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vesna_86 [32]
3 years ago
11

A cube has side length a.The side lengths are decreased to 30% of their original size.Write an expression in simplest form for t

he volume of the cube in terms of a.
Mathematics
1 answer:
jeka943 years ago
5 0

Answer:

Volume V = 0.027a^3

Step-by-step explanation:

Let a represent the length of the side length of the cube.

a.The side lengths are decreased to 30% of their original size;

l = 30% of a

l = 0.3a .....1

The volume of a cube can be expressed as;

V = l × l × l

V = l^3 .......2

Where;

l = side length

Substituting the value of l into equation 2;

V = l^3 = (0.3a)^3

V = 0.027a^3

Volume V = 0.027a^3

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Evaluate the expression below using the properties of operations. Show your steps.−36 ÷ 14 ⋅ (−18) ⋅ (−3) ÷ 6
s2008m [1.1K]

Answer:

(-162)/7 or -23 1/7 as mixed fraction

Step-by-step explanation:

Simplify the following:

(-36)/14 (-18) (-3)/6

Hint: | Express (-36)/14 (-18) (-3)/6 as a single fraction.

(-36)/14 (-18) (-3)/6 = (-36 (-18) (-3))/(14×6):

(-36 (-18) (-3))/(14×6)

Hint: | In (-36 (-18) (-3))/(14×6), divide -18 in the numerator by 6 in the denominator.

(-18)/6 = (6 (-3))/6 = -3:

(-36-3 (-3))/14

Hint: | In (-36 (-3) (-3))/14, the numbers -36 in the numerator and 14 in the denominator have gcd greater than one.

The gcd of -36 and 14 is 2, so (-36 (-3) (-3))/14 = ((2 (-18)) (-3) (-3))/(2×7) = 2/2×(-18 (-3) (-3))/7 = (-18 (-3) (-3))/7:

(-18 (-3) (-3))/7

Hint: | Multiply -18 and -3 together.

-18 (-3) = 54:

(54 (-3))/7

Hint: | Multiply 54 and -3 together.

54 (-3) = -162:

Answer:  (-162)/7

3 0
3 years ago
What is the fifth square root of x^16
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The fifth square root as in a^(1/2)^(1/2)^(1/2)^(1/2)^(1/2)

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Since a=x^16 in this case and the rule (b^a)^c=b^(a*c) we have:

(x^16)^(1/32)

x^(16/32)

x^(1/2) or if you prefer

√x


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3 years ago
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Whitepunk [10]
B) f(x) = 3x^2 -2x + 5
5 0
3 years ago
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