Which line has a slope of 2 and please tell me how to figure it out on my own

The elves at Santa’s Workshop are trying to wrap the biggest box they can with the last bit of wrapping paper they have. All of

valina [46]

Answer:

The length of the box is 2×√30 inches long, the width of the box is 2×√(10/3) inches long, while the height of the box is √30 inches long

Step-by-step explanation:

The given parameters are;

The length of the last rectangular prism box = 3 × The width of the box

The area of the available wrapping paper = 240 in.²

Let L represent the length of the rectangular prism box, let W represent the width of the rectangular prism box and let h, represent the height of the rectangular box

Therefore, we have;

L = 3 × W

The surface area of the box, A = 2 × L × W + 2 × L × h + 2 × W × h

Whereby, L = 3 × W, we have;

A = 2 × 3 × W × W + 2 × 3 × W × h + 2 × W × h = 8·h·W + 6·W²

A = 8·h·W + 6·W² = 240

8·h·W + 6·W² = 240

8·h·W = 240 - 6·W²

h = (240 - 6·W²)/(8·W)

The volume, V = L × W × h

∴ V = 3 × W × W × h = 3 × W² × h

V = 3 × W² × h

∴ V = 3 × W² × (240 - 6·W²)/(8·W) = 3/8 × W × (240 - 6·W²) = 90·W - 9/4·W³

dV/dW = d(90·W - 9/4·W³)/dW = 90 - 27/4·W²

At the maximum point, dV/dW = 0, which gives;

dV/dW = 90 - 27/4·W² = 0 at maximum point

27/4·W² = 90

W² = 4/27 × 90 = 40/3

W = ±√(40/3) = ±2×√(10/3)

Differentiating again and substituting gives;

d²V/dW² = d(90 - 27/4·W²)/dW = - 27/4·W

Given that when W = 2×√(10/3), d²V/dW² is negative, and when W = -2×√(10/3), d²V/dW² is positive, W = 2×√(10/3) is the local maximum point

Therefor, the dimensions of the box are;

W = 2×√(10/3)

L = 3 × W = 3 × 2×√(10/3)

L = 3 × 2×√(10/3) = 2×√30

L = 2×√30

L = 6 ×√(10/3)

h = (240 - 6·(2×√(10/3))²)/(8·(2×√(10/3))) = √30

h = √30

Therefore, the length of the box is 2×√30 inches long, the width of the box is 2×√(10/3) inches long, while the height of the box is √30 inches long.

6 0

2 years ago

How do you know pi x r x r x h

Nat2105 [25]

V= πr^2h

This is the formula for volume of a cylinder. The volume formula builds off the area formula. Where area is more 2-dimensional, volume is 3-dimensional. You can think of a flat sheet of paper for area (2-dimensional) and a solid box for volume (3-dimensional).

Usually your teacher would give the formulas when starting this section of math. From there, either keep a list of needed formulas in your math folder for easy reference, or try to memorize the formulas for the current section of math you are working on. Some teachers allow formula reference sheets and some do not.

Hope this answers your question! :)

4 0

3 years ago

{(-3,-8), (-2, - 12), (-1,-11), (0, - 7), (1,-6)}

7nadin3 [17]

Answer:

whats question ?

Step-by-step explanation:

7 0

2 years ago

Multiply the polynomials show steps

Karo-lina-s [1.5K]

Answer:

3 $a^{4}$ + 11a³ - 7a² + 18a - 18

Step-by-step explanation:

When multiplying with two brackets, you need to multiply the three terms, (a²), (4a) and (-6) from the first bracket to all the terms in the second brackets, (3a²), (-a) and (3) individually. I have put each multiplied term in a bracket so it is easier.

(a² + 4a - 6) × (3a² - a + 3) =

(a² × 3a²) + {a² × (-a)} + (a² × 3) + (4a × 3a²) + {4a × (-a)} + (4a × 3) + {(-6) × a²) + {(-6) × (-a)} + {(-6) × 3}

Now we can evaluate the terms in the brackets.

(a² × 3a²) + {a² × (-a)} + (a² × 3) + (4a × 3a²) + {4a × (-a)} + (4a × 3) + {(-6) × a²) + {(-6) × (-a)} + {(-6) × 3} =

3 $a^{4}$ + (-a³) + 3a² + 12a³ + (-4a²) + 12a + (-6a²) + 6a + (-18)

We can open the brackets now. One plus and one minus makes a minus.

3 $a^{4}$ + (-a³) + 3a² + 12a³ + (-4a²) + 12a + (-6a²) + 6a + (-18) =

3 $a^{4}$ -a³ + 3a² + 12a³ -4a² + 12a -6a² + 6a -18

Evaluate like terms.

3 $a^{4}$ -a³ + 3a² + 12a³ -4a² + 12a -6a² + 6a -18 = 3 $a^{4}$ + 11a³ - 7a² + 18a - 18

5 0

3 years ago

PLEASE HELP! 20 POINTS + BRANLIEST WILL BE GIVEN

SOVA2 [1]

Answer:

The answer is 22.5 miles

Step-by-step excplanation:

5 0

2 years ago