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worty [1.4K]
3 years ago
14

Between which two consecutive whole numbers does \sqrt{78} 78 ​ lie? Fill out the sentence below to justify your answer and use

your mouse to drag \sqrt{78} 78 ​ to an approximately correct location on the number line.
Mathematics
1 answer:
Artyom0805 [142]3 years ago
6 0

Answer:

A. 8 and 9

Step-by-step explanation:

Between which two consecutive whole numbers does √ 78 lie?

a.

8 and 9

b.

6 and 7

c.

9 and 10

d.

7 and 8

A. 8 and 9

8^2 = 8 × 8 = 64

9^2 = 9 × 9 = 81

B. 6 and 7

6^2 = 6 × 6 = 36

7^2 = 7 × 7 = 49

C. 9 and 12

9^2 = 9 × 9 = 81

12^2 = 12 × 12 = 144

D. 7 and 8

7^2 = 7 × 7 = 49

8^2 = 8 × 8 = 64

The correct answer is A. 8 and 9

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By using properties for <em>trigonometric</em> functions and <em>trigonometric</em> expressions, we find that the <em>exact</em> value of the sine of the angle 5π/12 radians is \frac{\sqrt{2+\sqrt{3}}}{2}.

<h3>How to find the exact value of a trigonometric expression</h3>

<em>Trigonometric</em> functions are <em>trascendent</em> functions, these are, that cannot be described algebraically. Herein we must utilize <em>trigonometric</em> formulae to calculate the <em>exact</em> value of a <em>trigonometric</em> function:

\sin \frac{5\pi}{12} = \sqrt{\frac{1 - \cos \frac{5\pi}{6} }{2} }

\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \cos \frac{\pi}{6} }{2} }

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\sin \frac{5\pi}{12} = \frac{\sqrt{2+\sqrt{3}}}{2}

By using properties for <em>trigonometric</em> functions and <em>trigonometric</em> expressions, we find that the <em>exact</em> value of the sine of the angle 5π/12 radians is \frac{\sqrt{2+\sqrt{3}}}{2}.

To learn more on trigonometric functions: brainly.com/question/15706158

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