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zzz [600]
2 years ago
8

After a storm damages the community center, Shanika and her friends hold fundraising events to help pay for repairs. After the f

irst event, they raise $240, which is 10% of the total amount that they want to raise
Mathematics
1 answer:
pantera1 [17]2 years ago
3 0

Answer:

Step-by-step explanation:

The total they want to raise is $2,400 if that is what you're asking?

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f(x)=\begin{cases}x^2&\text{for }x\le2\\mx+b&\text{for }x>2\end{cases}

In order to be differentiable everywhere, f must first be continuous everywhere, which means the limits from either side as x\to2 must be the same and equal to f(2). By definition, f(2)=2^2=4, and

\displaystyle\lim_{x\to2^-}f(x)=\lim_{x\to2}x^2=4

\displaystyle\lim_{x\to2^+}f(x)=\lim_{x\to2}(mx+b)=2m+b

so we need to have 4m+b=4.

For f to be differentiable at x=2, the derivative needs to be continuous at x=2, i.e.

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We then need to have

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Then

2m+b=4\implies\boxed{b=-4}

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