Math Discussion For ACT December 2009

<p>^ I’m pretty sure it was L shaped too. It did even out when I plugged numbers in. Once you got >1500, the percent change was like 2%, as compared to ~15% at 1000Kw</p>

<p>My son agrees with all of the (corrected) answers so far! Incidentally, on the April test, son missed one and got a 36 on math so it is possible. Agrees with the L shape electrical company. He also didn’t remember the boat question.</p>

<p>The boat question was like… A boat travels east until it has travelled 25 miles. It then makes a 40 degree turn north and travels for 30 miles. What is the distance between the endpoints? They supply you the law of cosine.</p>

<p>You could just plug in all the numbers they gave you without thinking about what they are for and get an answer. Maybe a couple people forgot to take the square root when they got a number in the thousands?</p>

<p>I actually forgot to did a^2+b^2-ab(CosC) instead of 2ab, took me like 5minutes to figure it out >_> Still had like 10minutes extra so meh.</p>

<p>How did you guys figure out what the sides of the trapezoid was for the perimeter trapezoid question?</p>

<p>I’m pretty sure it was l-shaped as well…</p>

<p>I just figured out what it had to be between somehow (it seemed like a good idea at the time, and guess it worked) and it had to be over 42 and like under 45ish so I put 44.</p>

<p>user - u could have made a 5-12-13 triangle with the 2 sides</p>

<p>how did u guys do the eletric old rate and new rate problem? i got 4% increase for some reason, i just plugged into 2000 to both equation and compared the price and it turned out to be roughlly 4 % >.></p>

<p>Kaiser, I did the same at first.</p>

<p>The only think it asked for was was the charge increase (from 7 to 11)…So it was 4/7 change ~ 57%.</p>

<p>On the electric bill one or whatever it was, what did you get as the new rate? Was it like 11 + .62x?</p>

<p>no the new rate was like 11 + 1500 (.67) + .62X</p>

<p>@zeek</p>

<p>i put 11+ .62x +(x-1500)</p>

<p>Boat: an alternate method to prove that 52 is correct is using the component method. (I believe these are the correct values but i am not positive)
30<em>cos(0)+25</em>cos(40) = 49.15
–this is the horizontal translation from the starting spot
30<em>sin(0)+25</em>sin(40) = 16.06
–vertical translation from starting spot
These values are the legs of a right triangle so pythagoras says distance is </p>

<h2>(49.15^2+16.06^2)^(1/2) = 51.5 which is about 52</h2>

<p>Company graph- The graph is L-shaped, proven by making the actual graph
First i graphed the % increase for X≤1500
<em>the ≤ and > signs are in your calculator in Test (2nd->Math)</em>
Y1=(7+.066<em>X)/(X≤1500) --turn this graph off
Y2=(11+.067</em>X)/(X≤1500) --turn this graph off
Y3=(Y1/Y2-1)*100 --making it a percent, graph ON</p>

<p>The second piece of the graph is for % increase X>1500
Y4=(7+.066<em>1500+.062</em>(X-1500))/(X>1500) --off
Y5=(11+.067<em>1500+.062</em>(X-1500))/(X>1500) --off
Y6=(Y5/Y6-1)*100 --making it a percent, graph ON</p>

<h2>This yields an L shaped graph.</h2>

<p>Trapezoid: Base=14 Top=4 Height=12
If you subtract the top from the base, you get 10
This creates a right triangle on the left and right of the trapezoid with the unknown length as the hypotenuse. The bottom of that triangle is 5, height is 12, therefore the hyp. is 13.
There is a hypotenuse valued at 13 on the other side, too, so 4+14+13+13=44</p>

<p>Answer=44</p>

<p>what was the one that was like root (c^2), the choices were like 3, -2,-5,pi,and 1/2</p>

<p>COMPANY GRAPH FULL EXPLANATION
The graph is L-shaped, and this is proven by making the actual graph of the equations</p>

<p>First i graphed the % increase for X≤1500
<em>the ≤ and > signs are in your calculator in Test (2nd->Math)</em>
Y1=(7+.066<em>X)/(X≤1500) --turn this graph off
Y2=(11+.067</em>X)/(X≤1500) --turn this graph off
Y3=(Y1/Y2-1)*100 --making it a percent, graph ON</p>

<p>The second piece of the graph is for % increase X>1500
Y4=(7+.066<em>1500+.062</em>(X-1500))/(X>1500) --off
Y5=(11+.067<em>1500+.062</em>(X-1500))/(X>1500) --off
Y6=(Y5/Y6-1)*100 --making it a percent, graph ON</p>

<p>This yields an L shaped graph.</p>

<p>DreamCornell- the answer was 3. It was the only non-negative integer.</p>

<p>thanks, i got it, i just wasn’t sure what the question meant exactly</p>

<p>How do y’all think the curve will be?</p>

<p>Okay, can someone answer my question/explain this:
Why is it 10/100 for the rational questions one?
Square root of 1 to the square root of 100
There are 10 integers (square root of 1, square root of 4, etc…), but shouldn’t there be more rational numbers? I put 75/100.</p>

<p>@claira</p>

<p>nope</p>

<p>it’s the squares of the integers and that’s all</p>