Simplify expression (7+x)+7x

2x+3y + 2z = 0<br>5x – 3y +4=1<br>7x+9y-4z=11

Butoxors [25]

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4 0

3 years ago

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

The Earth has a mass of about 6 x 10^24 kg. Neptune has a mass of 1.8 x 10^27kg. How many times bigger is Neptune than Earth

elena-s [515]

Answer:

300 times bigger.

Step-by-step explanation:

That would be (1.8 * 10^27 ) / (6 * 10^24)

= 0.3 * (10^27/10^24)

= 0.3 * 10^3

= 3 * 10^2

= 300.

5 0

3 years ago

Can someone please help me

borishaifa [10]

Add up all the sides and you get 10

4 0

3 years ago

Read 2 more answers

Which of the following mixed numberd is represented by the letter A in number line shown?

pentagon [3]

Answer:

A

Step-by-step explanation:

The line is divided into 9 parts between 1 and 2

A is situated 6 parts of the way between 1 and 2, that is

$\frac{6}{9}$ = $\frac{2}{3}$ ← cancelling by 3

Hence

A = 1 + $\frac{2}{3}$ = 1 $\frac{2}{3}$ → A

3 0

3 years ago