B = 2i - 3j-k, find vector normal to A and In plane of A and, B.

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Q: B)Is w = Zez analytical function or not?

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Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A: Given,        y=0, and y=x-x2

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Q: 6+ 5- 4 نیا 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -6+ The point symmetric across the x-axis is ( The…

A: We will find the point symmetric across  x-axis, y-axis, origin.

Q: Find the volume of the region E bounded by the paraboloids z = x² +₁² and z = 72 - 7x² - 7x².

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