Solve y = x + 8 for x. x= y + 8 x=y - 8 x= -y + 8 x = -y

From a thin piece of cardboard 30 in. by 30 in., square corners are cut out so that the sides can be folded up to make a box. Wh

Brilliant_brown [7]

Answer:

Dimensions 5in x 10in x 10in will yeild a box with a max. volume of 500 cubic inches

Step-by-step explanation:

Volume = height x length x width

considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

therefore,

V = x (30-2x) (30-2x) ---> eq(1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V= 4x³ - 120 x²+ 900x

Taking derivative w.r.t 'x'

dV/dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

dV/dx = 0

so, 4 (3x² - 60x +225)=0

3x² - 60x+225=0 (taking 3 common)

x² - 20x + 75 =0

Solving this quadratic equation

x² - 15x -5x + 75 =0

x(x-15) - 5(x-15) =0

Either (x-15)=0

x=15

Or x-5=0

x = 5

if we substitute x=15 in eq(1), volume becomes zero.

therefore, x cannot be 15

When x= 5

eq(1)=>V = 5 (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yeild a box with a max. volume of 500 cubic inches

7 0

3 years ago

Please plot this linear equation on a graph, and also explain how to plot it. <img src="https://tex.z-dn.net/?f=y%3D3x-7" i

olasank [31]

Answer:

See below:

Step-by-step explanation:

Hello! I hope you are having a nice day.

We can solve this equation in a single step, we just need a bit of theory and a graph.

We can first see that its in $y=mx+b$ form. Which is also known as Slope-Intercept form.

This means that we know the following.

$b$ is the y coordinate of the y intercept.
$m$ is the slope of the line.

Since we know that, we can see that from our equation that the slope of the line is 3 and the y intercept is (0,-7).

Now that we've gotten that, we can start graphing.

The y intercept is -7 so we can plot (0,-7) as one of our points.

The slope of 3 means that we got up 3 units then right a single unit.

Therefore, another point could be (1,-4).

With our two points, we can create our graph by creating a straight line through those two points and therefore plotting our line.

Cheers!

6 0

2 years ago

Read 2 more answers

Assume you have 4 fins, each with a mass of 8grams. what's the total weight of these 4 fines?

Kryger [21]

1 fin = 8 grams
4 fins = 4 x 8 = 24 grams total

3 0

3 years ago

Jo and Pete have collected some aluminum cans to be recycled. Pete has 47 pounds of cans and Jo has 52 pounds. They can get $0.2

Ksenya-84 [330]

Answer:

Step-by-step explanation:

Total weight of aluminum cans that Pete collected for recycling is 47 pounds.

Total weight of aluminum cans that Jo collected for recycling is 52 pounds.

They can get $0.21 per pound for the cans. Therefore,

The total amount that Pete will get for collecting 47 pounds of aluminum would be

0.21 × 47 = $9.87

The total amount that Jo will get for collecting 52 pounds of aluminum would be

0.21 × 52 = $10.92

The total amount of money that they would get is

9.87 + 10.92 = $20.79

3 0

2 years ago

PLSSS HELP AND EXPLAIN :)

vodka [1.7K]

Answer:

968

Step-by-step explanation:

Rectangular Prism: 11*11*5 = 605

Square Pyramid: 11*11 * 9 over 3 = 363

363+605= 968

3 0

2 years ago

Solve y = x + 8 for x. x= y + 8 x=y - 8 x= -y + 8 x = -y - 8