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3 years ago

15

there were 445 non-fiction books but 83 went missing and 45 were transferred to another Library how many non-fiction books are t

here

1 answer:

xxTIMURxx [149]3 years ago

3 0

Answer:

317 non-fiction books

Step-by-step explanation:

1. Start with 445

2. Then subtract 83 from 445

3. Should get 362

4. After subtract 45 from 362

5. Should get 317

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The median should be 16

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3 years ago

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A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
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We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

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3 years ago

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hoa [83]

Answer:

Plz mark me brainliest!!!!

Step-by-step explanation:

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3 years ago

Which expressions are equivalent to Negative 9 (two-thirds x + 1)? Check all that apply.

Sav [38]

<u><em>Answer:</em></u>

<u><em /></u> $-9(\frac{2}{3}x) + 9(1)\\ \\-6x + 9$

<u><em>Explanation:</em></u>

<u>Before we begin, remember the following rules:</u>

<u>1- Distribution property:</u>

<u /> $a(b+c) = ab+ac$

<u>2- Simplification of fractions:</u>

<u /> $\frac{xy}{yz}=\frac{x}{z}$

<u>3- Signs in multiplication:</u>

+ve * +ve = +ve

-ve * -ve = +ve

+ve * -ve = -ve

<u>Now, for the given problem, we have:</u>

<u></u> $9 (\frac{2}{3}x + 1)$

<u>Starting with the distributive property:</u>

<u /> $-9 (\frac{2}{3}x +1) = -9(\frac{2}{3}x) - (-9)(1) = -9(\frac{2}{3}x) + 9(1)$

..................>This corresponds to option 1

<u>Now, we simplify the output from the above step:</u>

<u /> $-9(\frac{2}{3}x) + 9 = \frac{-9*2}{3}x + 9 = -6x+9$

................> This corresponds to option 5

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Answer:

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