3 years ago

What is the 7th term of 25,10,4,8/5

Mathematics

1 answer:

anyanavicka [17]3 years ago

5 0

This is a SpongeBob we are friends 25

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Find the parabola with equation y = ax^2 + bx whose tangent line at (2, 4) has equation y = 8x − 12.

MrRissso [65]

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

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.

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

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3 years ago

jesse drives to work. The distance jesse's car travles (d) on a number of gallons of gas (g) is given y the equation d=15g.

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You need to know what the distance jesse traveled is and then the number of gallons of gas she has then you plug it it.

distance equals 15 times the amount of gas in gallons
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4 years ago

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