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Bess [88]
2 years ago
14

bicycle, A company that makes dice (cube), is looking to change The size of the days they produce. The current days have edge le

ngth of 5mm, in the company wants to increase them to 15mm. how will the volume of the day to be affected if this changes made?
Mathematics
1 answer:
stich3 [128]2 years ago
3 0

Answer: If that change is made, the new volume will be 3,375\ mm^3

Step-by-step explanation:

For this exercise it is important to remember that the formula used to calculate the volume of a cube is the following:

V=s^3

Where "s" is the lenght of any edge of the cube.

You know that the current days have edge length of 5 mm.

Then, knowing the formula for calculate the volume of a cube, you get that the current volume of any of those cubes made by the company is:

V_1=(5\ mm)^3\\\\V_1=125\ mm^3

Since they want to increase the length to 15 mm, you can identify that:

s=15\ mm

Therefore, knowing this new edge you can calculate the new volume.

You get that this is:

V_2=(15\ mm)^3\\\\V_2=3,375\ mm^3

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Factor 81z^4 - 16<br> Please answer asap
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81x%5E4-16 Start with the given expression.

%289x%5E2%29%5E2-16 Rewrite 81x%5E4 as %289x%5E2%29%5E2.

%289x%5E2%29%5E2-%284%29%5E2 Rewrite 16 as %284%29%5E2.

Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=9x%5E2 and B=4.

So let's use the difference of squares formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29 to factor the expression:

A%5E2-B%5E2=%28A%2BB%29%28A-B%29 Start with the difference of squares formula.

%289x%5E2%29%5E2-%284%29%5E2=%289x%5E2%2B4%29%289x%5E2-4%29 Plug in A=9x%5E2 and B=4.

So this shows us that 81x%5E4-16 factors to %289x%5E2%2B4%29%289x%5E2-4%29.

In other words 81x%5E4-16=%289x%5E2%2B4%29%289x%5E2-4%29.

Now let's factor 9x%5E2-4 further

-------------------------------------

 

9x%5E2-4 Start with the given expression.

%283x%29%5E2-4 Rewrite 9x%5E2 as %283x%29%5E2.

%283x%29%5E2-%282%29%5E2 Rewrite 4 as %282%29%5E2.

Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=3x and B=2.

So let's use the difference of squares formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29 to factor the expression:

A%5E2-B%5E2=%28A%2BB%29%28A-B%29 Start with the difference of squares formula.

%283x%29%5E2-%282%29%5E2=%283x%2B2%29%283x-2%29 Plug in A=3x and B=2.

So this shows us that 9x%5E2-4 factors to %283x%2B2%29%283x-2%29.

In other words 9x%5E2-4=%283x%2B2%29%283x-2%29.

----------------------------------------------------------------

Answer:

So 81x%5E4-16 completely factors to %289x%5E2%2B4%29%283x%2B2%29%283x-2%29

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