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vaieri [72.5K]
3 years ago
6

Help me solve this problem please

Mathematics
1 answer:
allochka39001 [22]3 years ago
6 0

Answer:

Step-by-step explanation:

4^2+x^2 = 15^2

x^2 = 15^2 - 4^2 = 225-16 = 209

x=sqrt(209)

x = 14.46

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PLZ SHOW ALL WORK
lara31 [8.8K]

Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width:  w = 12 - 2x
length: l = 18 - 2x
height: h = x

Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
v = (216 - 36x - 24x + 4x^2)x
v = (216 - 60x + 4x^2)x
v = 216x - 60x^2 + 4x^3
v = 4x^3 - 60x^2 + 216x

Part III
The length of the cut has to be greater than 0 and less than half the length of the smallest dimension of the cardboard (after all, there has to be something left over after cutting out the corners). So 0 < x < 6

Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
v = 4x^3 - 60x^2 + 216x
v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
v = 4 - 60 + 216
v = 160

Too small, so let's try 2.
v = 4x^3 - 60x^2 + 216x
v = 4*2^3 - 60*2^2 + 216*2
v = 4*8 - 60*4 + 216*2
v = 32 - 240 + 432
v = 224

And that's the desired volume.
So let's choose a value of x=2.
Reason?
It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.
3 0
3 years ago
If DE =22 cm and the radius=14cm, how long is GH?
Nadya [2.5K]
What is GH and DE? is there a picture lol
4 0
3 years ago
A box contains 5 plain pencils and 3 pens. A second box contains 4 color pencils and 4 crayons. One item from each box is chosen
LekaFEV [45]

Answer:

3/16

Step-by-step explanation:

3/8 * 4/8= 3/16

3/8= 3 pens out of 8 items

4/8= 4 crayons out of 8 items

7 0
3 years ago
Find the surface area of each figure. Round answers to two decimal places. Use 3.14 for pi​
ELEN [110]

Answer:

the top wpuld be 73.14 and i cant see the numbers at the bottom

Step-by-step explanation:

8 0
3 years ago
The value of w varies directly with z. If z = 4, then w = 12. What is the value
IrinaVladis [17]

Answer:

18

Step-by-step explanation:

w varies directly with z, let k be the constant of proportionality, hence this can be represented by the equation:

w = kz

When z = 4, w = 12, hence we need to find the value of the constant of proportionality, substituting:

12 = 4k

Dividing both sides by 4:

12/4 = 4k/4

k = 3

Therefore the equation becomes:

w = 3z

The value of w when z = 6 is given as:

w = 3(6)

w = 18

7 0
3 years ago
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