Question

como chegar a resposta

Answer 1

$L(x)=ax^2+bx+c$

$L(0)=0$

$a\cdot0^2+b\cdot0+c=0$

$c=0$

$L(200)=0$

$200^2a+200b+c=0$

$40~000a+200b=0$

$\boxed{200a+b=0}$

$L(15)=10~200$

$225a+15b+c=10~200$

$225a+15b=10~200$

$\boxed{15a+b=680}$

$\begin{cases} 200a+b=0 \\ 15a+b=680\end{cases}~\Rightarrow~\begin{cases} 200a+b=0 \\ -15a-b=-680\end{cases}$

$(200a+b)+(-15a-b)=0-680$

$185a=-680$

$a=-\dfrac{680}{185}$

$a=-\dfrac{136}{37}$

$15a+b=680$

$\dfrac{-(136)\cdot15}{37}+b=680$

$37b-2~040=25~160$

$37b=27~200$

$b=\dfrac{27~200}{37}$

$f(x)=-\dfrac{136}{37}x^2+\dfrac{27~200}{37}x$

$f(100)=-\dfrac{136}{37}\cdot100^2+\dfrac{27~200}{37}\cdot100$

$f(100)=\dfarc{-1~360~000+2~720~000}{37}=\dfrac{1~360~000}{37}$