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Vsevolod [243]
3 years ago
7

Suppose a box is to be constructed from a square piece of material of side length x by cutting out a 2-inch square from each cor

ner and turning up the sides. express the volume of the box as a polynomial in the variable x

Mathematics
1 answer:
alexgriva [62]3 years ago
8 0

Consider the attached figure. The central square is the "floor" of the box, and it is a (x-2)-by-(x-2) square.

The four rectangles of the side will be the "walls" of the box, and they are (x-2)-by-2 rectangles.

The volume is given by the base area multiplied by the height of the walls, so we have

\underbrace{(x-2)(x-2)}_{\text{base area}}\times 2 = 2(x^2-4x+4)= 2x^2-8x+8

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Step-by-step explanation:

There should be an option that says, “From the origin, move 0.5 unit to the right along the x-axis and 1 unit down, and place the point.”

6 0
3 years ago
to meet increased demand, world food production must rise 50% by 2030. write this percentage as a fraction in simplest form.
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4 0
3 years ago
Original price: $20 Discount %: 35%
dangina [55]

Answer:

$13 or $7 off

Step-by-step explanation:

20-35%=13

So that means that it is $7 off and it is now $13

4 0
3 years ago
1) Solve for x.<br><br> x+23=−22<br><br><br><br> 2) Solve for a.<br><br> a+(−1.3)=−4.5
8090 [49]
X+23=-22
  -23   -23

x=-45

a+(-1.3)=-4.5
        
         or

a-1.3+-4.5
  +1.3  +1.3

a=3.2
6 0
4 years ago
Read 2 more answers
Find the maxmium area of a rectangular plot of land which can be enclosed by rope of length 60 metres​
mario62 [17]

Answer:

225 m²

Step-by-step explanation:

If W is the width of the rectangle, and L is the length, then:

60 = 2W + 2L

A = WL

Use the first equation to solve for one of the variables:

30 = W + L

L = 30 − W

Substitute into the second equation:

A = W (30 − W)

A = 30W − W²

This is a parabola, so we can find the vertex using the formula x = -b/(2a).

W = -30 / (2 × -1)

W = 15

Or, we can use calculus:

dA/dW = 30 − 2W

0 = 30 − 2W

W = 15

Solving for L:

L = 30 − W

L = 15

So the maximum area is:

A = WL

A = (15)(15)

A = 225

3 0
3 years ago
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