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# Recent problems solved by 'longjonsilver'

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 Linear_Algebra/6857: If y = 39 and y = -x/4 + 15, what is the value of X?1 solutions Answer 3764 by longjonsilver(2297)   on 2005-08-09 06:38:20 (Show Source): You can put this solution on YOUR website!y = -x/4 + 15 39 = -x/4 + 15 --> subtract 15 from both sides 24 = -x/4 --> multiply both sides by 4 -x = 96 --> multiply both sides by -1 x = -96 the final 2 steps could be done in one...multiply by -4, but i split it into 2 for sake of ease. jon.
 Linear_Algebra/6858: If y = 32.56x + 27 and x = 0, what is the value of Y?1 solutions Answer 3763 by longjonsilver(2297)   on 2005-08-09 06:35:54 (Show Source): You can put this solution on YOUR website!i have done 3 of these...you try the rest Jon.
 Linear_Algebra/6855: If x = 72 and y = -54 - x/6, what is the value of y?1 solutions Answer 3762 by longjonsilver(2297)   on 2005-08-09 06:35:33 (Show Source): You can put this solution on YOUR website!i have done 3 of these...you try the rest Jon.
 Linear_Algebra/6854: If y = -38 and y = 24 + 8x, what is the value of X?1 solutions Answer 3761 by longjonsilver(2297)   on 2005-08-09 06:35:10 (Show Source): You can put this solution on YOUR website!i have done 3 of these...you try the rest Jon.
 Linear_Algebra/6853: If y = -33 and y = -5x - 3, determine the value of X?1 solutions Answer 3760 by longjonsilver(2297)   on 2005-08-09 06:34:29 (Show Source): You can put this solution on YOUR website!y = -5x - 3 -33 = -5x - 3 --> add 3 to both sides -30 = -5x --> divide both sides by -5 x = 6 jon.
 Linear_Algebra/6852: If X=14 and y = 6x - 42 determine the value of Y?1 solutions Answer 3759 by longjonsilver(2297)   on 2005-08-09 06:33:11 (Show Source): You can put this solution on YOUR website!y = 6x - 42 y = 6(14) - 42 y = 84 - 42 y = 42 jon.
 Linear_Algebra/6851: y= 2x + 8 and y = 18 What is the value of X?1 solutions Answer 3758 by longjonsilver(2297)   on 2005-08-09 06:31:54 (Show Source): You can put this solution on YOUR website!y = 2x + 8 18 = 2x + 8 --> subtract 8 from both sides 10 = 2x --> divide both sides by 2 x = 5 jon.
 Proportions/6849: Can u please help me solve this equation on quadratic equations: 5k^2+17k+6=0 I can do the quadratic equations without a constant infront of the k but i cant do the ones with a number infront of the k. I would be grateful if u could help me Thanks 1 solutions Answer 3757 by longjonsilver(2297)   on 2005-08-09 06:30:31 (Show Source): You can put this solution on YOUR website! --> you need to do some mental arithmetic, that is all. For , we will need 5k and k. Also for the 6, we will have either 1x6 or 3x2, if it is to be factorised... all you need do is write them down and look at them and figure out if any combination gives 17: 1x6 --> 5 lots of 6 is 30 + 1 is 31 --> too big to give 17 --> 5 lots of 1 is 5 then + 6 is 11 --> too small to give 17 2x3 --> 5 lots of 2 is 10 + 3 is 13 --> too small --> 5 lots of 3 is 15 + 2 is 17 --> wayyy-heyyy!!! So, the 5k has to be multiplied to the 3, to give 17. The answer is therefore (5k+2)(k+3) = 0 That is the process you need to use...write it down on paper to check your answers. The worst kind of question is etc, as this could be 1x12, 2x6 or 3x4. You could be there for ages trying to figure it out :-) jon.
 Distributive-associative-commutative-properties/6659: wat is -4(5c+7)-3c+13 1 solutions Answer 3641 by longjonsilver(2297)   on 2005-08-05 07:31:56 (Show Source): You can put this solution on YOUR website!-4(5c+7)-3c+13 -20c-28-3c+13 -23c-28+13 -23c-15 jon.
 Square-cubic-other-roots/6603: Simplify: 3/5- sqrt 2 The / means that the 3 is over the rest of the problem, not just the 5.1 solutions Answer 3639 by longjonsilver(2297)   on 2005-08-05 05:20:35 (Show Source): You can put this solution on YOUR website!so, . We shall multiply this by 1, to keep the same answer, but I shall write 1 as ... so jon.
 absolute-value/6654: Find the value of a if the points whose coordinates are given are the indicated distance apart. (-2,-5)(a,7);d=131 solutions Answer 3638 by longjonsilver(2297)   on 2005-08-05 05:16:18 (Show Source): You can put this solution on YOUR website!this is a reverse version of the typical question of giving 2 points and finding the distance between them. It uses Pythagoras' Theorem... Now, if you know anything about Pythagoras' theorm, you should know about a 5, 12, 13 triangle. We have this here...so a+2=5 --> a=3. But doing it this way is dangerous, because we will miss an answer... see below: The full proper answer is as follows: so, either or ie a+2 = 5 OR a+2 = -5 so a=3 or a=-7 so, a line joining point (-2,-5) to either (3,7) or (-7,7) will give a length of 13. jon.
 absolute-value/6607: I am having a hard time with Variation, Progression, and Theorems. My question is What is the quotient of b^3+4b^2-3b+126 ------------------ =? b+7 I have tried to do this question on my own and I am not having any luck, Can someone help me?1 solutions Answer 3637 by longjonsilver(2297)   on 2005-08-05 05:04:52 (Show Source): You can put this solution on YOUR website! So, use long division..i shall try to write this down here: b+7 | First... how many times does b go into ? Answer is times. So write over the cube term. Now, multiply the by both b and 7 and write those answers under, as: b+7 | ____ Now subtract from , to give: b+7 | ____ ____________________________ _____ Now repeat the process..how many times does b go into ? answer is -3b times...put this on top, then multiply that by both b and 7 and put the answer under. Subtract to leave 18b+126. Now repeat the process..how many times does b go into 18b? answer is 18 times...put this on top, then multiply that by both b and 7 and put the answer under. Subtract to leave 0. This means that b+7 divides into exactly, times. jon.
 absolute-value/6612: I am having trouble with Variation, Progression, and Theorems. My question is an infinate geometric series has 1 and 1/5 as it's first two terms: 1, 1/5, 1/25, 1/125, ........ What is the sum, S, of the infinate series? I have tried to do this question on my own and I am not having any luck, Can you please help me?1 solutions Answer 3636 by longjonsilver(2297)   on 2005-08-05 04:53:02 (Show Source): You can put this solution on YOUR website!to have a sum to infinity for a geometric progression/series, you need to have numbers that get successively smaller, so that adding them approaches some final answer... if the numbers got bigger, then the summation would always be increasing. So, that is why the one stipulation is |r|<1 ie -1 Formula: , so: Sum = Sum = Sum = Sum = 1.25 jon.
 Square-cubic-other-roots/6653: simplify: 6- sqrt 5 / 4+ sqrt 5 1 solutions Answer 3635 by longjonsilver(2297)   on 2005-08-05 04:44:40 (Show Source): You can put this solution on YOUR website! --> multiply this by 1, but "1" will be written as , So... this is the "simplified" version... basically for surds, simplified means "no surds on the denominator". jon.
 Geometric_formulas/6621: Find the geometric mean between 7 and 10 1 solutions Answer 3634 by longjonsilver(2297)   on 2005-08-05 04:32:35 (Show Source): You can put this solution on YOUR website!geometric mean is --> 8.367 to 4dp jon.
 Quadratic_Equations/6656: Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of each quadratic function. y=x^2-2x-8 Is (1,-9) x=1 the right answer?? Thanks1 solutions Answer 3633 by longjonsilver(2297)   on 2005-08-05 04:06:43 (Show Source): You can put this solution on YOUR website!yes, they are the correct answers Jon.
 Distributive-associative-commutative-properties/6537: 1. The length of a walkway is 3 more than 5 times the width of the walkway. If the perimeter is 90 feet, find the dimensions of the walkway. 2. The width of a rectangle is 10 feet less than the length, find the length of each side if the perimeter is 100 feet. 3. Dan and Charlie have bank accounts with \$96 between them. Dan as \$2 less than Charlie in his bank account. How much does each have in their bank accounts? I don't want you to do the problems for me, just set it them up for me, so I can know how to do them, then if my answers are not coming out right I e-mail you back. Thank You1 solutions Answer 3570 by longjonsilver(2297)   on 2005-08-04 09:39:06 (Show Source): You can put this solution on YOUR website!1. let w=width, so length = 5w+3. perimeter is which lengths? these total 90. You work it out. 2. Let x=length, so width=x-10. permeter again...work it out. 3. Let charlie have \$c in his account. Dan therefore has c-2 Together they add up to \$96. You work it out. jon.
 Linear_Algebra/6569: Some "x-values" make the denominator of a rational function undefined. Why can't the graph of that function cross the vertical lines (vertical asymptotes) that have those values for "x-intercepts"?1 solutions Answer 3567 by longjonsilver(2297)   on 2005-08-04 09:33:56 (Show Source): You can put this solution on YOUR website!you answered your own question.... the x-values that make the function undefined are values that are UNDEFINED, so you cannot have that/those values, so you will never have the curve crossing the asymptote (--> the line denoting the undefined value) jon.
 Linear_Algebra/6570: If you let x take on very large positive values, and very small negative values, what can this tell you about the far right and left sides of the graph of a rational function that has a horizontal asymptote?1 solutions Answer 3565 by longjonsilver(2297)   on 2005-08-04 09:31:10 (Show Source): You can put this solution on YOUR website!the values of y will tend towards the asymptote value. Jon.
 Graphs/6571: Can someone help with question: Graph the parabola: y=(x-3)^2-31 solutions Answer 3564 by longjonsilver(2297)   on 2005-08-04 09:17:59 (Show Source): You can put this solution on YOUR website!right then, is a u-shaped curve. When x=0, --> y=9-3 --> y=6 When y=0, x-3 = +- so either x = or x = this gives you enough info to sketch the curve. If you want to PLOT it properly, then pick various x values and find the y-values then plot them. jon.
 Linear_Algebra/6541: How do you determine the horizontal asymptotes, given the equation of a rational function? -------------------------------------------------------------------------- look for the highest power of x? I'm not sure.1 solutions Answer 3560 by longjonsilver(2297)   on 2005-08-04 06:14:28 (Show Source): You can put this solution on YOUR website!i would tend to re-write the equation for x= and then see what value(s) of y were not allowed...usually displayed on the denominator. Jon.
 Linear-systems/6556: Dear Sir/Madam, I am confronted with the following problem: "Give polar coordinates of a point whose rectangular coordinates are (-2,3)." I have never previously dealt with polar coordinates. I looked it up and am entirely confused. Could you help me in solving this question? Thanks in advance. Regards, -Mike 1 solutions Answer 3559 by longjonsilver(2297)   on 2005-08-04 06:12:23 (Show Source): You can put this solution on YOUR website!Mike, where is your teacher? Right then, polar and Cartesian coordinates. Imagine a set of axes and the point (2,3). This lies in the first quadrant. The +ve x-axis is the zero line, then the +y axis is the 90 degree line. The -ve x-axis is the 180 degree line etc., circling round back to the +ve x-axis at 360 degrees. Right...plot the point P(2,3). Create a right angled triangle OPX, where O is the origin, X is the vertical line from point P to the x-axis. OK, so far? We can describe the point P in 2 ways: 1. Cartesian Coordinates - reference the x and y values --> (2,3) 2. Polar Coordinates - reference the angle, A, from the zero line (the +ve x-axis) and the length, r, to the point from the origin. This length is the length of OP, the hypotenuse of the triangle. So, tanA = y/x and r = --> Pythagoras. --> this gives angle A = 56.3degrees and r = Now, your point is actually (-2, 3), so this lies in Quadrant 2. If you draw your triangle there again, you find another angle, call it B, also 56.3. However, strictly, this is 180-56.3 = 123.7 degrees. Check it..tan(123.7) is -1.5: correct! and r is still Is this OK for you? jon.
 logarithm/6549: I having a problem working this problem out, I am trying to FOIL it, but not sure I am coming up with the right answer or if I am missing something. Heres the problem... square root of 5 ( square root of 3 + square root of 2 ) Thank you for any help you may provide.1 solutions Answer 3557 by longjonsilver(2297)   on 2005-08-04 06:00:37 (Show Source): You can put this solution on YOUR website! jon.
 Linear_Algebra/6542: Describe what happens to the graph of a function as the value of the independent variable approaches its vertical asymptote. --------------------------------------------------------------- It goes up to positive or negative infinity?1 solutions Answer 3556 by longjonsilver(2297)   on 2005-08-04 05:58:07 (Show Source): You can put this solution on YOUR website!depends on what the function is and which side of the asymptote you are on..but yes, in general: for a x-value: it approaches the value of the asymptote for a y-value: it approaches either + or - infinity. Jon.
 Linear-systems/6557: Dear Sir/Madam, I am confronted with the following problem: "The expression tan^2(x)/(1+sec(x)) is identical to: a. 1 b. sec(x) - 1 c. tan(x) + sin(x) d. tan^2(x) + sin(x)tan(x) e. csc(x) + sin(x)" I know that tan^2(x) = sec^2(x) - 1, however, once the equation is (sec^2(x) - 1)/(1 + sec(x)) I don't know how to proceed. Could you help me in solving this question? Thanks in advance. Regards, -Mike1 solutions Answer 3555 by longjonsilver(2297)   on 2005-08-04 05:53:14 (Show Source): You can put this solution on YOUR website!(sec^2(x) - 1)/(1 + sec(x)) so, sec^2(x) - 1 can be written as (sec(x)+1)(sec(x)-1): this is just difference of 2 squares. Then you can cancel and you get one of the answers :-) jon.
 Permutations/6558: the conjugate of sqare_root(2)-square_root(3) is: square_root(2)+square_root(3). But can it be: -sqare_root(2)-square_root(3)? please note that even if they are not complex numbers , they are surds. For surds conjugate of 2-square_root(3) is 2+square_root(3), so why not -2-square_root(3)?1 solutions Answer 3554 by longjonsilver(2297)   on 2005-08-04 05:49:20 (Show Source): You can put this solution on YOUR website!i have looked on the web and not found much at all, however one pdf had an example where it multiplied by a "surd conjugate". Looking into this, it looks like has the conjugate . As for why...that is the definition of the conjugate. Simple as that. As for the reason behind using a conjugate...it removes any irrational/surd parts, since is --> . Jon.
 Sequences-and-series/6533: Please help me solve 1 solutions Answer 3533 by longjonsilver(2297)   on 2005-08-03 17:15:35 (Show Source): You can put this solution on YOUR website!this is just a quadratic...let , so the equation becomes so, now factorise to (a+5)(a-4) = 0 --> a = -5 or a = 4 so or so b = +2 or -2 or b = + or - jon.
 Linear-systems/6509: Dear Sir/Madam, I am confronted with the following problem: "The angles with measures listed are all coterminal except: A. π/3 B. -5π/3 C. -300 degrees D. 420 degrees E. -60 degrees" What does coterminal mean and how would I solve this problem? Thanks in advance. Regards, -Mike1 solutions Answer 3529 by longjonsilver(2297)   on 2005-08-03 16:09:13 (Show Source): You can put this solution on YOUR website!i found this website for you... file:///C:/Documents%20and%20Settings/Administrator/Local%20Settings/Temporary%20Internet%20Files/Content.IE5/QP3K1OV2/257,1,Positive Angles copy all that into your browser and watch the pages. Anyway coterminal means 2 angles that are the same (in terms of the "circle" view) so 0, 360, 720 etc are coterminal. 180, 540 and 900 etc are also coterminal. so, check your list of angles and figure out :-) jon.
 Linear-systems/6510: Dear Sir/Madam, I am confronted with the following problem: "The point (12,-16) is on the terminal side of the angle theta. Find tan(theta)." I am a little confused as to what they mean by terminal side. I played around with this question and got the answer to be -4/3, which is right, but could you explain the terminal side idea to me a bit? Thanks in advance. Regards, -Mike1 solutions Answer 3527 by longjonsilver(2297)   on 2005-08-03 15:56:08 (Show Source): You can put this solution on YOUR website!i have never come across this terminolgy before - i guess it is an Americanism. Anyway, looking on the web, it is as follows: Start with the x-axis as the "initial side". Then turn to point at the coordinate (here, (12,-16)). The line you end up on (the hypotenuse in this case) is the terminal side. So, sketching axes. Plot the point (12, -16) in the 4th quadrant. Start at the origin, pointing along the +ve x-direction and then turn to the point to create the hypotenuse..this is your angle , and then = opp/adj which gives tan = -16/12 tan = -4/3 jon.
 Square-cubic-other-roots/6307: my question says to simplify: sqrt 1/51 solutions Answer 3525 by longjonsilver(2297)   on 2005-08-03 15:46:20 (Show Source): You can put this solution on YOUR website!mathematicians do not like surds () on the denominator, so ...or rather needs to be altered: --> note the new fraction is really just 1, written oddly. jon.
 Square-cubic-other-roots/6513: Simplify sqrt6x^5y^3 sqrt8xy I'm having problems with this problem, any help you can give is appreciated. 1 solutions Answer 3524 by longjonsilver(2297)   on 2005-08-03 15:41:14 (Show Source): You can put this solution on YOUR website! --> i take it there is a multiply sign in the gap? I have taken it to mean multiply... I have done everything on a seperate line...you can do more things together once you get more confidence. jon.