Question

determine valor de k para que as retas (2k-1)x – 3y +2 =0 e a reta y= ¾ x – 2 sejam perpendiculares

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{(2k - 1)x - 3y + 2 = 0}$

$\mathsf{3y = (2k - 1)x + 2}$

$\mathsf{y = \dfrac{(2k - 1)x}{3} + \dfrac{2}{3}}$

$\mathsf{y = \dfrac{3x}{4} - 2}$

$\mathsf{m_1.m_2 = -1}$

$\mathsf{\left(\dfrac{2k - 1}{3}\right).\left(\dfrac{3}{4}\right) = -1}$

$\mathsf{\left(\dfrac{6k - 3}{12}\right) = -1}$

$\mathsf{6k - 3 = -12}$

$\mathsf{6k = -9}$

$\boxed{\boxed{\mathsf{k = -\dfrac{3}{2}}}}$