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2 years ago

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What does it mean in context of the example that Alyssa’s rate of change is greater than Sarah’s?

1 answer:

faltersainse [42]2 years ago

8 0

Answer:

Part 1) The rate of change is the amount of money saved by week

Part 2) The amount of money saved weekly by Alyssa is greater than the amount of money saved weekly by Sarah.

Part 3) see the explanation

Step-by-step explanation:

see the attached figure to better understand the problem

<u><em>The complete question is</em></u>

Part 1) What does the rate of change in the example represent?

Part 2) What does it mean in context of the example that Alyssa’s rate of change is greater than Sarah’s?

Part 3) Write ordered pairs for the initial values of each function. Tell what the initial values represent

Part 1) we know that

The rate of change is the slope or unit rate of the linear equation

The formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

In this context the rate of change is the amount of money saved by week

Part 2) we know that

Alyssa’s rate of change is equal to $8 per week

Sarah’s rate of change is equal to $6 per week

That means ----> The amount of money saved weekly by Alyssa is greater than the amount of money saved weekly by Sarah.

Part 3) we know that

The initial value or y-intercept is the value of y when the value of x is equal to zero

In this context , the initial value is the amount of money available at the time of beginning to save

so

<em>Sarah's Savings</em>

Looking at the graph

The initial value is the point (0,8)

That means ----> At the beginning (x=0), Sarah already had $8 saved.

<em>Alyssa's Savings</em>

Looking at the graph

The initial value is the point (0,0)

That means ----> At the begin (x=0), Alyssa had nothing saved.

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A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

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Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

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Such that:

$Length = x$

$Width = y$

So:

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The width becomes:

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$A = (\frac{128}{y} + 2) * (y + 4)$

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To calculate the smallest possible value of y, we have to apply calculus.

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$0 = -512y^{-2} + 2$

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$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

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$y = 16$

Recall that:

$x = \frac{128}{y}$

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Recall that the new dimensions are:

$Length = x + 2$

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So:

$Length = 8 + 2$

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To double-check;

Differentiate A'

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$A" = -2 * -512y^{-3}$

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$A" = \frac{1024}{y^3}$

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This means that the calculated values are at minimum.

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