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zhenek [66]
3 years ago
10

Write an equation expressing the volume of the box made by paper x by 16 from which a square with side length 2 is cut from each

corner and the sides of a box will are folded as shown.

Mathematics
1 answer:
Furkat [3]3 years ago
8 0

Answer: V = 24*(x - 4) with the condition x > 4.

Step-by-step explanation:

The volme of a cube/box is equal to:

V = W*L*H

where W = width, L = lenght and H = heigth.

First:

We know that the cubes cut in the corner have a side length of 2.

Then the remaining part is folded up, and this is now the height.

So the height of the box is equal to 2.

Now, we know that the initial measures of the piece of paper are x by 16

But now, in each extreme, we subtracted 2 units, that are now the new heiht, so now the piece of paper is (x -2 -2) by (16 -2 - 2)

or (x - 4) by 12.

Then the volume of the box is:

V = (x -4)*12*2 = 24*(x -4)

Notice something, if x is equal or smaller than 4, then we have a negative volume or a volume equal to zero. Those are problems in our model, so we should use the condition x > 4.

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It should be line MN
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3 years ago
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What two nonnegative real numbers with a sum of 64 have the largest possible product?
Otrada [13]

The two non negative real numbers with a sum of 64 that have the largest possible​ product are; 32 and 32.

<h3>How do we solve the nonnegative real numbers?</h3>

Let the two numbers be x and y.

Thus, if their sum is 64, then we have;

x + y = 64

y = 64 - x

Their product will be;

P = xy

Putting (64 - x) for y in the product equation we have;

P = (64 - x)x

P = 64x - x²

Since the product is maximum, let us find the derivative;

P'(x) = 64 - 2x

At P'(x) = 0, we have;

64 - 2x = 0

2x = 64

x = 64/2

x = 32

Thus; y = 64 - 32

y = 32

Read more about nonnegative real numbers

brainly.com/question/9580755

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6 0
1 year ago
Rewrite y=x^2+6x+2 in vertex form​
Greeley [361]

Answer:(x+3) 2−7

Step-by-step explanation:

5 0
3 years ago
PLS HELP ASAP ILL GIVE BRAINLKEST PLS THANKS
Lerok [7]
I think it would -2!! Sorry if I’m wrong
4 0
2 years ago
Which piecewise function is shown in the graph?
mash [69]

Based on the characteristics of <em>linear</em> and <em>piecewise</em> functions, the <em>piecewise</em> function f(x) = \left \{ {{-0.5\cdot x +1, \,x < 0} \atop {2\cdot x - 2, \,x \ge 0}} \right. is shown in the graph attached herein. (Correct choice: A)

<h3>How to determine a piecewise function</h3>

In this question we have a graph formed by two different <em>linear</em> functions. <em>Linear</em> functions are polynomials with grade 1 and which are described by the following formula:

y = m · x + b     (1)

Where:

  • x - Independent variable.
  • y - Dependent variable.
  • m - Slope
  • b - Intercept

By direct observation and by applying (1) we have the following <em>piecewise</em> function:

f(x) = \left \{ {{-0.5\cdot x +1, \,x < 0} \atop {2\cdot x - 2, \,x \ge 0}} \right.

Based on the characteristics of <em>linear</em> and <em>piecewise</em> functions, the <em>piecewise</em> function f(x) = \left \{ {{-0.5\cdot x +1, \,x < 0} \atop {2\cdot x - 2, \,x \ge 0}} \right. is shown in the graph attached herein. (Correct choice: A)

To learn more on piecewise functions: brainly.com/question/12561612

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3 0
1 year ago
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