Official June Math IIC Discussion!

<p>What was the answer for the question where there were two points p and q, where p was twice the distance to the origin than q, and going in the opposite direction. It asked for the coordinates of p.</p>

<p>About the G(x) X H(x) problem, it specifically stated that it had to be DISTINCT roots. I did an example where the graph came out to have 3 roots, but 2 were the same (thus not distinct)</p>

<p>Anyway, i did horrible on this test</p>

<p>pi/2=90 is correct.</p>

<p>Bog: Something concrete.</p>

<p>h(x) with 2 roots:
f(x) = 2(x-1)(x+2) ; g(x) = 3(x-1)(x+2)
f(3) = 2(2)(5) = 20 ; g(3) = 3(2)(5) = 30
h(x) = 6<em>(x-1)^2</em>(x+2)^2 ; two zeros: 1 and -2</p>

<p>h(x) with 3 roots:
f(x) = 2(x-1)(x+2) ; g(x) = 3(x-1)(x+3)
f(3) = 2(2)(5) = 20 ; g(3) = 3(2)(6) = 36
h(x) = 6<em>(x-1)^2</em>(x+2)(x+3) ; three zeros: 1, -2, -3</p>

<p>h(x) with 4 roots:
f(x) = 2(x-1)(x+2) ; g(x) = 3(x-4)(x+3)
f(3) = 2(2)(5) = 20 ; g(3) = 3(-1)(6) = -18
h(x) = 6(x-1)(x+2)(x+3)(x-4) ; four zeros: 4, 1, -2, -3</p>

<p>but wasnt the answer the same as the question for the logic?</p>

<p>Bog:</p>

<p>it can be four: consider the example f(x) = (x-a)(x-b) and g(x) = (x-c)(x-d)
it can be three: consider the example f(x) = (x-a)(x-b) and g(x) = (x-b)(x-c)
it can be two: consider the example f(x) = m(x-a)(x-b) and g(x) = n(x-a)(x-b), where m and n are different constants.</p>

<p>what was the answer that had the big polynomial in it and you had to find the zero. I put -.4. anyone?</p>

<p>i took the question to mean ALL the roots were distinct… meaning neither polynomial could have the same root</p>

<p>i put only 4 roots</p>

<p>did i misread?</p>

<p>“do you guys remember that question set with the function? there were two questions, the function was something like C(t)=55+20e^-.0273t?
the second question had parts I, II, and III (I=it approaches 55, II=? III=it will never be 50)”</p>

<p>As time goes to infinity, it does approach 55.
It starts at 75.
It never reaches 50.</p>

<p>“What was the answer for the question where there were two points p and q, where p was twice the distance to the origin than q, and going in the opposite direction. It asked for the coordinates of p.”</p>

<p>Use distance formula to find the distance between origin and first point. Double or half or w/e of that result is the distance from the origin that the second point should be. Since they’re going in opposite directions, the signs will be reversed (neg to pos, pos to neg).</p>

<p>There was an answer posted early in the threat.</p>

<p>The “t” problem: The answer was the opposite of the original t statement. So if they had put down t<x, then=“” the=“” answer=“” would’ve=“” been=“” t=“”>=x. If it was t>x, then t<=x.</x,></p>

<p>what was the answer to the prime number question? (i tried to find out from the rest of the thread but it was too confusing to follow) I got 8.</p>

<p>For the jeans (profit/loss question with the chart where she sold 1/2 at regular price, 1/4 at 50% off and 1/4 at 25% off), was there an answer choice of 15%? and what was the answer?</p>

<p>And for that percent increase question? what exactly was it asking? wasn’t the rate .03, so the equation would be 16.1 (1.03)^25, i remember getting E (which was like 107% or something)</p>

<p>“didnt the question say all the roots were distinct…”</p>

<p>Not that I recall.</p>

<p>The answer to the prime number question was 8.</p>

<p>The answer for the jeans was 30%. 15% may have been an answer choice.</p>

<p>It turns out the rate was .003 – I misread the question to mean a %3 (.03) increase as well. So E was wrong.</p>

<p>can someone explain the logic problem for me and tell me if i misread the polynomial question</p>

<p>i took the question to mean ALL the roots were distinct… meaning neither polynomial could have the same root</p>

<p>i put only 4 roots</p>

<p>the polynomials were distinct e.g.
x^2 - 3
x^2 - 4
are distinct since “they are different for at least one value of x” (which i think was the exact wording)
i got that question wrong too</p>

<p>what did people get for the t>3y 2<x<4 , y=5 question?</p>

<p>oh i see.</p>

<p>i hope i dont miss 800 on this damn test</p>

<p>^Was that the “if…then” question?</p>

<p>The “t” problem: The answer was the opposite of the original t statement. So if they had put down t<x, then=“” the=“” answer=“” would’ve=“” been=“” t=“”>=x. If it was t>x, then t<=x.</x,></p>

<p>why was that the answer…</p>

<p>if t<3, then 0 < y < 4</p>

<p>y=5 so _____?</p>

<hr>

<p>logic says that if a=>b, then ~b=>~a (not b implies not a)
~b (y=5) => ~a (t>=3)</p>

<p>since t>=3 is the opposite of t<3</p>

<p>The question was of the form “if x, then y”</p>

<p>They specifically told you that y was false. Thus, by modus tollens (if the consequence doesn’t happen, then the event that automatically leads to it doesn’t happen either), x isn’t true. If x isn’t true then the negation of x is true.</p>

<p>The negation of x is of one of the forms that I showed above.</p>