Solve 4n+2mn=3mn ² for m.

Mathematics

1 answer:

Anton [14]2 years ago

7 0

Answer:

m = sqrt(4/(3 n) + 1/(9 n^2)) + 1/(3 n) or m = 1/(3 n) - sqrt(4/(3 n) + 1/(9 n^2))

Step-by-step explanation:

Solve for m:

4 n + 2 m n = 3 m^2 n^2

Subtract 3 m^2 n^2 from both sides:

4 n + 2 m n - 3 m^2 n^2 = 0

Divide both sides by -3 n^2:

m^2 - 4/(3 n) - (2 m)/(3 n) = 0

Add 4/(3 n) to both sides:

m^2 - (2 m)/(3 n) = 4/(3 n)

Add 1/(9 n^2) to both sides:

m^2 + 1/(9 n^2) - (2 m)/(3 n) = 4/(3 n) + 1/(9 n^2)

Write the left hand side as a square:

(m - 1/(3 n))^2 = 4/(3 n) + 1/(9 n^2)

Take the square root of both sides:

m - 1/(3 n) = sqrt(4/(3 n) + 1/(9 n^2)) or m - 1/(3 n) = -sqrt(4/(3 n) + 1/(9 n^2))

Add 1/(3 n) to both sides:

m = sqrt(4/(3 n) + 1/(9 n^2)) + 1/(3 n) or m - 1/(3 n) = -sqrt(4/(3 n) + 1/(9 n^2))

Add 1/(3 n) to both sides:

Answer: m = sqrt(4/(3 n) + 1/(9 n^2)) + 1/(3 n) or m = 1/(3 n) - sqrt(4/(3 n) + 1/(9 n^2))

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evablogger [386]

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Answer:

a) (x³ -x² +x +2) +2/(x+1)

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Step-by-step explanation:

Polynomial long division is virtually identical to numerical long division, except that the quotient term does not require any guessing. It is simply the ratio of the leading terms of the dividend and divisor. As with numerical long division, the product of the quotient term and the divisor is subtracted from the dividend to form the new dividend for the next step.

The process stops when the dividend is of lower degree than the divisor.

In part (a), you need to make sure the dividend expression has all of the powers of x present. This means terms 0x³ and 0x² must be added as placeholders in the given dividend. They will become important as the work progresses.