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3 years ago

5

Find the midpoint of the line segment with endpoints (-9,-1,) and (7,0)

1 answer:

creativ13 [48]3 years ago

6 0

Answer:

The midpoint is;

(-1,-0.5)

Step-by-step explanation:

To do this, we shall use the midpoint formula

That would be;

(x,y) = (x1 + x2)/2 , (y1 + y2)/2

(x1,y1) = (-9,-1)

(x2,y2) = (7,0)

(x,y)

= (7-9)/2 , (0-1)/2

= -2/2 , -1/2

= (-1, -0.5)

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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:

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Such that:

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$Width = y$

So:

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$128 = x * y$

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When 1 inch margin is at top and bottom

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When 2 inch margin is at both sides

The width becomes:

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

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

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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

$\sqrt{256=y^2$

$16=y$

$y = 16$

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

$x = \frac{128}{16}$

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To double-check;

Differentiate A'

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

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The above value is:

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This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

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Step-by-step explanation:

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