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2 years ago

find the smallest number by which 29160 should be divided so that the quotient becomes a perfect cube

Mathematics

1 answer:

IgorLugansk [536]2 years ago

7 0

The smallest number by which 29160 should be divided so that the quotient becomes a perfect cube is 5

<h3>Perfect cube quotient of a division</h3>

The given number is 29160

Note that:

29160 can be factored into 5832

That is, 29160 = 5832 x 5

Take the cube of 5832:

$\sqrt[3]{5832}=18$

Since it has been confirmed that 5832 is a perfect cube, the smallest number by which 29160 should be divided so that the quotient becomes a perfect cube is 5

Learn more on perfect cube quotient here: brainly.com/question/17448146

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2 years ago

Express 2x+1/(x-2)(x²+1) as a partial fraction.

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Partial fraction = 1/(x-2) - x/(x^2+1)

Step-by-step explanation:

Question:

Express 2x+1/(x-2)(x²+1) as a partial fraction.

Note: it will be assumed that there was a typo in the interpretation of parentheses to mean

(2x+1) / ( (x-2)(x^2+1) )

Let

(2x+1) / ( (x-2)(x^2+1) ) = A/(x-2) + (Bx+C)/(x^2+1) .........................(0)

(2x+1) / ( (x-2)(x^2+1) ) = (A(x^2+1)+(Bx+C)(x-2)) / ( (x-2)(B/(x^2+1) )

(2x+1) / ( (x-2)(x^2+1) ) = (Ax^2+A+Bx^2+(C-2B)x-2C) / ( (x-2)(B/(x^2+1) )

(2x+1) / ( (x-2)(x^2+1) ) = ( (A+B)x^2+(C-2B)x+A-2C ) / ( (x-2)(B/(x^2+1) )

Match numerators

2x+1 = (A+B)x^2+(C-2B)x+A-2C

Match coefficients,

A+B = 0 ..................(1)

-2B+C = 2 .................(2)

A-2C = 1 ...................(3)

Solve for A, B and C

Substitute A from (1) in (3)

-B - 2C =1

transpose and solve for B

B = -2C-1 ....................(4)

Substitue B from (4) in (2)

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simplify

5C = 2-2 = 0

C=0 ..........................(5)

substitute (5) in (4)

B = -2C-1 = -1 ...............(6)

Substitue (6) in (1)

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Using values from (7), (6) and (5) to substitute in (0)

we get

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