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gregori [183]
3 years ago
7

Carla packed this box with 1 centimeter cubes what is the volume of the box

Mathematics
1 answer:
shusha [124]3 years ago
4 0

Answer: 60\ cm^3

Step-by-step explanation:

<h3> The complete exercise is attached.</h3>

You can observe in the picture attached that the box is a rectangular prism.

The volume of a rectangular prism can be found with this formula:

V=lwh

Where "l" is the length, "w" is the width and "h" is the height.

You know that the lenght of each side of those cubes is 1 centimeter. Therefore, you can multiply the number of cubes on each side of the box by 1 centimeter in order to find the lenght, the width and the height of the box:

 l=(4)(1\ cm)=4\ cm\\\\w=(3)(1\ cm)=3\ cm\\\\h=(5)(1\ cm)=5\ cm

Now you can substitute the lenght, the width and the height of the box into the formula shown at the beginning of the explanation:

V=(4\ cm)(3\ cm)(5\ cm)

Finally, evaluating, you get that the volume of the box is:

V=60\ cm^3

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kompoz [17]

Answer:

x < -12

Step-by-step explanation:

-1/2x > 6

Multiply by -2 to isolate x

Remember that when multiplying by a negative, we flip the inequality

-2 * -1/2x < 6*-2

x < -12

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3 years ago
14a^8c^9 + 2a^4c^3 [Algebra]
rosijanka [135]

Answer:

im not the best at algebra but

2a+3b+4c

Step-by-step explanation:

subtract

(2a−3b+4c) from the sum of (a+3b−4c),(4a−b+9c) and (−2b+3c−a).

add

=(a+3b−4c)+(4a−b+9c)+(−2b+3c−a)

=(a+4a−a)+(3b−b−2b)+(−4c+9c+3c)

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=(4a+8c)−(2a−3b+4c)

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3 0
2 years ago
Help please calculus
VLD [36.1K]

Let x, y, and z denote the side lengths of the box, with the bottom face having dimensions x-by-y and z is the height. Naturally this means each of x, y, and z must be greater than 0.

The box has a fixed volume of 252 cm³, so

xyz = 252

The surface area of the box is

2xy + 2xz + 2yz

and we're told that the material cost for each face is different. The total cost of the material needed to make the box is given by

C (x, y, z) = ($5/cm²) xy + ($2/cm²) xy + 2 ($3/cm²) (xz + yz)

or, omitting units and simplifying,

C (x, y, z) = 7xy + 6 (x + y) z

In the volume constraint, solve for any one variable; I'll do z.

z = 252/(xy)

Substitute this into the cost function:

C (x, y, 252/(xy)) = 7xy + 1512 (x + y)/(xy)

Since this is now a function of 2 variables, I'll rewrite this as

C* (x, y) = 7xy + 1512 (1/y + 1/x)

Compute the partial derivatives of C and find the critical points:

∂C/∂x = 7y - 1512/x² = 0   ⇒   x² y = 216

∂C/∂y = 7x - 1512/y² = 0   ⇒   x y² = 216

It follows that

x² y = x y²   ⇒   x = y

Just like before, we can think about C* as yet another function but only of 1 variable,

C** (x) = 7x² + 3024/x

Now find the critical points of C** :

dC**/dx = 14x - 3024/x² = 0   ⇒   x = 6

All of this tells us that C (x, y, z) has a critical point when x = y = 6 and z = 252/6² = 7. So the box that costs the least has dimensions 6 × 6 × 7 cm, which gives the box a surface area of 240 cm² and a total cost of $756.

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2 years ago
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Softa [21]
X=7 and y=4 are the correct equations
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Evaluate 3a+15+bc−6, when a=7, b=3, and c=15.<br><br> Enter your answer in the box.
melamori03 [73]
I think it's 75.
____________
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2 years ago
Read 2 more answers
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