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2 years ago

15

What is the greatest possible error when measuring to the nearest quarter of an inch?

1 answer:

SOVA2 [1]2 years ago

4 0

When trying to round off the answer

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Lin is running on a track. Lin runs 5 laps around a track in 6 minutes. How many laps per minute is that? (Find both Unit Rates)

grandymaker [24]

They got the 1.2 minutes by taking the total number of minutes (6) and dividing them by the number of laps run (5). So 6 divided by 5 gives you the 1.2.

3 0

2 years ago

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

2 years ago

WHATS THE MEASURE OF THE ANGLE INDICATED?<br> GEOMETRY/PLS HELP/GOD BLESS

ch4aika [34]

Answer:

∠SQR = 1/2 m ∠SR = 1/2 x 86 = 43°

5 0

2 years ago

The Rosarios are taking a trip midville is 248 miles from their home border city is 6 times as for how far is border city from t

Gnesinka [82]

Answer:

Border City is 1488 Miles

Step-by-step explanation:

Do 248*6

7 0

2 years ago

14=h/5<br><br> Help me please

ValentinkaMS [17]

Answer:

14=h/5

h=14*5

h=70

<u>Check</u>:

70/5=14

Hope this helps

6 0

2 years ago