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2 years ago

Someone please help me with this I can’t get it wrong

Mathematics

2 answers:

JulsSmile [24]2 years ago

5 0

Answer:

a = 7

Step-by-step explanation:

a² = b² + c² - 2bc × cos α

a² = 2² + ( 5√3 )² - 2 × 2 × 5√3 × $\frac{\sqrt{3} }{2}$

a² = 49

a = 7

natali 33 [55]2 years ago

3 0

Answer:

a = 7

Step-by-step explanation:

Using the Cosine rule in the triangle

a² = b² + c² - (2bc cosA )

= 2² + (5 $\sqrt{3}$ )² - (2 × 2 × 5 $\sqrt{3}$ × cos30° )

= 4 + 75 - (20 $\sqrt{3}$ × $\frac{\sqrt{3} }{2}$ ) ← exact value of cos30°

= 79 - ( 10 × 3)

= 79 - 30

= 49 ( take square root of both sides )

a = $\sqrt{49}$ = 7

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likoan [24]

It's easy to show that $7\tan(4x)$ is strictly increasing on $x\in\left[0,\frac\pi8\right]$ . This means

$M = \max \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/12} = 7\sqrt3$

and

$m = \min \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/16} = 7$

Then the integral is bounded by

$\displaystyle 7\left(\frac\pi{12} - \frac\pi{16}\right) \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le 7\sqrt3 \left(\frac\pi{12} - \frac\pi{16}\right)$

$\implies \displaystyle \boxed{\frac{7\pi}{48}} \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le \boxed{\frac{7\sqrt3\,\pi}{48}}$

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2 years ago

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kati45 [8]

Answer:

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Step-by-step explanation:

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3 years ago

Identify the point. y + 2 = 4/3(x - 7)

MA_775_DIABLO [31]

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