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Grade 12 Functions


Determining if a sum of trig functions is periodicDefining periodic functions?problem in Functions and PeriodicityIntegration of periodic functionsTransforming FunctionsPeriodic Functions $g(x)=f(kx)$Overlap of two periodic step functionsBoundedness of periodic functionsConversion of periodic functions into solids of specific widthA product of two functions is periodic; are the functions individually periodic?













-2












$begingroup$


I was hoping someone can explain to me step by step to get the answer for the following equation, I have no clue how to even begin solving the following questions.





  1. What is the period of this question: the tides at a cove show a predictable sinusoidal pattern. One day, the reach a maximum height of $10.7$ meters at 3:30am and a minimum height of $1.1$ meters at 9:45am. What is the period for the function?


  2. How do I calculate the average rate of change of the opening on the interval $1≤t≤3$ to the equation $d(t)= 200t(2)^{-t}$, where d represents the width of the opening in cm t seconds after opening the door.


  3. What would be the domain and range of the function $u(x)=v(x)-w(x)$?








graphing-functions periodic-functions







share|cite|improve this question











$endgroup$












  • $begingroup$
    You have three completely different questions here. They should be separated. I don't understand the formula for $d(t)$. What do you know about the domains and ranges of the functions on the right side in 3?
    $endgroup$
    – Ross Millikan
    Mar 12 at 15:06












  • $begingroup$
    Did you mean $d(t) = 200t2^{-t}$?
    $endgroup$
    – N. F. Taussig
    Mar 12 at 15:08










  • $begingroup$
    Yes, I meant that, sorry.
    $endgroup$
    – Chelsea Nankisore
    Mar 12 at 15:08










  • $begingroup$
    a) We are not here to do your homework, and b) Do not ask multiple different questions in the same post.
    $endgroup$
    – Alex Provost
    Mar 12 at 16:04
















-2












$begingroup$


I was hoping someone can explain to me step by step to get the answer for the following equation, I have no clue how to even begin solving the following questions.





  1. What is the period of this question: the tides at a cove show a predictable sinusoidal pattern. One day, the reach a maximum height of $10.7$ meters at 3:30am and a minimum height of $1.1$ meters at 9:45am. What is the period for the function?


  2. How do I calculate the average rate of change of the opening on the interval $1≤t≤3$ to the equation $d(t)= 200t(2)^{-t}$, where d represents the width of the opening in cm t seconds after opening the door.


  3. What would be the domain and range of the function $u(x)=v(x)-w(x)$?








graphing-functions periodic-functions







share|cite|improve this question











$endgroup$












  • $begingroup$
    You have three completely different questions here. They should be separated. I don't understand the formula for $d(t)$. What do you know about the domains and ranges of the functions on the right side in 3?
    $endgroup$
    – Ross Millikan
    Mar 12 at 15:06












  • $begingroup$
    Did you mean $d(t) = 200t2^{-t}$?
    $endgroup$
    – N. F. Taussig
    Mar 12 at 15:08










  • $begingroup$
    Yes, I meant that, sorry.
    $endgroup$
    – Chelsea Nankisore
    Mar 12 at 15:08










  • $begingroup$
    a) We are not here to do your homework, and b) Do not ask multiple different questions in the same post.
    $endgroup$
    – Alex Provost
    Mar 12 at 16:04














-2












-2








-2





$begingroup$


I was hoping someone can explain to me step by step to get the answer for the following equation, I have no clue how to even begin solving the following questions.





  1. What is the period of this question: the tides at a cove show a predictable sinusoidal pattern. One day, the reach a maximum height of $10.7$ meters at 3:30am and a minimum height of $1.1$ meters at 9:45am. What is the period for the function?


  2. How do I calculate the average rate of change of the opening on the interval $1≤t≤3$ to the equation $d(t)= 200t(2)^{-t}$, where d represents the width of the opening in cm t seconds after opening the door.


  3. What would be the domain and range of the function $u(x)=v(x)-w(x)$?








graphing-functions periodic-functions







share|cite|improve this question











$endgroup$




I was hoping someone can explain to me step by step to get the answer for the following equation, I have no clue how to even begin solving the following questions.





  1. What is the period of this question: the tides at a cove show a predictable sinusoidal pattern. One day, the reach a maximum height of $10.7$ meters at 3:30am and a minimum height of $1.1$ meters at 9:45am. What is the period for the function?


  2. How do I calculate the average rate of change of the opening on the interval $1≤t≤3$ to the equation $d(t)= 200t(2)^{-t}$, where d represents the width of the opening in cm t seconds after opening the door.


  3. What would be the domain and range of the function $u(x)=v(x)-w(x)$?








graphing-functions periodic-functions




graphing-functions periodic-functions






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Mar 12 at 16:15









Brian

733116




733116










asked Mar 12 at 14:58









Chelsea NankisoreChelsea Nankisore

11




11












  • $begingroup$
    You have three completely different questions here. They should be separated. I don't understand the formula for $d(t)$. What do you know about the domains and ranges of the functions on the right side in 3?
    $endgroup$
    – Ross Millikan
    Mar 12 at 15:06












  • $begingroup$
    Did you mean $d(t) = 200t2^{-t}$?
    $endgroup$
    – N. F. Taussig
    Mar 12 at 15:08










  • $begingroup$
    Yes, I meant that, sorry.
    $endgroup$
    – Chelsea Nankisore
    Mar 12 at 15:08










  • $begingroup$
    a) We are not here to do your homework, and b) Do not ask multiple different questions in the same post.
    $endgroup$
    – Alex Provost
    Mar 12 at 16:04


















  • $begingroup$
    You have three completely different questions here. They should be separated. I don't understand the formula for $d(t)$. What do you know about the domains and ranges of the functions on the right side in 3?
    $endgroup$
    – Ross Millikan
    Mar 12 at 15:06












  • $begingroup$
    Did you mean $d(t) = 200t2^{-t}$?
    $endgroup$
    – N. F. Taussig
    Mar 12 at 15:08










  • $begingroup$
    Yes, I meant that, sorry.
    $endgroup$
    – Chelsea Nankisore
    Mar 12 at 15:08










  • $begingroup$
    a) We are not here to do your homework, and b) Do not ask multiple different questions in the same post.
    $endgroup$
    – Alex Provost
    Mar 12 at 16:04
















$begingroup$
You have three completely different questions here. They should be separated. I don't understand the formula for $d(t)$. What do you know about the domains and ranges of the functions on the right side in 3?
$endgroup$
– Ross Millikan
Mar 12 at 15:06






$begingroup$
You have three completely different questions here. They should be separated. I don't understand the formula for $d(t)$. What do you know about the domains and ranges of the functions on the right side in 3?
$endgroup$
– Ross Millikan
Mar 12 at 15:06














$begingroup$
Did you mean $d(t) = 200t2^{-t}$?
$endgroup$
– N. F. Taussig
Mar 12 at 15:08




$begingroup$
Did you mean $d(t) = 200t2^{-t}$?
$endgroup$
– N. F. Taussig
Mar 12 at 15:08












$begingroup$
Yes, I meant that, sorry.
$endgroup$
– Chelsea Nankisore
Mar 12 at 15:08




$begingroup$
Yes, I meant that, sorry.
$endgroup$
– Chelsea Nankisore
Mar 12 at 15:08












$begingroup$
a) We are not here to do your homework, and b) Do not ask multiple different questions in the same post.
$endgroup$
– Alex Provost
Mar 12 at 16:04




$begingroup$
a) We are not here to do your homework, and b) Do not ask multiple different questions in the same post.
$endgroup$
– Alex Provost
Mar 12 at 16:04










2 Answers
2






active

oldest

votes


















0












$begingroup$

For a sine wave, the time from maximum to minimum is half the period.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    So I divide half the maximum from the minimum?
    $endgroup$
    – Chelsea Nankisore
    Mar 12 at 15:09










  • $begingroup$
    No, you take the time it takes from max to minimum and double it.
    $endgroup$
    – Matthew Liu
    Mar 12 at 15:30










  • $begingroup$
    No, plot a sine wave and look at it. You double the time from max to min to get a period.
    $endgroup$
    – Ross Millikan
    Mar 12 at 15:30



















0












$begingroup$

Even though you don't know where to start, you do.. Start by writing the definitions of period, average rate of change, domain, and range.



That being said:



1) Half the period is time from max to min (6.25 hours). So $Period=2cdot 6.25 = 12.5$



2) Average rate of change is the slope of the secant line of distance function. In this case, $frac{d(3)-d(1)}{3-1}$. you can take it from here



3) Domain of $u(x)$ can only be the $x$ where $v(x)$ and $w(x)$ exists. Therefore, domain of $u(x)$ is ${ xinmathbb{R} , | , x$ in domain of both $v(x)$ and $w(x)}$



Range of $u(x)$ is slightly trickier. Any chance you have actual equations for $v(x)$ and $w(x)$?






share|cite|improve this answer









$endgroup$













    Your Answer





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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    0












    $begingroup$

    For a sine wave, the time from maximum to minimum is half the period.






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      So I divide half the maximum from the minimum?
      $endgroup$
      – Chelsea Nankisore
      Mar 12 at 15:09










    • $begingroup$
      No, you take the time it takes from max to minimum and double it.
      $endgroup$
      – Matthew Liu
      Mar 12 at 15:30










    • $begingroup$
      No, plot a sine wave and look at it. You double the time from max to min to get a period.
      $endgroup$
      – Ross Millikan
      Mar 12 at 15:30
















    0












    $begingroup$

    For a sine wave, the time from maximum to minimum is half the period.






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      So I divide half the maximum from the minimum?
      $endgroup$
      – Chelsea Nankisore
      Mar 12 at 15:09










    • $begingroup$
      No, you take the time it takes from max to minimum and double it.
      $endgroup$
      – Matthew Liu
      Mar 12 at 15:30










    • $begingroup$
      No, plot a sine wave and look at it. You double the time from max to min to get a period.
      $endgroup$
      – Ross Millikan
      Mar 12 at 15:30














    0












    0








    0





    $begingroup$

    For a sine wave, the time from maximum to minimum is half the period.






    share|cite|improve this answer









    $endgroup$



    For a sine wave, the time from maximum to minimum is half the period.







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Mar 12 at 15:06









    Ross MillikanRoss Millikan

    299k24200374




    299k24200374












    • $begingroup$
      So I divide half the maximum from the minimum?
      $endgroup$
      – Chelsea Nankisore
      Mar 12 at 15:09










    • $begingroup$
      No, you take the time it takes from max to minimum and double it.
      $endgroup$
      – Matthew Liu
      Mar 12 at 15:30










    • $begingroup$
      No, plot a sine wave and look at it. You double the time from max to min to get a period.
      $endgroup$
      – Ross Millikan
      Mar 12 at 15:30


















    • $begingroup$
      So I divide half the maximum from the minimum?
      $endgroup$
      – Chelsea Nankisore
      Mar 12 at 15:09










    • $begingroup$
      No, you take the time it takes from max to minimum and double it.
      $endgroup$
      – Matthew Liu
      Mar 12 at 15:30










    • $begingroup$
      No, plot a sine wave and look at it. You double the time from max to min to get a period.
      $endgroup$
      – Ross Millikan
      Mar 12 at 15:30
















    $begingroup$
    So I divide half the maximum from the minimum?
    $endgroup$
    – Chelsea Nankisore
    Mar 12 at 15:09




    $begingroup$
    So I divide half the maximum from the minimum?
    $endgroup$
    – Chelsea Nankisore
    Mar 12 at 15:09












    $begingroup$
    No, you take the time it takes from max to minimum and double it.
    $endgroup$
    – Matthew Liu
    Mar 12 at 15:30




    $begingroup$
    No, you take the time it takes from max to minimum and double it.
    $endgroup$
    – Matthew Liu
    Mar 12 at 15:30












    $begingroup$
    No, plot a sine wave and look at it. You double the time from max to min to get a period.
    $endgroup$
    – Ross Millikan
    Mar 12 at 15:30




    $begingroup$
    No, plot a sine wave and look at it. You double the time from max to min to get a period.
    $endgroup$
    – Ross Millikan
    Mar 12 at 15:30











    0












    $begingroup$

    Even though you don't know where to start, you do.. Start by writing the definitions of period, average rate of change, domain, and range.



    That being said:



    1) Half the period is time from max to min (6.25 hours). So $Period=2cdot 6.25 = 12.5$



    2) Average rate of change is the slope of the secant line of distance function. In this case, $frac{d(3)-d(1)}{3-1}$. you can take it from here



    3) Domain of $u(x)$ can only be the $x$ where $v(x)$ and $w(x)$ exists. Therefore, domain of $u(x)$ is ${ xinmathbb{R} , | , x$ in domain of both $v(x)$ and $w(x)}$



    Range of $u(x)$ is slightly trickier. Any chance you have actual equations for $v(x)$ and $w(x)$?






    share|cite|improve this answer









    $endgroup$


















      0












      $begingroup$

      Even though you don't know where to start, you do.. Start by writing the definitions of period, average rate of change, domain, and range.



      That being said:



      1) Half the period is time from max to min (6.25 hours). So $Period=2cdot 6.25 = 12.5$



      2) Average rate of change is the slope of the secant line of distance function. In this case, $frac{d(3)-d(1)}{3-1}$. you can take it from here



      3) Domain of $u(x)$ can only be the $x$ where $v(x)$ and $w(x)$ exists. Therefore, domain of $u(x)$ is ${ xinmathbb{R} , | , x$ in domain of both $v(x)$ and $w(x)}$



      Range of $u(x)$ is slightly trickier. Any chance you have actual equations for $v(x)$ and $w(x)$?






      share|cite|improve this answer









      $endgroup$
















        0












        0








        0





        $begingroup$

        Even though you don't know where to start, you do.. Start by writing the definitions of period, average rate of change, domain, and range.



        That being said:



        1) Half the period is time from max to min (6.25 hours). So $Period=2cdot 6.25 = 12.5$



        2) Average rate of change is the slope of the secant line of distance function. In this case, $frac{d(3)-d(1)}{3-1}$. you can take it from here



        3) Domain of $u(x)$ can only be the $x$ where $v(x)$ and $w(x)$ exists. Therefore, domain of $u(x)$ is ${ xinmathbb{R} , | , x$ in domain of both $v(x)$ and $w(x)}$



        Range of $u(x)$ is slightly trickier. Any chance you have actual equations for $v(x)$ and $w(x)$?






        share|cite|improve this answer









        $endgroup$



        Even though you don't know where to start, you do.. Start by writing the definitions of period, average rate of change, domain, and range.



        That being said:



        1) Half the period is time from max to min (6.25 hours). So $Period=2cdot 6.25 = 12.5$



        2) Average rate of change is the slope of the secant line of distance function. In this case, $frac{d(3)-d(1)}{3-1}$. you can take it from here



        3) Domain of $u(x)$ can only be the $x$ where $v(x)$ and $w(x)$ exists. Therefore, domain of $u(x)$ is ${ xinmathbb{R} , | , x$ in domain of both $v(x)$ and $w(x)}$



        Range of $u(x)$ is slightly trickier. Any chance you have actual equations for $v(x)$ and $w(x)$?







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Mar 12 at 15:17









        NazimJNazimJ

        47419




        47419






























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