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# The Kirby Question!

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### The Kirby Question!

1. 1. The Kirby Plan Picture by deviantart.com user =NNBTK
2. 2. This is what we need to do… 1. We have decided on a target, Kirby, and a method of attack, our evil demon frog, all that’s left is figuring out WHEN to attack. Kirby needs to eat every 3 hours, for some reason he NEVER deviates from this pattern. Kirby fills up at a constant rate for 1.5 hours until he feels full. We are going to rate Kirby’s hunger on a scale from 1-10, 1 being the hungriest and 10 being when he is the fullest. Kirby first starts to eat at 1:00am. A. Sketch a sinusoidal graph of Kirby’s eating habits B. Write a sine and cosine equation for the graph C. We plan to attack Kirby when he’s at the park at 2:00pm. He can’t seem to fight with much gusto if his fullness is above 8. i. Is 2:00pm a good time to attack? ii. What is a good time near 2:00pm to attack?
3. 3. It’s graphing time! • Don’t panic! Let’s take some important information from the question! • Kirby needs to eat every 3 hours. 3 hours is our period! • Rate Kirby’s hunger on a scale from 1-10. 1 is our min and 10 is our max! • Kirby first starts to eat at 1:00am. 1:00am is going to be our starting point!
4. 4. Using what we learned in the last slide let’s make our graph! Sinusoidal axis Period NOTE: we are using the 24 hour clock for our x-axis (:
5. 5. Parts of the Equation! Parameter What is it? A- amplitude This is the distance from the minimum or maximum to the sinusoidal axis. B- determines It is the distance along the x-axis required 2π period to make one wave. The period is equal to 3 C: Phase shift This determines the horizontal shift of the graph. D: Vertical shift It determines the sinusoidal axis. f(x)= Asin B(x- C) +D g(x)= Acos B(x- C)+ D
6. 6. It’s Equation time! Sin A: 4.5 B: 3 So our sin equation is C: 1.75 f(Kirby)= 4.5sin 2π (x- 1.75) + 5.5 3 D: 5.5 NOTE: Make sure your calculator is in radians! NOT degrees! Otherwise you’ll end up with some wonky answers!
7. 7. Now let’s do cosine! Cos A: -4.5 B:3 So our cosine equation is C: 1 g(Kirby)= -4.5cos 2π (x-1) +5.5 3 D: 5.5
8. 8. 2:00, good or bad time to attack? NOTE: We are using the 24 hour clock. 2:00pm is the equivalent of 14:00 hours.
9. 9. Let’s try using our cosine equation to confirm!
10. 10. So how do we figure out a good time to attack? 1. Write down your equation. 2π 2. Letθ= 3 (x- 1.75) because it makes our equations easier to work with. 3. Re write the equation using θ. 4. Add -5.5 to both sides of your equation. 5. Divide both sides of the equations by 2.5. 5 6. Find the inverse sin of 9 , and were done! Or are we…
11. 11. Remember θ? 7. Convert θ back to the original value. 8. Now solve for x!
12. 12. Lets see if we get the same answer with cosine! Now let’s turn 2.03124 into TIME! 2.03124 (60)= 121.8744 min It’s common sense time! There are 2 hours in 120 minutes, and 1.78 minutes left over. So that means we should attack at approximately 2:02 am.
13. 13. So When Do We Attack?? 02:02 14:02 How did we do that?! Well minions the answer to that is quite simple. Our period is 3 hours, so we added 12 (which is a multiple of 3) to 02:02 to arrive at 14:02.
14. 14. TOA (time of attack)= 14:02 Now that have all the math out of the way it’s time for us to get ready to attack! SAY GOODBYE KIRBY!