Question

a 1. In the Investigate, the sinusoidal function h(t) = 5 sin (30(t + 3)] is used to model the height of tides in a particular location on a particular day. On a different day, the maximum height is 8 m, the minimum height is -8 m, and high tide occurs at 5:30 a.m.
a) Modify the function such that it matches the new data.
b) Predict the times for the next high and low tides.​

Answer 1

Answer:

hi plice give Brainliests answers

Step-by-step explanation:

The height, h, in metres of the tide in a given location on a given day at t hours after midnight can be modelled using the sinusoidal function

h(t)=5sin(30(t−5))+7

At the time of high tide h(t)will be maximum when sin(30(t−5)) is maximum

This means sin(30(t−5))=1

⇒30(t−5)=90⇒t=8

So first high tide after midnight will be at 8 am

Again for next high tide 30(t−5)=450⇒t=20

This means second high tide will be at 8 pm

So at 12 hr interval the high tide will come.

At the time of low tide h(t)will be minimum when sin(30(t−5)) is minimum

This means sin(30(t−5))=−1

⇒30(t−5)=−90⇒t=2

So first low tide after midnight will be at 2 am

Again for next low tide 30(t−5)=270⇒t=14

This means second low tide will be at 2 pm

So after 12 hr interval the low tide will come.

Here period is2πω=36030