Question

se x*y = 40 e x/y = 2.4 qual o valor de x e y?

Answer 1

Resposta:

Encontrando y:

$\left \{ {{x\times y =40}\atop {\frac{x}{y}=2,4}} \right.\\\\\frac{x}{y}=2,4\\\\x=2,4y\\\\x\times y=40\\2,4y\times y=40\\2,4y^2=40\\\\y^2=\frac{40}{2,4}\\\\y^2=\frac{50}{3}\\\\y=\sqrt{\frac{50}{3} }$

Calculando x:

$x\times y=40\\x\times \sqrt{\frac{50}{3}}=40\\x=\frac{40}{\sqrt{\frac{50}{3} } } \\\\x=\frac{40}{\sqrt{\frac{50}{3}}}\times\frac{\sqrt{\frac{50}{3} } }{\sqrt{\frac{50}{3} } } \\\\x=\frac{40\sqrt{\frac{50}{3} } }{\frac{50}{3} } \\\\x=\frac{120\sqrt{\frac{50}{3} } }{50}\\\\x=\frac{12\sqrt{\frac{50}{3} } }{5}$

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\begin{cases}\sf{x\:.\:y = 40}\\\sf{\dfrac{x}{y} = 2,4}\end{cases}$

$\sf{\dfrac{24}{10}\:.\:y\:.\:y = 40}$

$\sf{24y^2 = 400}$

$\sf{y = \dfrac{20}{2\sqrt{6}}}$

$\boxed{\boxed{\sf{y = \dfrac{5\sqrt{6}}{3}}}}$

$\mathsf{x\:.\:\dfrac{5\sqrt{6}}{3} = 40}$

$\mathsf{x = \dfrac{120}{5\sqrt{6}}}$

$\boxed{\boxed{\sf{x = 4\sqrt{6}}}}$