$\bf y=ax^2+bx\implies \cfrac{dy}{dx}=2ax+b$

now, we know the tangent line at (2,4) is y = 8x - 12, now, that's already in slope-intercept form, so, the slope of that tangent at (2,4) is "8" then.

now, that means when x = 2, the slope is 8, so let's use that.

$\bf \left. \cfrac{dy}{dx} \right|_{x=2}\implies 2a(2)+b=\stackrel{\textit{from tangent equation}}{8}\implies 4a+b=8
\\\\\\
4a=8-b\implies a=\cfrac{8-b}{4}\implies \boxed{a=2-\cfrac{b}{4}}\\\\
-------------------------------\\\\
\begin{cases}
x=2\\
y=4\\\\
a=2-\cfrac{b}{4}
\end{cases}\implies \stackrel{y = ax^2+bx}{4=\left( \boxed{2-\frac{b}{4}} \right)(2)^2+b(2)}\implies 4=8-b+2b
\\\\\\
\boxed{-4=b}\qquad thus\qquad a=2-\cfrac{-4}{4}\implies \boxed{a=3}\\\\
-------------------------------\\\\
y=3x^2-4x$

5 0

3 years ago

What is the value of the dot shown on the number line below? If the answer is not an integer, enter it as a fraction or mixed nu

Arada [10]

Value of the dot is -0.6 or 1/6

3 0

2 years ago

Heeelllppp meeee please

garri49 [273]

A= 100; b= 0,9
f(x)= 100.(0,9)^x

3 0

2 years ago