Determina o valor de x em cada caso

by AMMA · Published 1 de Fevereiro de 2018 · Updated 17 de Janeiro de 2022

Enunciado

Determina o valor de x em cada caso.

Resolução

Ora,
\[x = \frac{{\overparen{AB}}}{{360^\circ }} \times {P_\bigcirc } = \frac{{2 \times 45^\circ }}{{360^\circ }} \times 2 \times \pi \times 5 = \frac{{5\pi }}{2}\]
Ora,
\[\begin{array}{*{20}{l}}{\frac{{\overparen{AB}}}{{360^\circ }} = \frac{{10\pi }}{{{P_\bigcirc }}}}& \Leftrightarrow &{\frac{{{\rm{144}}^\circ }}{{360^\circ }} = \frac{{10\pi }}{{2\pi \times x}}}\\{}& \Leftrightarrow &{x = \frac{{5 \times 360^\circ }}{{144^\circ }}}\\{}& \Leftrightarrow &{x = 12,5}\end{array}\]
Ora,
\[\begin{array}{*{20}{l}}{\frac{{\overparen{AB}}}{{360^\circ }} = \frac{{8\pi }}{{{P_\bigcirc }}}}& \Leftrightarrow &{\frac{{2x}}{{360}} = \frac{{8\pi }}{{2\pi \times 9}}}\\{}& \Leftrightarrow &{\frac{x}{{180}} = \frac{4}{9}}\\{}& \Leftrightarrow &{x = 80}\end{array}\]