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evablogger [386]
4 years ago
9

10^2+12^2+14^2+......+26^2=??

Mathematics
1 answer:
Kazeer [188]4 years ago
3 0

Answer:

3156

Step-by-step explanation:

  • <em>Used formula:</em>
  • <em>(1² + 2² + 3² + ... + n²) =1/6*n(n + 1)(2n + 1)</em>

--------

  • 10²+12²+14²+......+26² =
  • (2*5)²+(2*6)² + (2*7)² + ... + (2*13)² =
  • 4*(5²+6²+7²+...+13²) =
  • 4*(1²+2²+...+13² - (1²+2²+3²+4²)) =
  • 4*(1/6*13(13+1)(2*13+1) - (1+4+9+16)) =
  • 4*(1/6*13*14*27- 30) =
  • 4*(819 - 30) =
  • 4*789 =
  • 3156
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3 years ago
the height of a triangle is 9m less than its base. the area of the triangle is 56 m^2 find the length of the base (SHOW STEPS)
Veronika [31]
Hey there :)

We know the area formula of a triangle
\frac{1}{2} (base)(height)

We are given:
The area = 56 m²
The base = let p represent this
The height = 9 m less than the base = p - 9

Apply the formula
56 = \frac{1}{2} × ( p ) × ( p - 9 )
56 = \frac{1}{2} × ( p² - 9p )

Divide \frac{1}{2} on both sides
56 ÷ \frac{1}{2} = p² - 9p
112 = p² - 9p

Bring 112 to the other side and equate equation to 0
p² - 9p - 112

Factorise { Sum = -9 , Product = - 112 , therefore suitable factors = - 16 × 7 )
( p - 16 )( p + 7 ) = 0
     ↓          ↓
 p = 16    p = - 7  ←  Reject p = - 7 since length cannot be negative

So, the length  of the base is 16 m

Check:
56 m² = \frac{1}{2} × 16 × ( 16 - 9 )
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7 0
3 years ago
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Art [367]

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8 0
1 year ago
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Answer:

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Step-by-step explanation:

i dont have step by step but the problome is 30x20=600

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