<p>The sum of the positive odd integers less than 100 is
subtracted from the sum of the positive even integers
less than or equal to 100. What is the resulting
difference?</p>
<p>I don't have the answer. I got 150, but that's basically just an educated guess. I understand that you get a pattern like 2-1. 6-5, etc but I just can't figure out how many times it happens. I.E. do you do that operation where you get 1 fifty times, 45 times, etc. </p>
<p>f(x)=kg(x)+2
The function f above is defined in terms of another
function g for all values of x, where k is a constant.
If t is a number for which f (t ) = 30 and g(t) = 8, what does k equal?</p>
<p>Is it 3.5? I don't have the answer to this</p>
<p>1) The answer is 50.</p>
<p>**** im ■■■■■■■■. I had a brain fart and thought the 100 didn’t get canceled with anything lol.</p>
<p>1) </p>
<p>Sum of even numbers: n(n+1)
Sum of odd numbers: n^2</p>
<p>Where n = number of terms. </p>
<p>So the sum of even numbers from 0 to 100 is 50(51) = 2550
The sum of odd numbers is 50^2 = 2500</p>
<p>Subtract and get 50. </p>
<p>–</p>
<p>2) I concur. The answer is 3.5, unless I’m missing a College Board trick. Where was this question? Towards the beginning of the section, the middle, or the end?</p>
<p>you got the second one right…probably by doing something like:</p>
<p>f(x)=kg(x)+2</p>
<p>so f(t)=k g(t) + 2</p>
<p>30 = k times 8 + 2</p>
<p>28 = 8k</p>
<p>k = 3.5</p>
<p>It’s a nice problem. Where is it from?</p>
<p>Ice’s way of doing this is hard! Try this:</p>
<p>(2+4+6+…+98+100) - (1+3+5+…+97+99) =
(2-1) + (4-3) + (6-5) + … + (98-97) + (100-99) =
1 + 1 + 1 + … + 1 + 1.</p>
<p>How many ones is that, all added together? Fifty of them, because there are 50 positive integers less than or equal to 100, and 50 positive integers less than 100.</p>
<p>ITA with pckeller about the second one.</p>
<p>One can also intuitively arrive at 50. Just do it with all the evens and odds from 0 to 10.</p>
<p>(2 + 4 + 6 + 8 + 10) -
(1 + 3 + 5 + 7 + 9) </p>
<p>= 1 + 1 + 1 + 1 + 1</p>
<p>= 5 </p>
<p>Clearly, the even and odds cancel out to become 1s. How many even/odd pairs are there from 0 to 100? 50. So the answer is 50.</p>
<p>These questions came from the official online course (that i don’t have answers for, ugh) tests. The second question came towards the end, and it seemed a little too easy so I thought I missed a trick since it’s really just asking if you understand basic function notation and PEMDAS.</p>