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2 years ago

9

The area of quadrilateral ABCD in the below figure is

2 answers:

Cerrena [4.2K]2 years ago

8 0

Answer:

a)57

Step-by-step explanation:

muminat2 years ago

4 0

Its a 57 hope it helps

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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

1 year ago

A force of 500.0 is represented graphically with its tail at the origin and the tip pointed in a direction 30.0° above the posit

trapecia [35]

Answer:

$F^{'}=(250\sqrt{3},250 })$

Step-by-step explanation:

We have F´ =500 and $\alpha$ =30º, so x and y components:

F´ = $(F_{x} , F_{y})$ this is

$F_{x} = F^{'} *Cos\alpha$

$F_{y} = F^{'} *Sin\alpha$

$F_{x} = F`*Cos\alpha =500*Cos30=500*\frac{\sqrt{3} }{2} =250\sqrt{3}$

$F_{y}=F*Sin\alpha =500*Sin30=500*\frac{1}{2}=250$ ;

Finally

F' = $(250\sqrt{3} , 250)$

3 0

2 years ago

n winter, the price of apples suddenly went up by \$0.75$0.75dollar sign, 0, point, 75 per pound. Sam bought 333 pounds of apple

RSB [31]

$1.21 is the original price per pound...i too am having trouble with figuring out how to setup the equation!!

5 0

2 years ago

How many numbers are 10 units from zero on number line

Lelu [443]

Answer:

I think 2.

Step-by-step explanation:

10, and negative ten

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2 years ago

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Write 55,426 using the number names

Aleks04 [339]

Answer:

fifty five thousand four hundred and twenty six.

Step-by-step explanation:

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2 years ago

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