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If P(r) =8r/1-r, for what value of r does P(r^2)
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19 Feb 2024, 10:27
19 Feb 2024, 10:27
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If \(P(r) =\frac{8r}{1-r}\), for what value of r does \(P(r^2)=\frac{1}{2} P (\frac{1}{2})\) ?
Indicate all that apply
A. \(\dfrac{1}{\sqrt{3}}\)
B. \(\frac{1}{3}\)
C. 0
D. \(- \frac{1}{3}\)
E. \(- \dfrac{1}{\sqrt{3}}\)
Indicate all that apply
A. \(\dfrac{1}{\sqrt{3}}\)
B. \(\frac{1}{3}\)
C. 0
D. \(- \frac{1}{3}\)
E. \(- \dfrac{1}{\sqrt{3}}\)
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If P(r) =8r/1-r, for what value of r does P(r^2)
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24 Feb 2024, 11:59
24 Feb 2024, 11:59
1
\(P(r^2) = \frac{8r^2}{1-r^2}\)
\(\frac{1}{2}P(\frac{1}{2}) = \frac{1}{2} * \frac{8*\frac{1}{2}}{1-\frac{1}{2}} = 4\)
\(P(r^2) = \frac{1}{2}P(\frac{1}{2})\)
\(\frac{8r^2}{1-r^2} = 4\)
Divide both sides by 4
\(\frac{2r^2}{1-r^2} = 1\)
Cross multiply
\(2r^2 = 1-r^2\)
\(3r^2 = 1\)
\(r^2 = \frac{1}{3}\)
\(r = - \frac{1}{\sqrt{3}}\) and \(\frac{1}{\sqrt{3}}\)
\(\frac{1}{2}P(\frac{1}{2}) = \frac{1}{2} * \frac{8*\frac{1}{2}}{1-\frac{1}{2}} = 4\)
\(P(r^2) = \frac{1}{2}P(\frac{1}{2})\)
\(\frac{8r^2}{1-r^2} = 4\)
Divide both sides by 4
\(\frac{2r^2}{1-r^2} = 1\)
Cross multiply
\(2r^2 = 1-r^2\)
\(3r^2 = 1\)
\(r^2 = \frac{1}{3}\)
\(r = - \frac{1}{\sqrt{3}}\) and \(\frac{1}{\sqrt{3}}\)
gmatclubot
If P(r) =8r/1-r, for what value of r does P(r^2) [#permalink]
24 Feb 2024, 11:59
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