3 years ago

The sum of a number and its reciprocal is 13/6. find the number

1 answer:

6 0

Suppose the number is x, its reciprocal is 1/x
x+1/x=13/6
(x^2+1)/x=13/6
6(x^2+1)=13x
6x^2-13x+6=0
(3x-2)(2x-3)=0
x=2/3 or x=3/2

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The quantity y varies directly with the square of x and inversely with z. When x is 9 and z is 27, y is 6. What is the constant

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$\bf \qquad \qquad \textit{double proportional variation}
\\\\
\begin{array}{llll}
\textit{\underline{y} varies directly with \underline{x}}\\
\textit{and inversely with \underline{z}}
\end{array}\implies y=\cfrac{kx}{z}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------$

$\bf \stackrel{\textit{\underline{y} varies directly with the square of \underline{x} and inversely with \underline{z}}}{y=\cfrac{kx^2}{z}}
\\\\\\
\textit{we also know that }
\begin{cases}
x=9\\
z=27\\
y=6
\end{cases}\implies 6=\cfrac{k9^2}{27}
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