<p>ALSO post some links regarding the questions. I never attempted such questions.</p>
<p>Write a formula representing the following function.</p>
<pre><code>The energy, E, expended by a shark is proportional to the cube of the speed, v, of the shark.
</code></pre>
<p>E(v)= ??? i think its -V^3</p>
<p>2.(a) Write an equation for the graph obtained by vertically stretching y = x2 by a factor of 9, followed by a vertical upward shift of 6 unit(s). </p>
<p>y(x) =</p>
<p>(b) What is the equation if the order of the transformations (stretching and shifting) is part (a) is interchanged?
y(x) =</p>
<p>3.Put the function in the form P = P0ekt
P = 138(0.6)t
P0 =<br>
k = </p>
<p>4.The Bay of Fundy in Canada has the largest tides in the world. The difference between low and high water levels is 15 meters. At a particular point the depth of the water, y meters, is given as a function of time, t, in hours since midnight by the following y = D + A cos(B(t - C))</p>
<pre><code>(a) What is the physical meaning of D?
the time of high tide
the average depth of the water
the depth of the water at high tide
the time of low tide
the depth of the water at low tide
none of these
(b) What is the value of A?
(c) What is the value of B? Assume the time between successive high tides is 12.4 hours.
(d) What is the physical meaning of C?
</code></pre>
<p>this is for prep.</p>
<ol>
<li>E=c<em>v^3 where c is a non zero constant (possibly 1)
2a. y=(x2)</em>9+6
2b. y=(x2+6)*9 </li>
<li> I don’t follow the question.</li>
<li> I’m not sure. Let me think about it. I’ll get back to you if anything comes to me.</li>
</ol>
<p>how do you know these stuff? This is a sample placement exam, i didnt learn this stuff in high school. There are 40 other questions of such type.</p>
<p>My math is rusty and I could be wrong, but I think D would be the average depth of water (again I could be wrong, but I think a sine/cosine function would have zero as its average, I’ll use Mathematica to confirm this :P). The value of A is, I believe is one half the difference between the low and the high tides, which is 7.5 meters.</p>
<p>I have completely forgotten how frequency relates to the value of B, but I think it differs by the value of 2 pi or something. They said that the time between successive high tides is 12.4 hours, and this would be the frequency of the cosine function. I think you got to multiply or divide that with 2 pi or something. I just don’t remember (being an engineering major that always does all calculations like these with matlab and mathematica for 4 years has certainly taken its toll on me :P). I would just look it up on wikipedia. </p>
<p>C would be the equivalent of the phase shift for the trig function. If C was zero (or any multiplies of 2 pi [or just pi] IIRC), then the tide would be highest at midnight. C would then determine the relative height of the tide with respect to D at the initial condition. </p>
<p>As for no. 3, I’m not quite sure what the question is asking as well. Is it to express that equation in an exponential term or something? And did you mean to write P(t) = P0 e^(kt)?</p>
<p>I think B is the angular frequency, so B = w = 2<em>pi</em>f</p>
<p>Everything else looks good to me.</p>
<p>For #3, if you’re trying to express P = 138<em>0.6^t as P = P0</em>e^kt, then P0 = 138, k = ln(0.6)</p>
<p>And to the OP, did you go to school in Canada or the US? I learned those things in gr. 10-12</p>
<p>in pakistan, we are army fellows travelling all over the place. :D</p>
<p>This is a typical precalc problem testing trig functions and graphs
The easiest way is just to draw the graph of the equation without determining any length and using the abstract quantities D, B, and C by labeling the graph. The x axis would be time, and y axis would be the level of the water. The graph is the curve of a cosine function shifted upward (if D>0), shifted to the right by C units, with a period of 2 pi/ B. A is the magnitude the maximum value y on the graph (the crest of the wave), minus D.
A= 15/2<br>
I think A is the magnitude
D is the average depth of the water (it’s clearer when you try to draw the graph by labeling A,B,C… on the graph)</p>
<p>Since the period is give (12.4 hours), B=2pi/12.4 (derived from the equation period=2pi/B</p>
<p>C is the value by which the graph is shifted to the right. So it means the value of the time passed 0 when the level of the water will reach a peak height (or a minimum if A<0)</p>
<p>If you still are confused, review trig graph and it will be fine. (review horizontal stretch/shrink which I think are the most confusing)</p>
<p>PS: my precalc is also rusty, so if there are errors, I apologize for them.</p>
<p>If you don’t have a precalc book, google trig graph and you will find a bunch of it.</p>
<p>Yes he’s right about B = 2pi/12.4</p>
<p>“how do you know these stuff? This is a sample placement exam, i didnt learn this stuff in high school. There are 40 other questions of such type.”</p>
<p>Well, I guess that’s the point of a placement exam. Don’t fret if you can’t answer most of the questions - it just means you’ll be placed into a course that’ll teach you a lot of stuff you didn’t know.</p>
<p>I did pre calculus in 10 and 11, i did Calculus 1 already + i got a an A+ grade. but this stuff is kinda new to me. i never made my own formulas. i just solved the exercises and thats it.</p>
<p>I think the 4th question should be answered like this:
(a)The unit of y is meter.So D should be a depth.Then think about the function cosx.Sometimes it’s positive and sometimes negative.So D is an average depth.
(b)cos(B(t - C))varies from -1 to 1.“The difference between low and high water levels is 15 meters”.So A should be 7.5 or -7.5.Mostly we choose the positive number because it looks more beautiful when drawing the function.
(c) B should be 2pi/12.4
(d) C is the time since midnight when the tide reaches its peak height.</p>
<p>I study English as a foreign language.I apologize for my poor expression.
P.S. I major in electrical engineering.</p>
<p>I actually think that D should be the depth of the water during low tide.</p>
<p>I think the previous posters were correct to say that D is the average depth. Ignore all the other transformations that are applied to cos x in question 4 and look at the simpler equation y= D + cos t. If D=0 you just have the cos function, which has an average of 0. If D= 2, the graph of the function is identical to the cos function translated 2 positive units in the y direction. If you take the average of the function now, the average value is 2. This isn’t a formal proof, but it should be clear that D represents the average depth of the water. </p>
<p>It should also be noted, that to examine true averages of the cos x function, you need to look at the function over the interval [0, 2pi*c] where c is a positive nonzero integer.</p>