Complete the statements.<br> f(4) is<br> f(x) = 4 when x is

You are designing a rectangular poster to contain 7575 in2 of printing with a 33-in margin at the top and bottom and a 11-in m

erma4kov [3.2K]

Answer:

The dimensions of the rectangular poster is 15 in by 5 in.

Step-by-step explanation:

Given that, the area of the rectangular poster is 75 in².

Let the length of the rectangular poster be x and the width of the rectangular poster be y.

The area of the poster = xy in².

$\therefore xy=75$

$\Rightarrow y=\frac{75}{x}$ ....(1)

1 in margin at each sides and 3 in margin at top and bottom.

Then the length of printing space is= (x-2.3) in

=(x-6) in

The width of printing space is = (y-2.1) in

=(y-2) in

The area of the printing space is A =(x-6)(y-2) in²

∴ A =(x-6)(y-2)

Putting the value of y

$\Rightarrow A =(x-6)(\frac{75}{x}-2)$

$\Rightarrow A = 87-\frac{450}{x}-2x$

Differentiating with respect to x

$A '= \frac{450}{x^2}-2$

Again differentiating with respect to x

$A''=-\frac{900}{x^3}$

To find the minimum area of printing space, we set A' = 0

$\therefore \frac{450}{x^2}-2=0$

$\Rightarrow 450 =2x^2$

$\Rightarrow x^2=225$

$\Rightarrow x=\pm 15$

Now putting x=±15 in A''

$A''|_{x=15}=-\frac{900}{15^3}$

$A''|_{x=-15}=-\frac{900}{(-15)^3}=\frac{900}{(15)^3}>0$

Since at x=15 , A"<0 Therefore at x=15 , the area will be minimize.

From (1) we get

$y=\frac{75}{x}$

Putting the value of x

$y=\frac{75}{15}$

=5 in

The dimensions of the rectangular poster is 15 in by 5 in.

4 0

3 years ago

What is the surface area of this cylinder (round to the nearest tenth) 6.4 m2 25.1 m2 37.7 m2 62.8 m2

denpristay [2]

Answer: 62.8m^2

Step-by-step explanation:

Surface area of a cylinder = $2\pi r^{2} + 2\pi rh$

r = 2m, h = 3m

$2\pi (2)^{2} + 2\pi (2)(3)$

= 62.83185

8 0

3 years ago

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Which of the following reasons could be used to conclude that the lines are parallel based on the given information?

rewona [7]

We have been given three statements. From those statements, we have to pick the statement that can conclude that that two lines are parallel.

Statement 1:

If right angles are formed, then lines are parallel.

This is not valid because if the angle formed is right angle then lines forming right angle will be perpendicular.

Statement 2:

If two lines are perpendicular to another line, then they are parallel.

This is valid because the line on which other two lines are perpendicular will work as transversal and the alternet interior angles will be equal. Hence the two perpendicular lines on given line will be parallel to each other.

Statement 3:

If alternate interior angles are equal, then lines are parallel.

This is valid as explained above.

Hence final answer are statement 2 and statement 3 both.

7 0

3 years ago

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Plz someone answer this with an explanation

worty [1.4K]

Answer:

1/3

Step-by-step explanation:

8 0

3 years ago

Please help me out with this equation! <br> i will mark you as brainliest

BigorU [14]

<h3>Answer: -19, -15, -9, -1, 9 (choice A)</h3>

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Explanation:

If we plug in x = -2, then we get,

y = x^2 + 7x - 9

y = (-2)^2 + 7(-2) - 9

y = 4 - 14 - 9

y = -10 - 9

y = -19

So x = -2 leads to y = -19. The answer is between A and D.

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If you repeat those steps for x = -1, then you should get y = -15

Then x = 0 leads to y = -9

x = 1 leads to y = -1

Finally, x = 2 leads to y = 9

The outputs we get are: -19, -15, -9, -1, 9 which is choice A

Choice D is fairly close, but we won't have a second copy of -15, and we don't have an output of -19.

7 0

3 years ago

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Complete the statements. f(4) is f(x) = 4 when x is