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ikadub [295]
2 years ago
8

The sum of three consective even integers if the largest number is y

Mathematics
1 answer:
coldgirl [10]2 years ago
6 0

Step-by-step explanation:

If y is largest number, you want y, and the two next smaller even integers smaller than y - i.e. y, y-2, and y-4

The sum of these is y + (y-2) + (y-4).

This simplifies to 3y - 6 or 3(y - 2)

Since we don’t know what y is, this is as far as we can solve the problem.

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2x²- x -3 = 0 ⇒ 2x²-x= 0 + 3 ⇒ 2x² - x = 3 ⇒ 2x = 3 ⇒ x = 1.5
            
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Tcecarenko [31]

\bold{\huge{\green{\underline{ Solution}}}}

\bold{\underline{ Given :- }}

  • <u>We </u><u>have </u><u>given </u><u>a</u><u> </u><u>right</u><u> </u><u>angled </u><u>triangle </u><u>whose </u><u>values </u><u>are </u><u>m</u><u>, </u><u> </u><u>n </u><u>and </u><u>2</u><u> </u>

\bold{\underline{ To \: Find :- }}

  • <u>We </u><u>have </u><u>to </u><u>find </u><u>the </u><u>value </u><u>of </u><u>m </u><u>and </u><u>n</u>

\bold{\underline{ Let's \: Begin :- }}

<u>In </u><u>the </u><u>given </u><u>right </u><u>angled </u><u>triangle</u><u>, </u><u>we </u><u>have </u>

  • Perpendicular height = n units
  • Base = 2 units
  • Hypotenuse = m units

<u>Now</u><u>, </u><u> </u><u>By </u><u>using </u><u>trigonometric </u><u>ratios </u>

\bold{\pink{ Sin Φ = }}{\bold{\pink{\frac{Perpendicular }{Hypotenuse}}}}

\bold{\red{ Cos Φ = }}{\bold{\red{\frac{Base}{Hypotenuse }}}}

\bold{\blue { tan Φ = }}{\bold{\blue{\frac{Perpendicular }{Base }}}}

<u>According </u><u>to </u><u>the </u><u>question </u><u>:</u><u>-</u>

\bold{ Cos \: 45° = }{\bold{\frac{2}{m}}}

\bold{ 1/√2= }{\bold{\frac{2}{m}}}

\bold{\red{ m = 2√2 \: units }}

  • <u>We </u><u>know </u><u>that </u><u>,</u><u> </u><u>Sum </u><u>of </u><u>Angles</u><u> </u><u>of </u><u>triangle </u><u>is </u><u>1</u><u>8</u><u>0</u><u>°</u><u> </u><u>.</u>

<u>Therefore</u><u>, </u>

Let the unknown angle be x

\sf{ 45° + x + 90° = 180° }

\sf{ x = 180° - 135 °  }

\sf{ x = 45°   }

<u>Now</u><u>, </u>

\bold{ Cos \: x° = }{\bold{\frac{n}{2√2}}}

\bold{ Cos \: 45° = }{\bold{\frac{n}{2√2}}}

\bold{ 1/√2= }{\bold{\frac{n}{2√2}}}

\bold { n = 2√2/√2  }

\bold{\red{ n = 2\: units }}

Thus, The value of m = 2√2 and n = 2

\sf{\blue{ Hence, \: option \: D \: is \: Correct }}

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