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3 years ago

PLEASE PLEASE HELP ME ON THIS

Mathematics

1 answer:

Rufina [12.5K]3 years ago

4 0

Divide to get a constant of proportionality its basically asking per what ever the case may be

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A rectangular box with a volume of 272ft^3 is to be constructed with a square base and top. The cost per square foot for the bot

ASHA 777 [7]

Answer:

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

The length of one side of the base of the given box is 3 ft.

The height of the box is 30.22 ft.

Step-by-step explanation:

Given that, a rectangular box with volume of 272 cubic ft.

Assume height of the box be h and the length of one side of the square base of the box is x.

Area of the base is = $(x\times x)$

$=x^2$

The volume of the box is = area of the base × height

$=x^2h$

Therefore,

$x^2h=272$

$\Rightarrow h=\frac{272}{x^2}$

The cost per square foot for bottom is 20 cent.

The cost to construct of the bottom of the box is

=area of the bottom ×20

$=20x^2$ cents

The cost per square foot for top is 10 cent.

The cost to construct of the top of the box is

=area of the top ×10

$=10x^2$ cents

The cost per square foot for side is 1.5 cent.

The cost to construct of the sides of the box is

=area of the side ×1.5

$=4xh\times 1.5$ cents

$=6xh$ cents

Total cost = $(20x^2+10x^2+6xh)$

$=30x^2+6xh$

Let

C $=30x^2+6xh$

Putting the value of h

$C=30x^2+6x\times \frac{272}{x^2}$

$\Rightarrow C=30x^2+\frac{1632}{x}$

Differentiating with respect to x

$C'=60x-\frac{1632}{x^2}$

Again differentiating with respect to x

$C''=60+\frac{3264}{x^3}$

Now set C'=0

$60x-\frac{1632}{x^2}=0$

$\Rightarrow 60x=\frac{1632}{x^2}$

$\Rightarrow x^3=\frac{1632}{60}$

$\Rightarrow x\approx 3$

Now $C''|_{x=3}=60+\frac{3264}{3^3}>0$

Since at x=3 , C''>0. So at x=3, C has a minimum value.

The length of one side of the base of the box is 3 ft.

The height of the box is $=\frac{272}{3^2}$

=30.22 ft.

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

7 0

3 years ago

during a trip to the supermarket, Jim bought the following items bread $1.45 beans $0.88 toothpaste $2.90 milk $3.55 dog food $6

mr Goodwill [35]

15.28 I think it is the answer bc it said total so u add all the numbers. I added them and it gave me 15.28

5 0

4 years ago

Read 2 more answers

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kupik [55]

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3 years ago

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please help me evaluate this. the answer is B but im not sure how to get the answer without using a calculator. please show step

iragen [17]

Answer:

b. 9/100

Step-by-step explanation:

It helps if you have memorized the cubes of small integers. Of course, the ones needed here are ...

3³ = 27

10³ = 1000

The desired value can be simplified to ...

$\left(-\dfrac{1000}{27}\right)^{-2/3}=\left(-\sqrt[3]{\dfrac{3^3}{10^3}}\right)^2=\dfrac{(-3)^2}{10^2}=\dfrac{9}{100}$

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3 years ago

Suppose that each of the numbers 0,1,2,3,4,5,6,7,8,9 is written on a piece of paper in a jar. If each number is equally likely,

PIT_PIT [208]

Answer:

Step-by-step explanation:

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3 years ago