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Vlada [557]
3 years ago
14

Heather works in a circular showroom for wallpaper and tiles. Aisles divide the showroom like the spikes of a wheel. Each spoke

aisle is 25 feet long. A spoke aisle goes from the center to the outer corridor that circles the entire showroom. In one eight-hour workday, Heather estimates that she walks around the outer corridor at least 17 times, and walks the length of 6 spoke aisles. What is the approximate distance that she walks in one day?

Mathematics
1 answer:
harina [27]3 years ago
4 0

Answer:

2820.36 feet

Step-by-step explanation:

First we need to find the length of the outer corridor, and we do that by finding the length of the circunference with a radius of 25 feet:

C = 2 * pi * r = 2 * pi * 25 = 157.08 feet

Now, as Heather walks the outer corridor 17 times and the length of 6 spoke aisles (the radius of the circunference), we have that the total distance she walks is:

Distance = 17 * 157.08 + 6 * 25 = 2820.36 feet

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The correct works are:

  • Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3.
  • \frac{Blue(s + h) - Blue(s)}{h} = 4s + 2h

<h3>Function Notation</h3>

The function is given as:

Blue(s) = 2s^2 + 3

The interpretation when Steven is asked to calculate Blue(s + h) is that:

Steven is asked to find the output of the function Blue, when the input is s + h

So, we have:

Blue(s + h) = 2(s + h)^2 + 3

Evaluate the exponent

Blue(s + h) = 2(s^2 + 2sh + h^2) + 3

Expand the bracket

Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3

So, the correct work is:

Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3

<h3>Simplifying Difference Quotient</h3>

In (a), we have:

Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3

Blue(s) = 2s^2 + 3

The difference quotient is represented as:

\frac{f(x + h) - f(x)}{h}

So, we have:

\frac{Blue(s + h) - Blue(s)}{h} = \frac{2s^2 + 4sh + 2h^2 + 3 - 2s^2 - 3}{h}

Evaluate the like terms

\frac{Blue(s + h) - Blue(s)}{h} = \frac{4sh + 2h^2}{h}

Evaluate the quotient

\frac{Blue(s + h) - Blue(s)}{h} = 4s + 2h

Hence, the correct work is:

\frac{Blue(s + h) - Blue(s)}{h} = 4s + 2h

Read more about function notations at:

brainly.com/question/13136492

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