Question

TEMA FORMULA DE CONVERSION

Answer 1

Respuesta:

R = 2π/5 rad.

Explicación paso a paso:

SISTEMA DE MEDIDAS ANGULARES.

Conversion de medidas angulares.

$\mathsf{S = (10x + 2)°} \\ </u></em></p><p><em><u>[tex]\mathsf{S = (10x + 2)°} \\ \mathsf{C = {(12x - 4)}^{g}}$

Conversion al sistema Centesimal.

$\mathsf{S = (10x + 2)°} \\ </p><p>\mathsf{C= \frac{{10}^{g} }{9} (10x + 2)°} \\ \mathsf{C = {(100x + 20)}^{g}} \\ </p><p>$

Igualamos las dos medidas en el sistema Centesimal

$\mathsf{ {(\frac{100x + 20}{9})}^{g} = {(12x - 4)}^{g}} \\ \mathsf{{(100x + 20)}^{g} = 9 {(12x - 4)}^{g}} \\ \mathsf{{(100x + 20)}^{g} = {(108x - 36)}^{g}} \\\mathsf{108x - 100x = 36 + 20} \\ \mathsf{8x = 56} \\ \mathsf{x = \frac{56}{8}} \\ \boxed{\mathsf{x= 7}}$

$\mathsf{{(12x - 4) }^{g} = {(12(7) - 4)}^{g}} \\ \mathsf{{(84 - 4)}^{g} = {80}^{g}}$

Convertir a Sistema Radial.

$\mathsf{R = \frac{{80}^{\cancel{g}} }{{200}^{\cancel{g}} } \pi rad} \\ \boxed{\mathsf{R = \frac{2\pi}{5}rad}}$