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Ksenya-84 [330]

2 years ago

5

Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 11, 7,

3, ... This is_ sequence and the _ is equal to_

2 answers:

stiv31 [10]2 years ago

5 0

The sequence 11,7,3,... is arithmetic because there is a constant increase of (-4)

Must click thanks and mark brainliest

lara31 [8.8K]2 years ago

4 0

the sequence is arithmetic because it's incrementing by a constant ratio of -4

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2 years ago

What is the coefficient of 4(3)(2)Q

inysia [295]

Answer:

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2 years ago

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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3 years ago