Question 1037573: Solve the equation for the indicated variable.
1/r+6/(1-r)=12/r^2
Please explain step by step if possible! Thank you. Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! 1/r+ 6/(1-r) = 12/r^2
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use r(1-r)r^2 as the common denominator and multiply both sides of = by it
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r^2(1-r) + 6rr^2 = 12r(1-r)
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r^2-r^3 + 6r^3 = 12r - 12r^2
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combine like terms
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5r^3 + 13r^2 -12r = 0
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divide both sides of = by r
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5r^2 + 13r - 12 = 0
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use quadratic equation to solve
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r = ( -13 + square root( 13^2 - 4(5)(-12) ) ) / 2(5) = 0.7224
r = ( -13 - square root( 13^2 - 4(5)(-12) ) ) / 2(5) = -3.3224
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check answer
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original equation is
1/r+ 6/(1-r) = 12/r^2
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substitute 0.7224 for r
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(1/0.7224) + 6 / (1 - 0.7224) = 12 / (0.7224)^2
:
1.3843 + 21.6138 = 22.9946
22.9981 approx equal to 22.9946
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answer checks
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I will leave it to you to check the other answer for r
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