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# Recent problems solved by 'scott8148'

scott8148 answered: 6619 problems
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 Trigonometry-basics/168933: Verify the identity: (1-cosx)/(sinx)+(sinx)/(1-cosx)=2cscx1 solutions Answer 124560 by scott8148(6628)   on 2008-11-21 13:54:40 (Show Source): You can put this solution on YOUR website!multiplying by sinx __ (1-cosx) + (sinx^2)/(1-cosx) = 2 substituting __ (1-cosx) + (1-cosx^2)/(1-cosx) = 2 factoring __ (1-cosx) + [(1+cos)(1-cosx)]/(1-cosx) = 2 cancelling __ 1-cosx + 1+cosx = 2 __ 2=2
 Complex_Numbers/168915: please help me i dont understand any of this i am supposed to take algebra 2 next year this is is my problem i need this in vertex form with the work and steps so i can understand it thank you1 solutions Answer 124549 by scott8148(6628)   on 2008-11-21 12:52:55 (Show Source): You can put this solution on YOUR website!vertex form is y=a(x-h)^2+k, where (h,k) is the vertex y=x^2-16x+56 __ subtracting 56 __ y-56=x^2-16x completing the square by adding half of the x coefficient, squared __ y-56+(-16/2)^2=x^2-16x+(-16/2)^2 y-56+64=x^2-16x+64 __ y+8=(x-8)^2 __ subtracting 8 __ y=(x-8)^2-8 the vertex is (8,-8)
 absolute-value/168929: Translate the statement into an equation (multiple choice): "An unknown number is 27 units from zero" A) B) C) D) I think it's B, but I'm not sure. Thanks...1 solutions Answer 124547 by scott8148(6628)   on 2008-11-21 12:39:44 (Show Source): You can put this solution on YOUR website!you are correct
 Linear_Algebra/168846: This question is from textbook Prentice Hall algebra2 with trigonometry Please help me solve this equation: Number solving Using three equations: Kristen has a total of 225 on three tests. The sum of the scores on the first and second tests exceeds her third score by 61. her first score exceeds her second by 6. Find the 3 scores.1 solutions Answer 124510 by scott8148(6628)   on 2008-11-20 22:12:05 (Show Source): You can put this solution on YOUR website!letx="1st test", y="2nd test", and z="3rd test" "Kristen has a total of 225 on three tests" __ x+y+z=225 " The sum of the scores on the first and second tests exceeds her third score by 61" __ x+y=z+61 "her first score exceeds her second by 6" __ x=y+6 substituting from 2nd equation into 1st __ (z+61)+z=225 __ 2z+61=225 __ 2z=164 __ z=82 substituting from 3rd eqn into 2nd __ (y+6)+y=(82)+61 __ 2y+6=143 __ 2y=137 __ y=68.5 substituting into 3rd eqn __ x=(68.5)+6 __ x=74.5
 Expressions-with-variables/168744: A girl standing 6 feet from a lamp post cast ashadow 3 fet long. If the girl is 4 feet tall, how tall is the lamp?1 solutions Answer 124389 by scott8148(6628)   on 2008-11-20 14:54:33 (Show Source): You can put this solution on YOUR website!if you draw a picture, you will see that the height (of the girl or the lamp post) __ is proportional to the distance from the end of the shadow let x="height of lamp post" 4/3=x/(3+6) __ 36=3x __ 12=x
 Miscellaneous_Word_Problems/168421: This question is from textbook Algebra and Trigonometry Structure and Method book 2 I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Problem Solving Using Polynomial Equations Solve. A farmer plans to use 25m of fencing to enclose a rectangular pen that has a area of 63m^2. Only three side of the pen need fencing because part of a existing wall will be used for one of the longer sides. Find the dimensions of the pen.1 solutions Answer 124132 by scott8148(6628)   on 2008-11-18 22:08:23 (Show Source): You can put this solution on YOUR website!L * W = 63 L + 2W = 25 __ L = 25 - 2W __ substituting __ (25-2W)*W=63 __ 2W^2-25W+63=0 factoring __ (2W-7)(W-9)=0 2W-7=0 __ W=7/2 __ substituting __ L+2(7/2)=25 __ L=18 W-9=0 __ W=9 __ substituting __ L+2(9)=25 __ L=7 the length is more than the width, so the 1st solution is the correct one
 Rate-of-work-word-problems/168043: Grain pouring from a chute at the rate of 8 feet cubed per minute forms a conical pile whose altitude is always twice its radius. How fast is the altitude of the pile increasing when the pile is 6 feet high?1 solutions Answer 123866 by scott8148(6628)   on 2008-11-17 13:47:53 (Show Source): You can put this solution on YOUR website!sooo...we're now in calculus.com... r=h/2 __ V=π(r^2)h/3 __ substituting __ V=π(h^3)/12 differentiating __ dV/dT=(π/12)(3h^2)dh/dT __ dh/dT=(dV/dT)/[(π/12)(3h^2)] dh/dT=8/(π/4)(6^2)=32/(36π)=.283ft/min (approx)
 Inequalities/167948: Find the slope of each line. Then tell what the slope represents. coordinates: 4,80 12,160 would the answer be 3/80? Im confused1 solutions Answer 123818 by scott8148(6628)   on 2008-11-16 21:09:18 (Show Source): You can put this solution on YOUR website!the slope is the difference in the y-values divided by the difference in the x-values in this case __ (160-80)/(12-4)=80/8=10 the slope represents the ratio of the rates of change of y and x
 Mixture_Word_Problems/167794: walnuts that cost \$4.05 kilogram were mixed with cashews that cost \$7.25 per kilogram.How many kilograms of each were used to make a 50 kilogram mixture that costs \$6.25 per kilogram. ROUND each to the nearest tenth. we use a sheet that confuses me. 1st column has the item mixing going down then the 2nd has amount you have , then 3rd item mixing/amount you have/X/ cost or %/=/ value (equation) I just find it alittle confusing as to where everything goes. Thank you .1 solutions Answer 123695 by scott8148(6628)   on 2008-11-15 22:43:02 (Show Source): You can put this solution on YOUR website!this being algebra.com...let's use an equation... let x="kg of walnuts", so 50-x="kg of cashews" __ 50 kg total, right? 4.05(x)+7.25(50-x)=6.25(50) __ 4.05x+362.5-7.25x=312.5 __ -3.2x=-50 __ x=15.6 50-x=34.4
 Sequences-and-series/167753: Miku and John began biking from the same place on the same road, heading in the same direction. Each day, Miku bikes 25 miles. John bikes 5 miles the first day, 8 miles the second day and so on. Each day, biking three more miles than he biked the previous day. If they began on July 1, on waht date did John passed Miku? I got the answer with a table but i dont know how to show it into algebraic equation. How do you change John's pattern into an equation? 5,13,24,38,56,76,99,125........... My work so far: Miku= 25x x = days John= 5+(5+3)+(5+3+3)+(5+3+3+3)..... 5x+???= nth term so far, the only part of the equation ive figured out is the 5x.... though i think that there should be a disributive property in the equation. Im really confused and have been working this problem for hours. I really need help.1 solutions Answer 123692 by scott8148(6628)   on 2008-11-15 22:32:17 (Show Source): You can put this solution on YOUR website!the sum of the terms for an arithmetic sequence is the number of terms (n) multiplied by the average value of the terms __ (T1+Tn)/2 S = n(5+5+3(n-1))/2 = n(10+3n-3)/2 = (3n^2+7n)/2 (3n^2+7n)/2 = 25n __ 3n^2+7n=50n __ 3n^2-43n=0 __ n(3n-43)=0 n=0 __ they are together on July 1 3n-43=0 __ 3n=43 __ n=14 1/3 __ John passed Miku on July 15
 Quadratic_Equations/167432: A rectangular swimming pool is surrounded by a walk. The area of the pool is 323 sq ft, and the outside dimensions of the walk are 20x22 ft. How wide is the walk? I know this should be simple, but I'm struggling with it! Thank you so much for your help, what ever kind person answers my question! Lauren1 solutions Answer 123343 by scott8148(6628)   on 2008-11-13 15:15:34 (Show Source): You can put this solution on YOUR website!the walk is on all four sides of the pool, so the dimensions of the pool are 20-2w and 22-2w __ where w is the width of the walk (20-2w)(22-2w)=323 __ 440-84w+4w^2=323 __ 4w^2-84w+117=0 use quadratic formula to find w answer below w=1.5
 Graphs/167304: how do you write an equation in slope intercept form when the y-intercept is 3 and the slope is 3/2?1 solutions Answer 123225 by scott8148(6628)   on 2008-11-12 19:15:07 (Show Source): You can put this solution on YOUR website!the general form is y=mx+b, where m is the slope and b is the y-intercept y=(3/2)x+3
 Quadratic_Equations/167203: x^2=4-8x1 solutions Answer 123146 by scott8148(6628)   on 2008-11-12 12:33:28 (Show Source): You can put this solution on YOUR website!subtracting 4-8x __ x^2+8x-4=0 __ this is not factorable adding 4 __ x^+8x=4 __ completing the square by adding (8/2)^2 __ x^2+8x+16=20 taking square root __ x+4=ħsqrt(20) __ x=-4 ħ 2(sqrt(5))
 Probability-and-statistics/167211: I have 27 balls. 14 are red and 13 blue. I deceded to group the balls into a group of 3s ? the balls will be choosen randomly. What is the probablity that the group will have 2 red and 1 blue. 2)-the probability that the group will have all reds or all blue1 solutions Answer 123144 by scott8148(6628)   on 2008-11-12 12:25:19 (Show Source): You can put this solution on YOUR website!possible groups of 3 out of 27 __ 27C3 __ 27*26*25/(3*2*1) __ 2925 possible groups of 2 red out of 14 __ 14C2 __ 14*13/(2*1) __ 91 possible groups of 1 blue out of 13 __ 13 probability of 2 red and 1 blue __ 91*13/2925 __ .404 (approx) possible groups of 3 red out of 14 __ 14C3 __ 14*13*12/(3*2*1) __ 364 probability of 3 red __ 364/2925 __ .124 (approx) possible groups of 3 blue out of 13 __ 13C3 __ 13*12*11/(3*2*1) __ 286 probability of 3 blue __ 286/2925 __ .098 (approx)
 Probability-and-statistics/167212: I have 27 balls. 14 are red and 13 blue. I deceded to group the balls into a group of 3s ? the balls will be choosen randomly. What is the probablity that the group will have 2 red and 1 blue. 2)-the probability that the group will have all reds or all blue1 solutions Answer 123143 by scott8148(6628)   on 2008-11-12 12:24:48 (Show Source): You can put this solution on YOUR website!possible groups of 3 out of 27 __ 27C3 __ 27*26*25/(3*2*1) __ 2925 possible groups of 2 red out of 14 __ 14C2 __ 14*13/(2*1) __ 91 possible groups of 1 blue out of 13 __ 13 probability of 2 red and 1 blue __ 91*13/2925 __ .404 (approx) possible groups of 3 red out of 14 __ 14C3 __ 14*13*12/(3*2*1) __ 364 probability of 3 red __ 364/2925 __ .124 (approx) possible groups of 3 blue out of 13 __ 13C3 __ 13*12*11/(3*2*1) __ 286 probability of 3 blue __ 286/2925 __ .098 (approx)
 Probability-and-statistics/167214: I have 27 balls. 14 are red and 13 blue. I deceded to group the balls into a group of 3s ? the balls will be choosen randomly. What is the probablity that the group will have 2 red and 1 blue. 2)-the probability that the group will have all reds or all blue1 solutions Answer 123142 by scott8148(6628)   on 2008-11-12 12:23:43 (Show Source): You can put this solution on YOUR website!possible groups of 3 out of 27 __ 27C3 __ 27*26*25/(3*2*1) __ 2925 possible groups of 2 red out of 14 __ 14C2 __ 14*13/(2*1) __ 91 possible groups of 1 blue out of 13 __ 13 probability of 2 red and 1 blue __ 91*13/2925 __ .404 (approx) possible groups of 3 red out of 14 __ 14C3 __ 14*13*12/(3*2*1) __ 364 probability of 3 red __ 364/2925 __ .124 (approx) possible groups of 3 blue out of 13 __ 13C3 __ 13*12*11/(3*2*1) __ 286 probability of 3 blue __ 286/2925 __ .098 (approx)
 Miscellaneous_Word_Problems/167133: This question is from textbook Algebra and Trigonometry Structure and Method book 2 I have been working on this math problem and I can't figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Problem Solving Using Polynomial Equations Solve each problem. If there are two correct answers, give both of them. The top of a 15-foot ladder is 3ft farther up a wall than the foot of the ladder is from the bottom of the wall. How far is the foot of the ladder from the bottom of the wall?1 solutions Answer 123141 by scott8148(6628)   on 2008-11-12 12:04:14 (Show Source): You can put this solution on YOUR website!let x="distance from wall" "The top of a 15-foot ladder is 3ft farther up a wall than the foot of the ladder is from the bottom of the wall" __ x+3 by Pythagoras __ x^2+(x+3)^2=15^2 __ x^2+x^2+6x+9=225 __ 2x^2+6x-216=0 __ x^2+3x-108=0 factoring __ (x+12)(x-9)=0 x+12=0 __ x=-12 __ negative value not realistic x-9=0 __ x=9
 logarithm/167210: log base 6 (3x-2) + log base 6 (x-3)=1 i worked out this problem, and got an incorrect answer. 1 solutions Answer 123139 by scott8148(6628)   on 2008-11-12 11:50:57 (Show Source): You can put this solution on YOUR website!using rules for logs __ (3x-2)(x-3)=6 3x^2-11x+6=6 __ 3x^2-11x=0 __ x(3x-11)=0 x=0 __ not realistic __ logs are not defined for negative values 3x-11=0 __ x=11/3
 logarithm/167147: This question is from textbook How do you multipy a logarithmic function by a logarithmic function? This is what I am stuck on: (log base 12(log base 2 x))= 3 X is not included in the base. 1 solutions Answer 123137 by scott8148(6628)   on 2008-11-12 11:45:04 (Show Source): You can put this solution on YOUR website!this is the log of a log using rules for logs __ log2(x)=12^3 __ x=2^(12^3) __ x=2^1728 __ x=1.513x10^520 (approx)
 Length-and-distance/167146: This question is from textbook Geometry Can somebody please help solving the below problem? Given points P(2,1) and D(7,11). Find the coordianates of T on the line PD such that PT/TD = 2/3. 1 solutions Answer 123135 by scott8148(6628)   on 2008-11-12 11:35:48 (Show Source): You can put this solution on YOUR website!since 2+3=5, divide PD into 5 parts with PT equal to 2 parts and TD equal to 3 parts this is very straight forward because the x-distance and the y-distance are both divisible by 5 Tx=Px+(2/5)(7-2) __ Tx=2+2 __ Tx=4 Ty=Py+(2/5)(11-1) __ Ty=1+4 __ Ty=5 T=(4,5)
 Graphs/167079: can someone EXPLAIN the steps of finding the x- and y- intercepts of this prblem?1 solutions Answer 123098 by scott8148(6628)   on 2008-11-11 20:53:04 (Show Source): You can put this solution on YOUR website!the x-intercept is when the graph crosses the x-axis __ at this point, y=0 __ similarly, the value of x is zero at the y-intercept to find the x-intercept, substitute zero for y; and vice versa x-intercept __ 12(0)+15(0)+21=4x-5(0)+7 __ 21=4x+7 __ 14=4x __ 3.5=x __ so the x-intercept is (3.5,0) y-intercept __ 12y+15y+21=4(0)+5y+7 __ 27y+21=5y+7 __ 22y=-14 __ y=-7/11 __ so the y-intercept is (0,-7/11)
 Matrices-and-determiminant/167114: Use the Gaussian Elimination to solve for x, y, & z: x + 2y + 3z = 8 x - y - z = 3 2x + y - 2z = 3 I don't even know how to begin, can anyone please help? Greatly appreciated.1 solutions Answer 123094 by scott8148(6628)   on 2008-11-11 20:40:22 (Show Source): You can put this solution on YOUR website!adding the 2nd eqn to the 3rd eqn ELIMINATEs the y __ 3x-3z=6 adding two times the 2nd eqn to the 1st eqn also eliminates the y __ 3x+z=14 subtracting the 2nd NEW eqn from the 1st NEW eqn eliminates the x __ -4z=-8 __ z=2 substituting __ 3x+(2)=14 __ x=4 substituting __ (4)+2y+3(2)=8 __ 2y=-2 __ y=-1
 Quadratic-relations-and-conic-sections/166883: PLEASE HELP!!! Write an equation for the parabola with focus (4,0) and directrix y=2 I must show my work. Thanks1 solutions Answer 123004 by scott8148(6628)   on 2008-11-11 02:42:43 (Show Source): You can put this solution on YOUR website!a general form for the equation of a parabola is __ (x-h)^2=4p(y-k) __ where (h,k) is the vertex and p is the distance from the vertex to the focus the vertex is midway between the focus and the directrix __ in this case, (4,1) __ so p=-1 the equation would be (x-4)^2=-4(y-1) solving for y gives y=(-1/4)(x-4)^2 + 1
 Miscellaneous_Word_Problems/166911: Not from a textbook. Not sure how to show or explain the answer. I can figure out the first 3 years (108, 116.64, 125.97) I'm not sure about the n and algebraic equation needed. Thank you in advance for any and all help given. Here is the problem. Suppose a population of initial size 100 grows at the rate of 8% per year. What is the size of the population at the end of year 1? What is the size of the population at the end of year 2? What is the size of the population at the end of year 3? What is the size of the population at the end of year n? What algebraic equation would you need to solve to find the number of years x that it would take for our population to reach 200? Use a calculator to solve to x?1 solutions Answer 123003 by scott8148(6628)   on 2008-11-11 02:21:12 (Show Source): You can put this solution on YOUR website!to find the population at the end of any year, you take 8% of the starting population and add it P2=P1+(8%)P1 __ factoring __ P2=P1(1+8%)=P1(1.08) P3=P2+(8%)P2 __ factoring __ P3=P2(1+8%)=P2(1.08) __ substituting P3=(P1(1.08))(1.08) __ P3=P1(1.08)^2 __ 2 is the number of years between P1 and P3 in general __ Pn=P0(1.08)^n __ where P0 is the original starting population 200=100(1.08)^n __ dividing by 100 __ 2=1.08^n __ taking log __ log(2)=n(log(1.08)) dividing by log(1.08) __ (log(2))/(log(1.08))=n __ 9=n (approx)
 percentage/166703: Tickets for a concert were sold to adults for \$3 and to students for \$2. If the total receipts were \$824 and twice as many adult tickets as student tickets were sold, then how many of each were sold? How is this sort of problem set up? and the necessary steps to solve? Thanks, Zach Cottrell1 solutions Answer 122846 by scott8148(6628)   on 2008-11-09 17:30:49 (Show Source): You can put this solution on YOUR website!cost times number equals receipts "total receipts were \$824" __ 3a+2s=824 "twice as many adult tickets as student tickets were sold" __ a=2s substituting __ 3a+(a)=824 __ 4a=824 __ a=206 substituting __ 206=2s __ 103=s
 Equations/166430: I HAVE TO SOLVE FOR THREE VARIABLES IN THREE DIFFERENT SOLUTIONS. PLEASE HELP. 9x-y+z=-30 3x+2y-3z=-3 x-3y+2z=-12 i thought i knew how to figure it out but i have been at this well over 20 minutes so any suggestions would be greatly appreciated.1 solutions Answer 122668 by scott8148(6628)   on 2008-11-07 22:35:55 (Show Source): You can put this solution on YOUR website!eliminate the same variable from two different PAIRS of equations, leaving two new equations with two unknowns multiply 2nd eqn by -3 and add to 1st eqn __ -7y+10z=-21 multiply 3rd eqn by -3 and add to 2nd eqn __ 11y-9z=33 multiplying 1st new eqn by 11 __ -77y+110z=-231 multiplying 2n new eqn by 7 __ 77y-63z=231 adding eqns __ 47z=0 __ z=0 substituting __ 11y-9(0)=33 __ y=3 substituting __ x-3(3)+2(0)=-12 __ x-9=-12 __ x=-3
 Travel_Word_Problems/166412: Can someone please help me with the following problem? A plane has a cruising speed of 280 miles per hour and the wind velocity is 40 miles per hour. How far can the plane fly and return in 7 hours? So far I have begun to make a chart to help solve the problem, but I am just very confused. 1 solutions Answer 122647 by scott8148(6628)   on 2008-11-07 16:37:28 (Show Source): You can put this solution on YOUR website!d=rt __ distance out is the same as distance back the total time is 7hr __ if t is the time out, then 7-t is the time back rate with the wind is 280+40 or 320 rate back is 280-40 or 240 320 * t = 240 * (7-t) __ 320t=1680-240t __ 560t=1680 __ t=3 substituting __ d=320(3) __ d=960 (one way)
 Geometry_Word_Problems/166264: Will you help me with this problem: A square and a rectangle have the same perimeter. The lenghth of the rectangle is 4cm less than twice the side of the square,and the width of the rectangle is 6cm less than the side of the square. Find the perimeter of each figure.1 solutions Answer 122551 by scott8148(6628)   on 2008-11-06 20:46:29 (Show Source): You can put this solution on YOUR website!"A square and a rectangle have the same perimeter" __ 4S=2L+2W "The lenghth of the rectangle is 4cm less than twice the side of the square" __ L=2S-4 "the width of the rectangle is 6cm less than the side of the square" __ W=S-6 substituting __ 4S=2(2S-4)+2(S-6) __ 4S=4S-8+2S-12 __ 4S=6S-20 __ 20=2S __ 10=S so the perimeter is 4*10 or 40
 Linear-systems/166266: Solve the following equation for x: 3(x + 2) = 7x – 10 Can someone please help me with this equation. Thank you1 solutions Answer 122550 by scott8148(6628)   on 2008-11-06 20:39:43 (Show Source): You can put this solution on YOUR website!distributing the 3 __ 3x+6=7x-10 adding 10 __ 3x+16=7x subtracting 3x __ 16=4x dividing by 4 __ 4=x
 Human-and-algebraic-language/166271: Three lighthouses on three nearby islands flash their lights every evening beginning at 8:35pm. On one island, the ligh flashes every 45 seconds. The lighthouse on the second island has a light that flashes every 2 minutes. The third lighthouse flashes a light every 1 1/4 minutes. At what time will all three lights flash together again? This is a problem of the week just given to my child on a single piece of paper. 1 solutions Answer 122547 by scott8148(6628)   on 2008-11-06 20:35:13 (Show Source): You can put this solution on YOUR website!you are looking for the lowest common multiple 45sec = 3 * 15 2min = 120sec = 8 * 15 1 1/4 min = 75sec = 5 * 15 LCM = 15 * 3 * 8 * 5 = 1800sec = 30min so, every half hour they flash together