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inn [45]
3 years ago
9

The legs of a right triangle are 29.25 and 13. What is the hypotenuse?

Mathematics
1 answer:
Ivan3 years ago
4 0

Answer:

32.008

Step-by-step explanation:

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Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive
Elena L [17]

Answer:

Constructive Proof

Step-by-step explanation:

Let x be a positive integer

x must be equal to sum of all positive integers exceeding it

i.e.

x = x + (x - 1) + ( x - 2) + ......... + 2 + 1

Equivalently,

x = ∑i (where i = 1 to x)

The property finite sum;

∑i (i = 1 to x) = x(x + 1)/2

So,

x = x(x + 1)/2 ------- Multiply both sides by 2

2 * x = 2 * x(x + 1)/2

2x = x(x + 1)

2x = x² + x ------- subtract 2x from both sides

2x - 2x = x² + x - 2x

0 = x² + x - 2x ----- Rearrange

x² + x - 2x = 0

x² - x = 0 ------ Factorise

x(x - 1) = 0

So,

x = 0 or x - 1 = 0

x = 0 or x = 1 + 0

x = 0 or x = 1

But x ≠ 0

So, x = 1

The statement is only true for x = 1

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1 = 1

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8 0
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