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3 years ago

A parking lot covers 32,420 square feet. What is its area to the nearest thousand feet? Explain how you round the number.

1 answer:

8 0

The thousands place (1000) is the fourth number to the left of the decimal, so round that one either up or down based on the number just one spot closer to the decimal, in this case, the hundreds place (100).

so we have 32,420

we can ignore the numbers that are going to become zeros as a result of the rounding . .

32,400

let's round 32,XXX either up or down based on the value in the hundreds place. if that value is 5 or greater, than we round up. if it is less than 5, than we round down.

4 is in the hundreds place, so we round down

32,000 is the answer

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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

Grace [21]

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:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

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

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

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

Open Brackets

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

Collect Like Terms

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

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

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

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

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

Collect Like Terms

$512y^{-2} = 2$

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

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

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

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

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

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

$A" = 1024y^{-3}$

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

The above value is:

$A" = \frac{1024}{y^3} > 0$

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>

3 0

3 years ago

Please don’t just comment for points

masha68 [24]

1. no because 2x+10 is not equal to 2x+7
2. no. you cant add una like terms so 4x+4 doesn’t equal 8x
3. yes. the terms still retain their same value although they are not in the same order
4. yes. when u distribute the -3, you get -3x-6 which is of course equal to -3x-6

7 0

3 years ago

The equation through the point (5,3) and is parallel the equation y=2/5x+7

nignag [31]

Answer:

Point - Slope Form: (y - 3) = 0.4(x - 5)

Slope - Intercept Form: y = 0.4x + 1

Step-by-step explanation:

Well if it's parallel, they have the same slope

Slope = 0.4

I'll do it in two forms:

Point - Slope Form: (y - 3) = 0.4(x - 5)

Slope - Intercept Form: y = 0.4x + b

3 = 2 + b

b = 1

y = 0.4x + 1

I might be wrong

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3 years ago