The volume of a cube is 8cm3, find the length of one of it's sides

The side length is 2 cm

Step-by-step explanation:

The volume of a cube is s^3

V = s^3

8 = s^3

Take the cube root of each side

8 ^ 1/3 = s^3 ^ 1/3

2 = s

The side length is 2 cm

2 cm

Step-by-step explanation:

The volume of a cube can be found using the following formula:

V=s^3

where s is the length of one side. We know the volume is 8 cm^3, therefore we can substitute that value in for V.

8 cm^3=s^3

We want to find what the side length is. The side length is being cubed. The inverse of a cube is the cube root. Therefore, we must take the cube root of both sides, or raise both sides to the power of 1/3.

(8 cm^3)^1/3=(s^3)^1/3

(8 cm^3)^1/3=s

2 cm=s

The length of one side is 2 centimeters.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!