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Triss [41]
2 years ago
11

The price of an item has been reduced by 85%. The original price was $37.

Mathematics
1 answer:
Tema [17]2 years ago
7 0

Answer:  <em>Multiply the original price by the decimal form of the percent and subtract that from the original price. </em>

<em>37*0.85=31.45 </em>

<em>37-31.45=5.55 </em>

<u><em>Answer: New price is $5.55</em></u>

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We have the sum of cubes identity

a^3 + b^3 = (a + b) (a^2 - ab + b^2)

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and

2^3 + 3^3 = (2 + 3) (2^2 - 6 + 3^2) = 5 \times 7

Then

\sqrt{1^3+2^3+3^3+4^3+5^3} = \sqrt{5\times13 + 5\times7 + 5\times5^2} = \sqrt{5 \times (20 + 25)} \\\\ ~~~~~~~~ = \sqrt{5^2 \times (4 + 5)} = \sqrt{5^2\times9} = \sqrt{5^2\times3^2} = 5\times3 = \boxed{15}

Alternatively, we have the well-known sum of cubes formula

\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}4

The sum under the square root is this sum with n=5. Then

1^3+2^3+3^3+4^3+5^3 = \dfrac{5^2\times6^2}4 = 225 = 15^2

and so the square root again reduces to 15.

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