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3 years ago

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+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.

Anon25 [30]

Answer:

Rob saved $24 on Saturday.

Step-by-step explanation:

Given:

Rob is saving to buy a new MP3 player.

Money earned in baby sitting = $11

Money saved =$6

First we will find the Percentage of amount he saved.

Percentage of amount he saved can calculated by Amount saved divided by total money earned and then multiplying by 100.

framing in equation form we get;

Percentage of amount he saved = $\frac{6}{11} \times 100 \approx 54.55\%$

Now Given:

Money earned in babysitting on Saturday = $44

We need to find the Money he saved on Saturday.

Money Saved can be calculated by Percentage of amount he saved multiplying by Money earned in babysitting on Saturday and then divided by 100.

framing in equation form we get;

Money Saved on Saturday = $\frac{54.55}{100}\times 44 = \$24$

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3 years ago

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sveticcg [70]

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3 years ago

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]

Short answer: r = 8
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
Find the volume of the sphere.

Givens
r = 6 cm

Formula
V = (4/3) pi r^3

Sub and Solve
V = 4/3 pi * 6^3
V = 288 * pi

Step two
Find the radius of the cylinder

Givens
V = 288* pi cm^3
h = 4.5 cm

Formula
V = pi r^h

Sub and solve
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288 cm^3 = 4.5 r^2 Divide both sides by 4.5
388 / 4.5 = r^2
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r = square root( 64)
r = 8 <<<<< Answer

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3 years ago

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enot [183]

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