Question

L(t) models the length of each day (in minutes) in Manila, Philippines tt days after the spring equinox. Here, t is entered in radians. L(t)=52 sin (2pie/365 t) =728 What is the first day after the spring equinox that the day length is 750 minutes?

Answer 1

25 is answer from k han acedmy

Explanation:

Answer 2

Given that:

`L(t) = 52\sin((2 \pi t)/(365))+728`

where

L(t) represents the length of each day(in minutes) and t represents the number of days.

Substitute the value of L(t) = 750 minutes we get;

`750= 52\sin((2 \pi t)/(365))+728`

Subtract 728 from both sides we get;

`22= 52\sin((2 \pi t)/(365))`

Divide both sides by 52 we get;

`0.42307692352= \sin((2 \pi t)/(365))`

or

`(2 \pi t)/(365) = \sin^(-1) (0.42307692352)`

Simplify:

`(2 \pi t)/(365) =0.43683845`

or

`t = (365 * 0.43683854)/(2 * \pi) = (365 * 0.43683854)/(2 * 3.14)`

Simplify:

`t \approx 25` days

Therefore, the first day after the spring equinox that the day length is 750 minutes, is 25 days