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 10-16-2012, 08:51 AM #1 New Member   Join Date: Jul 2012 Posts: 25 SAT 6th Oct MATH Anyone remember this math question? a graph with 2 lines they ask when will the money they receive are equal? remember? They give coordinates of the lines too so i'm assuming i have to use it for what to find slope? they what next? Another question asks smth like 76^1600, they're asking what is the ones term. How do you do it? Please help, thanks Reply
 10-16-2012, 10:52 AM #2 Senior Member   Join Date: Mar 2012 Location: Cambridge, MA Posts: 1,913 For the first question, you probably have to find the intersection of the lines. If you're given the equations of the lines, you have to set up a system of two equations, two variables, which can be solved. For the second question, note that 76^1 ≡ 6 (mod 10) (This is shorthand of saying "the remainder when 76^1 is divided by 10 is 6"). 76^2 ≡ 6 (mod 10) 76^3 ≡ 6 (mod 10) Basically, the units digit is always 6. So the answer is 6. Reply
 10-16-2012, 11:13 AM #3 New Member   Join Date: Oct 2012 Posts: 18 The same is the case for numbers ending with 4, the unit's place will always have a 6. Reply
 10-18-2012, 05:00 AM #4 New Member   Join Date: Jul 2012 Posts: 25 Can you elaborate it more? I don't really get it also for the first question how do you find the intersection of those 2 lines? they give us the coordinates for 2 points for each line i assume you need to do something to find the slope too right? Then what next what can you use it for, same goes for number 2 How do you find the digit place? i try putting it in the calculator but what i get was math error Reply
 10-18-2012, 06:08 AM #5 New Member   Join Date: Jul 2012 Posts: 25 Thank you , i got it now but does (mod 10) works for every other numbers too? Because sometimes they have more than 1 different remainder also how do you find the intersection? Like what if the question is different now? like 19^1600 etc. what will be its ones digit? Thanks in advance, Reply
 10-18-2012, 08:43 AM #6 Senior Member   Join Date: Mar 2012 Location: Cambridge, MA Posts: 1,913 For 19^1600: 19^1 ≡ 9 (mod 10) 19^2 ≡ 1 (mod 10) (because the last digit of 19^2 is 1) 19^3 ≡ 9 (mod 10) 19^4 ≡ 1 (mod 10) This always cycles between 9 and 1. Note that 19^(odd) ≡ 9, and 19^(even) ≡ 1. 1600 is even, so 19^1600 will be 1 mod 10, i.e. last digit 1. Reply
 10-18-2012, 08:49 AM #7 Senior Member   Join Date: Mar 2012 Location: Cambridge, MA Posts: 1,913 Also, your questions on the intersection of two lines are a little vague... If you need to find the intersection of two lines, you should find the equations of the two lines first (e.g. y1 = a(x1) + b, y2 = c(x2) + d). The two lines intersect when x1 = x2, y1 = y2 --> solve for (x1,y1) or (x2,y2) (provided there is a solution). Also note that the intersection of the two lines is simply the intersection of the diagonals of the quadrilateral formed by those four points, so for certain quadrilaterals (e.g. parallelograms) this method is easier. Reply
 10-18-2012, 11:07 AM #8 Member   Join Date: Jun 2012 Posts: 340 The answer to the intersecting lines question was about 160 if i remember correctly. In the oct 6 math thread you can find the answer, I just plugged it into my calc and used then find intersect button. Reply
 10-19-2012, 11:08 AM #9 New Member   Join Date: Jul 2012 Posts: 25 Thanks to all the answer i sincerely appreciate , thank you! I will try to recall the questions. Reply

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