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Natasha_Volkova [10]
3 years ago
5

The sum of the squares of three consecutive integers is 509. Determine the integers.

Mathematics
1 answer:
GalinKa [24]3 years ago
6 0

Answer:

12, 13, 14

Step-by-step explanation:

Denote the integers as:

x

x+1

x+2

The sum of their squares, so that would be;

(x^(2)) + (( x + 1 )^(2)) + (( x + 2 )^(2)) = 509

write out the squares

x^2 + x^2 + 2x + 1 + x^2 + 4x + 4 = 509

combine like terms

3x^2 + 6x + 5 = 509

inverse operations

3x^2 + 6x + 5 = 509

                -5     -5

3x^2 + 6x = 504

factor

3x^2 + 6x = 504

3 ( x^2 + 2x ) =504

Inverse operations

3 ( x^2 + 2x ) = 504

/3                       /3

x^2 + 2x = 168

Factor again

x ( x + 2 ) = 168

At this point, it should be obvious that x is 12 (because 12 * 14 = 168)

So now substitute back into the consecutive numbers

x = 12

x + 1 = 13

x + 2 = 14

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4 0
3 years ago
Rob is saving to buy a new MP3 player. For every $11 he earns babysitting, he saves $6. On Saturday, Rob earned $44 babysitting.
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Step-by-step explanation:

Given:

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A sphere with a radius of 6cm has the same volume as a cylinder with a height of 4.5cm. What is the radius of the cylinder
yawa3891 [41]
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Remark
The easiest way to do this is to solve the sphere's volume in terms of pi. When you do this, you can equate that to the formula for a cylinder and cancel the pi values. 

Step One
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<em>Givens</em>
r = 6 cm

<em>Formula</em>
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<em>Sub and Solve</em>
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Step two 
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<em>Formula</em>
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<em>Sub and solve</em>
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