Periodic Functions - Applications

I have the following equation $\displaystyle y= -4sin15x+25 $ ( y represents the temperature and x represents time in hours, so x=0 means midnight and x=1 means 1:00 am) and I am given a question with the graph of the given equation, and to get the solution to the question you can you use the graph (which is also what my teacher told us to do) and so i do use the graph and get the correct answer of 13 hours. My question is how would i use the equation to solve for what i need?

The question:

The pool is comfortable for swimming at 23 degrees Celsius. The pool is open from 6:00 am to 11:00 pm. How many hours of comfortable swimming are available on a sunny day?

Any help is appreciated and thank you in advance!

Re: Periodic Functions - Applications

Hey sakonpure6.

For this problem you will need to say what values of y can be taken.

You mention 23 degrees but are you allowed to have a range of values (like less than 23 degrees or greater than 23 degrees)?

Once you have this you solve your inequality.

Re: Periodic Functions - Applications

Quote:

Originally Posted by

**chiro** Hey sakonpure6.

For this problem you will need to say what values of y can be taken.

You mention 23 degrees but are you allowed to have a range of values (like less than 23 degrees or greater than 23 degrees)?

Once you have this you solve your inequality.

no y must be exactly 23 degrees

Re: Periodic Functions - Applications

Well can you set y to 23 and solve for x?

Re: Periodic Functions - Applications

Oh sorry y must be 23 degrees untill the peak shich is what i believe to be 29

Re: Periodic Functions - Applications

Can you setup an inequality where you solve for y = 29 and y = 23 to get the values inbetween?

Re: Periodic Functions - Applications

Quote:

Originally Posted by

**chiro** Can you setup an inequality where you solve for y = 29 and y = 23 to get the values inbetween?

I don't know what "inequality" is, do you mind if you show me the equations?

Re: Periodic Functions - Applications

Well, the point of an "**in**equality is that it isn't an equation!

If what you have told us is correct, you want $\displaystyle 23\le -14 sin(15x)+ 25\le 29$. And the simplest way to solve that is to solve the equations -14 sin(15x)+ 25= 23 and -14sin(15x)+ 25= 29. The correct range for x will be between those values.

Re: Periodic Functions - Applications

Quote:

Originally Posted by

**HallsofIvy** Well, the point of an "**in**equality is that it isn't an equation!

If what you have told us is correct, you want $\displaystyle 23\le -14 sin(15x)+ 25\le 29$. And the simplest way to solve that is to solve the equations -14 sin(15x)+ 25= 23 and -14sin(15x)+ 25= 29. The correct range for x will be between those values.

Oh okay thank you! Ill do them and compare my answers!