Problem 1. Let R be a ring. Construct an isomorphism between¹ R[X,Y]/(XY) and the subring A CR[X] × R[Y] consisting of pairs (f, g) such that f(0) = g(0).

Q: Evaluate if x=4,8,3,-2 ∑x ∑x+1 ∑(x+1) 3∑x - 4

A: Given that  if x=4,8,3,-2

Q: 2= c2  + c

A: 2=C2+C We need to solve the equation.

Q: Find a2, a3, a4, a1= -3,  an= 10+2an-1

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Q: (xマ+)

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Q: Find / (+62+3) de + C

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A: DefinitionsAddition: x⊕y=x+y (standard addition of real numbers).Scalar Multiplication: α⋅x=xαfor…

Q: Don't use chat gpt

A: The rank of a matrix is equal to the number of linearly independent rows (or columns) in it.Since it…

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Q: I2x-1 1. \sx+61

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Q: 6 - 7z + 5) dz Find Preview +C

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Q: Integrate +9 +C

A: topic- indefinite integral

Q: 23) 9 &x + 10

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Q: A professor use chi-square test to examine the relationship between smoking and colon cancer. He…

A: Number of rows, a = 2 Number of columns, b = 2

Q: Don't use chat gpt

A: Step 1:Let z=f(x,y) be a function of two variables x and y. The partial derivative ∂x∂f​(x0​,y0​)…

Q: SxV4 + x?dx

A: We have to find integral

Q: Plz don't use chat gpt

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Q: Caroline takes 50 selfies in an hour, and 20 additional selfies in the next hour. If the pattern…

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Q: passes through (-4, -3)

A: Given: (-4, -3), (-9, 26), and (-3, 3

Q: Evaluate 2x2 +1+2/ dr.

A: First we distribute the x and write using exponents.

Q: 18x-23 Jan?-24 4416 -244+16

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Q: 2x-323

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Q: can u double check and answer this again

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Q: (-5,3)and(-1,0)

A: Topic:- geometry