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3 years ago

6

Darcy and Leah are looking at some fabric selections in a store. All of the selections are marked the same price, and the amount

, in yards, of each fabric is written as an improper fraction. Which amount is the greatest? A. 43⁄5 B. 33⁄4 C. 78⁄9 D. 22⁄3

2 answers:

alex41 [277]3 years ago

5 0

We know that the price of all the fabrics is the same. However, the length of the fabrics is different. We have to determine which fabric is the longest.

Option A: $\frac{43}{5}$ = 8.6

Option B: $\frac{33}{4}$ = 8.25

Option C: $\frac{78}{9}$ = 8.6667

Option D: $\frac{22}{3}$ = 7.33....

Hence, the longest fabric is the one given in option C, and its length is 8.6667

Viefleur [7K]3 years ago

4 0

Lets convert all values in the decimal expanded form.

A. 43/5 = 8.6

B. 33/4 = 8.25

C. 78/9 = 8.666...

D. 22/3 = 7.333...

From above, 8.666... is the greatest among all.

Hence, the greatest amount is 78/9.

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3 years ago

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mezya [45]

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3 years ago

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vfiekz [6]

Answer:

Step-by-step explanation:

given a point $(x_0,y_0)$ the equation of a line with slope m that passes through the given point is

$y-y_0 = m(x-x_0)$ or equivalently

$y = mx+(y_0-mx_0)$ .

Recall that a line of the form $y=mx+b$ , the y intercept is b and the x intercept is $\frac{-b}{m}$ .

So, in our case, the y intercept is $(y_0-mx_0)$ and the x intercept is $\frac{mx_0-y_0}{m}$ .

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph $(x_0,\frac{1}{x_0})$ . Which means that $y_0=\frac{1}{x_0}$

The slope of the tangent line is given by the derivative of the function evaluated at $x_0$ . Using the properties of derivatives, we get

$y' = \frac{-1}{x^2}$ . So evaluated at $x_0$ we get $m = \frac{-1}{x_0^2}$

Replacing the values in our previous findings we get that the y intercept is

$(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}$

The x intercept is

$\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0$

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$\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2$

So regardless of the point we take on the graph, the area of the triangle is always 2.

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3 years ago