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daser333 [38]
3 years ago
14

Step by step how to solve this math question? 60÷5(7-5)

Mathematics
1 answer:
ValentinkaMS [17]3 years ago
4 0
Hey I would first do the one in parentheses so 7-5 is 2 so your equation is now 60/5*2 so now what will you do? 
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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}}

7 0
2 years ago
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