Question

a área entre as retas Y=(-x+8)\2 , y=(x+4)\2 e x=0 é :

Answer 1

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$\boxed{\begin{array}{l}\sf Seja~A(x_A,y_A),B(x_B,y_B)~e~C(x_C,y_C)\\\sf os~v\acute ertices~de~um~tri\hat angulo~qualquer~no~plano~cartesiano.\\\sf a~\acute area~deste~tri\hat angulo~\acute e~dada~por\\\sf A=\dfrac{|det~M|}{2}\\\sf onde~M=\begin{bmatrix}\sf x_A&\sf y_A&\sf1\\\sf x_B&\sf y_B&\sf 1\\\sf x_C&\sf y_C&\sf1\end{bmatrix}\end{array}}$

$\large\boxed{\begin{array}{l}\sf a~\acute area~da~regi\tilde ao~pedida~passa~pelos~v\acute ertices\\\sf A(0,4)~B(2,3)~e~C(0,2)\\\sf M=\begin{vmatrix}\sf0&\sf4&\sf1\\\sf2&\sf3&\sf1\\\sf0&\sf2&\sf1\end{vmatrix}\\\sf det~M=0\cdot(3-2)-4\cdot(2-0)+1\cdot(4-0)\\\sf det~M=0\cdot1-4\cdot2+1\cdot4\\\sf det~M=-8+4\\\sf det~M=-4\\\sf A=\dfrac{|det~M|}{2}\\\sf A=\dfrac{|-4|}{2}\\\sf A=\dfrac{4}{2}\\\sf A=2~u\cdot a\end{array}}$