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Mandarinka [93]
3 years ago
10

A 27 1⁄2-mile stretch of road needs repaving. A company bid on the repaving project, saying they would repave 2 1⁄4 miles of roa

d per week. How many weeks will the company take to completely remove the stretch of road?
Mathematics
1 answer:
Umnica [9.8K]3 years ago
8 0

Answer:

The correct answer is 12 and a half or 13 weeks.

Step-by-step explanation:

First, convert the values to decimals.

27 1/2 = 27.5

2 1/4 = 2.25

Then, divide miles of road that need to be repaved by the number of miles that are repaved per week.

27.5/2.25 = 12.2222222222222

Round that up to 12 and a half weeks or 13 weeks.

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Step-by-step explanation:

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B. Determine the values of a and b so that f is continuous.<br><br> Please help!
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Answer:

following are the solution to this question:

Step-by-step explanation:

Please find the complete question in the attached file.

\lim_{x\to 2}+f(x) = \lim_{x\to 2}+ (ax^2-bx+3) = 4a-2b+3\\\\ \to  4a-2b+3 = 4\\\\  \therefore \ \ 4a-2b = 1\\\\

The one-sided limits of F(x) at x = 3 must be equivalent for f(x) to be continuous at x = 3.

\to \lim_{x\to 3}- f(x) = \lim_{x\to 3}- (ax^2-bx+3) = 9a-3b+3\\\\ \to \lim_{x\to 3}+ f(x) = \lim_{x\to 3}+ (2x-a+b) = 6-a+b\\\\  

So,

\to 9a-3b+3 = 6-a+b\\\\\therefore\\ \to 10a -4b = 3

\to 4a - 2b = 1......(a)\\\to 10a - 4b = 3.......(b)\\

In equation a multiply the by -2 and then add in the equation b:

\to -8a + 4b = -2\\\to 10a - 4b = 3\\ \to 2a = 1\\\\ \to   a = \frac{1}{2}\\\\ \to \ 4(\frac{1}{2}) - 2b = 1\\\\ \to 2 - 2b = 1\\\\ \to   -2b = -1\\\\ \to b = \frac{1}{2}  

So, the value of a \ and \ b= \frac{1}{2}

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