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anonymous
 one year ago
The depth of water in a tank oscillates every 5 hours. The smallest depth is 0.5, and that the largest depth is 7.5. Find a formula for the depth as a function of time t measured in hours for which the depth at time t=0 is the largest depth.
anonymous
 one year ago
The depth of water in a tank oscillates every 5 hours. The smallest depth is 0.5, and that the largest depth is 7.5. Find a formula for the depth as a function of time t measured in hours for which the depth at time t=0 is the largest depth.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, I have to log off now. Good luck.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@zepdrix Can you help? :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443488320174:dwSo we've got our low and our high point.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the amplitude is 7.5.5/2 which is 3.5?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443488404092:dwWe start at our highest point. And you've calculated the amplitude correctly, ok good!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Where is the middle of our function going to be located?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.13.5 + 0.5 Hmm that doesn't sound right :d

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohhhh oops I see now, 4

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443488682271:dwOk great. And it completes one full oscillation in 5 hours. So the shape should look something like this, ya?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1So should we model this curve with `sine` or `cosine`? What do you think? :) One will be a bit easier than the other. You have to think about your starting point.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is where I always have a problem. How exactly do you decide whether to use sine or cosine?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Does sine always cross at (0,0)?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443489123175:dwSo which one seems more appropriate? :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Sine always crosses through the middle point at the start. It won't necessarily be (0,0), especially if we have any kind of vertical shift.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok! Is the period 2pi/5 or did I do that incorrectly?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Example: \(\large\rm f(x)=\sin(x)+1\)dw:1443489226950:dwYes, normally this curve would go through (0,0) to start, but it's been shift up by 1.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh ok that makes so much sense

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1The period is 5 hours. The letter b that we're going to stick into our formula:\[\large\rm f(x)=A \sin(bx)+d\]Is given by \(\large\rm b=\frac{2\pi}{period}\). So if that's what you meant, then yes. Our b is going to be 2pi/5.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yep that's what I meant, great!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Woops cosine :) not sine, my bad. Let's stick in what we know so far, amplitude and our b,\[\large\rm f(x)=3.5 \cos\left(\frac{2\pi}{5}x\right)+d\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ummm depends how you like to think of it I guess... I like to think of it as a vertical shift of the middle line.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1normally that middle line is the xaxis. But now it's up at 4, ya?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1sounds right!\[\large\rm f(x)=3.5 \cos\left(\frac{2\pi}{5}x\right)+4\] And to be a little more accurate, it's shifting the entire function up by 4. You could calculate that shift from any point on the curve. I think it's just easier to work from the middle.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0YAY! Thanks so much, you're the bomb!!
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