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For what value of x does 6 sin (2x - 25)o attain its maximum value...

Mathematics
JAMB 1998

For what value of x does 6 sin (2x - 25)o attain its maximum value in the range 0o \(\leq\) x \(\leq\) 180o

  • A. 12\(\frac{1}{2}\)
  • B. 32\(\frac{1}{2}\)
  • C. 57\(\frac{1}{2}\)
  • D. 147\(\frac{1}{2}\)
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Correct Answer: Option C
Explanation

y = 6 sin (2x - 25)º

\(\frac{dy}{dx}\) = 12 cos(2x - 25)º

\(\frac{dy}{dx}\) = 0

12 cos x (2x - 25º) = 0

= cos(2x - 25º) = 0

= 2x - 25º = cos\(^{-1}\)(0)

= 2x - 25º = 90º

x = \(\frac{115}{2}\)


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