Question

Help please, adv functions problem set

Answer 1

15th February.

Explanation:

We have to solve the equation
`h = 3.98 \sin 2\pi (n-80)/(365) +12.16` for the value of h = 10 hours.

Now,
`10 = 3.98 \sin 2\pi (n-80)/(365) +12.16`

⇒
`3.98 \sin 2\pi (n-80)/(365) =-2.16`

⇒
`\sin 2\pi (n-80)/(365) = -0.5427`

⇒
`2\pi (n-80)/(365) = \sin^(-1)(-0.5427) =-32.868 = -0.1826\pi`

{Since π = 180°}

⇒
`(n-80)/(365) = -0.913`

⇒ n - 80 = - 33.325

⇒ n = 46.6749

Therefore, at the 46th day of the year i.e. (46 - 31) = 15th February there should be about 10 hours of day light. (Answer)