Find the partial fraction decomposition for the following rational expression. -9t² - 12t + 36 (t + 4) (t − 1) (t — 2) A = B= C= = A t +4 + B t 1 + C t - 2

Q: Find r(t) and v(t) if a(t) = tk, v(0) = 15i, r(0) = 14j.

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Q: Find the coefficients of the partial fractions expansion. 6x4 12x³ + 115x2 - 211x + 284 (x-4) (x² +…

A: Use partial fractions.     ............(1)     ............(2)Substitute A=2   ..............Put it…

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A: We have,   x3 + 4x2 - 23x -20 by x-3

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Q: Synthetic Division Divide. 1) (n* – 5n3 _n +5) + (n -5)

A: Ans= (n^3-1) For detail...go through the solution

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Q: When x³ + x² - kx - 5 is divided by x - 2 the remainder is 1. Find the value of k.

A: Remainder Theorem:If a polynomial p(x) is divided by x-a then the remainder is p(a)

Q: The complex fraction -36 2x. can be written in simplest form as -+- 6x 12 (1) *+2 - 2 (3) 3 (2) x-9…

A: Answer and explanation is given below...

Q: F(x) 1/ (x-3)(x-5) Find the domian of the follwing fractions. No symplifying the equations.

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Q: Match each rational expression to its equivalent. 55(x+9) 11x + 143x+ 396 20x+ 11y 1. 45x y 2..2 - 4…

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Q: Choose the rational expression that simplifies to –1. а — Ь (а) b — а а — (b) - b b — а a + b (с) а…

A: To find the rational expression that gives -1 on simplify a a-bb-a b a-ba-b c a+ba-b d b-qb+a

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Q: 1-x+2x²–1 r° dx 1(r²–1)² xp-

A: Given

Q: 6. (a) Solve the equation In(x) + In(3) =2 In(r). %3D (b) Convert the equation to exponential form.…

A: We have to solve the