Solve for a
a=\frac{81}{2401rf^{2}}
f\neq 0\text{ and }r\neq 0
Solve for f
f=\frac{9}{49\sqrt{ar}}
f=-\frac{9}{49\sqrt{ar}}\text{, }\left(a>0\text{ and }r>0\right)\text{ or }\left(r<0\text{ and }a<0\right)
Share
Copied to clipboard
raf^{2}=\frac{\frac{3}{7}\times \left(\frac{3}{7}\right)^{2}\times \left(\frac{3}{7}\right)^{3}}{\left(\frac{3}{7}\right)^{2}}
Multiply f and f to get f^{2}.
raf^{2}=\frac{\left(\frac{3}{7}\right)^{3}\times \left(\frac{3}{7}\right)^{3}}{\left(\frac{3}{7}\right)^{2}}
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
raf^{2}=\frac{\left(\frac{3}{7}\right)^{6}}{\left(\frac{3}{7}\right)^{2}}
To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.
raf^{2}=\left(\frac{3}{7}\right)^{4}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 6 to get 4.
raf^{2}=\frac{81}{2401}
Calculate \frac{3}{7} to the power of 4 and get \frac{81}{2401}.
rf^{2}a=\frac{81}{2401}
The equation is in standard form.
\frac{rf^{2}a}{rf^{2}}=\frac{\frac{81}{2401}}{rf^{2}}
Divide both sides by rf^{2}.
a=\frac{\frac{81}{2401}}{rf^{2}}
Dividing by rf^{2} undoes the multiplication by rf^{2}.
a=\frac{81}{2401rf^{2}}
Divide \frac{81}{2401} by rf^{2}.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}