Posts by Reiny

Total # Posts: 40,239

  1. math

    term(1) = a term(n) = a + (n-1)d = a + (n-1)(4a) = 37a (n-1)(4a) = 36a n-1 = 9 n = 10
  2. math

    term(1) = a = 6.1 term(14) = a + 13d = 7.1 6.1 + 13d = 7.1 13d = 1 d = 1/13
  3. Math

    so female = (3/8)(5000) = 1875 then male = 3125 total admitted= .4(5000) = 2000 so half were male, half were female male admitted = 1000 female admitted = 1000 percentage of females admitted = 1000/1875 = 53.3% percentage of males admitted = 1000/3125 = 32%
  4. Math

    (k+ 1/k)^2 = k^2 + 2(K)(1/k) + (1/k) = 36 k^2 + (1/k)^2 + 2 = 36 so k^2 + (1/k)^2 = 34 you are correct
  5. Math

    each equation can be solved indivually to get two answers. I suppose you want the value of x which satisfies both equations. so .... x^2 + 5x+6 = x^2 - x - 6 6x = -12 x = -2 or: x^2 - x - 6 (x-3)(x+2) = 0 so x = 3 or x = -2 x^2 + 5x+6 = 0 (x+2)(x+3) = 0 x = -2 or x = -3 so the...
  6. Calculus

    Since you want the average velocity, you don't even need the derivative when t = 1, s = 6(1) + 2(1) = 8 when t = 4, s = 6(16) + 2(4) = 104 average speed = total distance/total time = (104-8)/(4-1) = 32 mph
  7. Algebra

    Since distance = time x rate number of miles = 66h
  8. Algebra

    Meg---- m Jill ---- m-2 Beth ---- m/2 or Meg ---- 2x Jill ----- 2x - 2 Beth ---- x or Jill ---- x Meg --- x+2 Beth ---- (x+2)/2 or Meg ---- 10x Jill ----- 10x-2 Beth ---- 5x or .....
  9. statistics

    -1.00 ? z is the same as z ? -1 or 1 - P(z ? -1.00) ----> .8413 I don't know how old your tables are or what they look like, but for most of them ... here is a typical one: http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf find -1.0 in the horizontal under the 00 ...
  10. math

    What is a square qt ??
  11. Algebra

    You must know the basic formulas for a geometric sequence. term(n) = a r^(n-1), where a is the first term, r is the common ratio and n is the term number for yours: ar = 9 and ar^3 = 81 divide one equation by the other: ar^3/(ar) = 81/9 r^2 = 9 r = ± 3 then ar = 9 So if...
  12. math

    Why do you have a double division sign? Did you mean (d+g)/h ?? the way you typed it: d+g/h = 15 + 27/7 = 132/7 , not one of the choices if you meant: (d+g)/h = (15+27)/7 = 42/7 = 6 Now, tell me why you could not have done this yourself?
  13. math 5th

    original: Beena ---- x Alisha --- x+114 after give-away: Beena ---- x+96 Alisha ---- x+114 - 96 = x + 18 x+96 = 2(x+18) solve for x
  14. correction - mathh

    in the line near the end: x = ? - .60136... = 2.5102 it should be x = ? - .60136... = 2.5402>/b>
  15. mathh

    I am sure bobpursly had already answered this for you, but I could not find the post. I recall he took you as far as the quadratic. Why did you not finish it ?? 2sec^2x -3tanx =5 for [0,2pi) make use of your identities sec^2 A = 1 + tan^2 A 2(1 + tan^2 x) - 3tanx - 5 = 0 2 + ...
  16. calc

    Because it is customary, and it often makes it easier, if the coefficient of the square term is positive. So I switched all the signs, you must have known that this would not change the solution to the equation.
  17. calc

    Final word: http://www.wolframalpha.com/input/?i=solve+2cos(2x)%3D-sinx look at the graph, let your mouse hover over the red intersection points.
  18. calc

    Nope, my equation is correct, I should not have skipped that one step: 2cos2x=-sinx 2cos2x + sinx = 0 2(1 - 2sin^2 x) + sinx = 0 2 - 4sin^2 x + sinx = 0 times -1 -2 + 4sin^2 x - sinx = 0 4sin^2 x - sinx - 2 = 0 checking one of your answers in the original equation: let x = 2....
  19. calc

    2cos2x=-sinx 2cos 2x + sinx = 0 2( 1 - 2sin^2 x) + sinx = 0 4sin^2 x - sinx - 2 = 0 sinx = (1 ± ?1 - 4(4)(-2)) /8 = (1 ± ?33)/8 = appr .84307.... or appr -.59307... If sinx = .84307 x is in quads I or II, and x = appr 1.002967 or appr. 2.1386 if sinx = -.59307.. ...
  20. Maths

    How does this question and its solution tie in with your problem? /display.cgi?id=1447959082
  21. Maths

    "sum of circumferences of two circles wirh radii r1 & r2" = 2?r1 + 2?r2 "the circumference of a circle of radius r" = 2?r they are equal .... 2?r1 + 2?r2 = 2?r 2?(r1 + r2) = 2?r divide both sides by 2?
  22. math

    really ??
  23. math

    sum(21) = 28 (21/2)(2a + 20d) = 28 2a+20d = 56/21 sum(28) = 21 (28/2)(2a + 27d) = 21 2a+27d = 42/28 = 3/2 subtract the two equations: 7d = 3/2 - 56/21 = -7/6 d = -1/6 in 2a + 20d = 56/21 2a - 20/6 = 56/21 2a = 6 a = 3 so we need: a + (n-1)d = 0 3 + (n-1)(-1/6) = 0 3 - (-1/6)n...
  24. Math

    1/4 square inches = 5 ft <---- makes little sense or 1/4 square inches = 5 square ft ?? is this a continuation of your previous "scale factor" question? if so, the scale was 1 : 24?5 then model : 46950 = 1 : 24?5 model = 874.86 I sure some author did not embarrass...
  25. math

    let the sum be x x(1.05)^2 - x - x(.05)(2) = 205 x(1.05^2 - 1 - .05(2) ) = 205 .... let me know what you got
  26. Math

    1/4 square inches -----> 5 square ft 1/2 inch -----> ?5 ft 1 inch -----> 2?5 ft 1 inch ----- 2?5(12) = 24?5 inches scale : 1 : 24?5 or appr 1 : 53.67 , just like Arora had.
  27. Maths

    let the areas of the flats be 5x , 6x, and 8x for a, b, c respectively Now use your given data: "the difference in the area of flat c and flat a is 270 square metres" ----> 8x - 5x = 720 solve for x, and sub into my definitions
  28. Math

    Use your definitions 2nd term : ar = 1 5th term : ar^4 = 1 divide: r^3 = 1 r = 1 the ar = 1 a(1) = 1 a = 1 your GP is 1,1,1,.... (not a very exciting sequence, some authors would exclude r = 1 in a GP)
  29. calculus 1-chemistry

    It will reach a max when R '(T) = 0 R'(T) = .1(-.15T^2 + 8T) = 0 .15t^2 - 8t = 0 t(.15t - 8) = 0 t = 0 , (at the beginning) or t = 8/.15 sec = 160/3 sec find R(160/3) to get that maximum
  30. continued - Algebra and Geometry

    take a line segment of length 1 , and divide it into a larger and a smaller segment , so that the ratio of the whole line to the larger = the ratio of the larger segment to the smaller. Let the larger segment be x then the smaller is 1 - x 1/x = x/(1-x) x^2 = 1 - x x^2 + x - 1...
  31. continued - Algebra and Geometry

    list the first 20 or so Fibonacci numbers. From left to right, divide one number by the number before it, noting the result. What do you notice about the answers ??
  32. continued - Algebra and Geometry

    after you find the golden ratio, take its reciprocal on your calculator. Notice the decimal sequence does not change. No other number has that property
  33. Algebra and Geometry

    One of my favourite websites: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html It would take you weeks to follow all the links and side-interests of this wonderful webpage It starts with the Fibonacci numbers, which are very closely linked with the Golden ...
  34. algebra math, 8th grade

    Or, to illustrate Scott's concept, just plot the given points.
  35. Math

    R = mE + b case1: R = 530, E = 16000 530 = 16000m + b ** case2: R = 730, E = 3600 730 = 3600m + b *** subtract *** from ** -200 = 12400m m = -1/62 back in *** 3600(-1/62) + b = 730 b = 24430/31 R = (-1/62)E + 24430/31 so when E = 1300 R = (-1/62) + 24230/31 = 23780/31 or appr 767
  36. Math

    well, if 1 inch ---> 15 ft then 8 inches ---> 8(15) ft or 120 ft and 12 inches ........
  37. Algebra

    in 3 - 3/x , x cannot be zero ! did you mean x ? 0 ?? 3- 3/x = x+7 times x 3x - 3 = x^2 + 7x x^2 + 4x + 3 = 0 (x+3)(x+1) = 0 x = -3 or x = -1 what do you think?
  38. AP Calculus 12

    I will assume you mean lim (1 - cosx)/sinx , as x ---> 0 = lim (1 - cosx)/sinx * (1+cosx)/(1+cosx) = lim (1 - cos^2 x)/(sinx(1+cosx) = lim sin^2 x/(sinx(1+cosx) , as x ---> 0 = lim sinx/(1+cosx) , as x ---> 0 = 0/2 = 0
  39. algebra

    what is 6 + 5(-2) ? = 6 - 10 = -4
  40. algebra

    just replace n with 6 a(6) = 6 + (5)(-2) = -4 2nd question: correct let x = -8, y = -3(-8)+7 = 31 let x = -6, y = -3(-6)+7 = 25 ... let x = 2, y = -3(2)+7 = 1 so the range is {31, 25, ... ,1}
  41. algebra 1

    from mailroom at floor x : x + 4 - 7 + 9 - 6 + 2 - 8 = 1 x = ....
  42. Math

    in your repertoire of factoring techniques and formulas, you should have: x^3 + y^3 = (x+y)(x^2 - xy + y^2) and x^3 - y^3 = (x-y)(x^2 + xy + y^2) so .... x^3 + 125 = x^3 + (5)^3 = (x+5)(.....) let me know what you get
  43. Algebra

    the domain of the inverse of f(x) is the range of f(x) if f^-1 (x) = x^2 - 4/5 the inverse of that is x = y^2 - 4/5 5x = 5y^2 - 4 (5x+4)/5 = y^2 f(x) = y = ±?((5x+4)/5) <----- the range of that is any real number
  44. Math

    after first discount: cost = .8(149.99) = 119.99 so yes, you qualify for the second discount. cost after second discount = .9(119.99) = 107.99 total savings = 149.99 - 107.99 = $42.00 none of the choices are correct, unless you have a typo in a)
  45. Math

    Yes
  46. Math Algebra 1

    Cost A = 125 + 50t Cost B = 200 + 25t You really should have been able to do this.
  47. Math

    I am sure you meant: f(x) = (x+1)/(x-1) or y = (x+1)/(x-1) f(y) = ( (x+1)/(x-1) + 1) / ( (x+1)/(x-1) - 1) multiply top and bottom by x-1 f(y) = ( x+1 + x-1) / ( x+1 - (x-1) ) = 2x/2 = x
  48. math

    If I recall those old non-metric units ... 1 gallon = 4 quarts, so 3 gallons = 12 quarts 2 cups juice : 3 quarts punch = x cups juice : 12 quarts punch 2/3 = x/12 x = 12(2/3) = 8
  49. math

    yes, of course, hit the wrong key
  50. math

    The areas of two similar figures are proportional to the square of their corresponding sides so 225 : 81 = side1^2 : side2^2 then ?225 : ?81 = side1 : side2 side1 : side2 = 15 : 8
  51. Math

    A) 1 cm : 5 m = 1 cm : 500 cm = 1 : 500 B) ... C) 5 cm : 10 m = 5 cm : 1000 cm = 5 : 1000 = 1 : 200 D) ... you work out the other two, then decide
  52. MATH

    correct
  53. Algebra 1

    I would choose elimination: first one times 2 ---> 6x + 4y = -20 2nd times 3 -------> 6x - 15y = 9 subtract them: 19y = -29 y = -29/19 back into the original first: 3x - 58/19 = -10 3x = 58/19-10 = -132/19 x = -44/19
  54. Math

    Was there a question? What are those decimals in your second post ?
  55. Math

    Start with y = | x | you should be able to graph this if not, look at Wolfram: http://www.wolframalpha.com/input/?i=y+%3D+%7Cx%7C a big V with nothing below the x-axis consider: y = |x| - 2 , we just moved the entire graph down 2 units. http://www.wolframalpha.com/input/?i=y+%...
  56. Math

    you stated correctly, that the depth depends on the time? - so doesn't the depth depend on time, making time the independent variable, and depth the dependent one ?? Usually the independent variable goes on the vertical axis, (the y-axis), and the independent variable ...
  57. @ Candi

    Candi, do not put a new question as an answer to somebody else's. It may not be looked at , since we might think the first question has been answered. '2/3 of a given number is 40' --- (2/3)x = 40 x = 40(3/2) = 60 now 2/5 of that is (2/5)(60) = 24 Where did the 200...
  58. Math

    No, did you notice that the y values are all powers with base 5 ? (1,5) ---> (1, 5^1) (2, 25) ---> (2, 5^2) ... (5, 3125) ---> (5, 5^5) So y = 5^x , which I don't see as one of the options, unless you have typo in either B or C
  59. Math

    2(18) + 2(1.5) + soda = 10 + 30.25 solve for 'soda'
  60. math

    Draw your sketch and find the intersection of the two straight lines. The y of that intersection point is the height of your triangle. In your head, you can see that the x-intercept of x+y=24 is (24,0) and the x-intercept of 3x - 2y = 12 is (4,0) so you know the base length of...
  61. math geometry

    Find the volume of the first cone. You know r = 5 and h = 18 You MUST know the formula for the second cone you know r = 7.5 and you have to find h sub in r = 7.5 and h in the formula and set it equal to the volume of the first cone. Solve for h let me know what you get.
  62. Algebra

    john's rate = 5 cups/2 min = 2.5 cups/min sam's rate = 6 cups/2.5 min = 2.4 cups/min combined rate = 4.9 cups/min so time to make 245 cups = 245/4.9 = 50 minutes check: in 50 minutes, john can make 50(5/2) = 125 cups in 50 minutes , sam can make 50(6/2.5) = 120 cups ...
  63. Math

    Again, what formula are you using ??
  64. Math

    That's what I used to call mathemagics - unfortunately you are wrong! "I just added in the numbers to the formula and 59 just appeared" ---- nonsense! What formula? Show me if you want help
  65. Math

    no show me your work so I can tell you where you went wrong.
  66. Math

    correct, if you use all the digits that you can hold in your calculator's memory, you will get it exactly to the cent.
  67. Math

    i = .05/12 = .0041666.. (keep it in your calculator, don't round off) n = 60 paym( 1 - (1.04166...)^-60)/ ..041666... = 2000 solve for paym let me know what you got.
  68. math

    original: number of math books -- 5x number of geogr books -- 7x number of science books - 8x new numbers: math ----- 1.4(5x) = 7x geography-- 1.5(7x) = 10.5x science ----- 1.75(8x) = 14x new ratio = 7x : 10.5x : 14x = 7 : 10.5 : 14 = 14 : 21 : 28 = 2 : 3 : 4
  69. calc

    or Newton's method: let y = lnx - x^3 + 1 dy/dx = 1/x - 3x^2 newx = x - (lnx - x^3 + 1)/(1/x - 3x^2) = (1 - 3x^3 - lnx + x^3 - 1)/(1/x - 3x^2) = (-2x^3 - lnx)/(1/x - 3x^2) guess: x = .5 newx1 = .3545... newx2 = .38789... nrwx3 = .39042.. newx4 = .39044046 newx5 = .39044046...
  70. Math

    log?62 = a , 4^a = 62 , I know 4^3 = 64 , so a = appr 3 , but a < 3 log?36 = b , 6^b = 36, so b = 2 log?10 = c , 3^c = 10, I know 3^2 = 10 , so c = appr 2, but c >2 log?20 = d , 5^d = 20 , I know 4^2 = 25, so d < 2 order: log?20 , log?36 , log?10 , log?62
  71. Calculus

    Looks pretty straight forward ... f(x)=9x^(1/3) + (9/2)x^(4/3) f ' (x) = 3x^(-2/3) + 6x^(1/3) f''(x) = -2x^(-5/3) + 2x^(-2/3) for relative max/min, f'(x) = 0 3x^(-2/3) + 6x^(1/3) = 0 3x^(-2/3) (1 + 2x) = 0 3x^(-2/3) = 0 ---> no solution or 1+2x = 0 x = -1/2 ...
  72. Calculus

    Your lack of brackets leave the interpretation of the equation very ambiguous. e.g. do you mean: f(x)=9x^(1/3) + (9/2)x^(4/3) ? please retype before I attempt it
  73. Maths

    What is a rectangular pentagonal garden? Where is point A ?
  74. Algebra 2

    or , assuming you meant : 4* 4^(x/2) =1024 4^(x/2 + 1) = 4^5 x/2 + 1 = 5 x/2 = 4 x = 8 If you meant: 4* (4^x)/2 =1024, the way you typed it (4^x)/2 = 256 4^x = 512 xlog4 = log512 x = log512/log4 = 4.5
  75. Math

    Your hyperbola has centre (0,1) , a = 3, and b = 1 vertices would be (3,1) and (-3,1) To sketch this hyperbola I would faintly sketch a rectangle with corners at (3,2), (-3,2) , (-3,0) and (3,0) One asymptote would run through (3,2) and (-3,0) and of course (0,1) slope = 1/3 y...
  76. math

    I noticed that the coefficients of y are ± 1 , so ... add the first and the second: 6x = 1 x = 1/6 , well that was lucky add the second and third: 3x + 3z = -3 x + z = -1 1/6 + z = -1 z = -7/6 sub into the last: 1/6 + y - 7/6 = 6 times 6 1 + 6y - 7 = 36 y = 42/6 = 7
  77. math

    Did you make a sketch? draw a horizontal at the 3 m height, and you will get a right-angled triangle with sides 12 and 5. You might recognize the 5-12-13 right-angled triangle, if not ... h^2 = 5^2 + 12^2 = 25 + 144 = 169 h = ?169 = 13 m
  78. physics

    I am going to do this question with actual numbers let u0 = 20 m/s let v0 = 28 m/s let á = 5 m/s^2 let â = 4 m/s^2 case 1: á = 5 m/s^2 then u0 = 5t+ c when t = 0 , 20 = 0 + c velocity1 = 5t + 20 similarly velocity2 = 4t + 28 distance1 = (5/2)t^2 + 20t + k, ...
  79. Math

    just translate and use your definitions of an AS a+3d = a+4d - 3 d = 3, hey, we got the common difference already a+6d = 3(a+4d) a + 6d = 3a + 12d -2a = 6d = 18 a = -9 check: terms are: -9 -6 -3 0 3 6 9 12 15 .... all conditions check out.
  80. Math

    If possible, I prefer to work without fractions (27\8)A+7=(4\9)-3A times 72 243A + 504 = 32 - 216A 459A = -472 A = -472/459 I verified this answer in the left and right sides.
  81. Algbra

    Here is a quick way to find the slope of a line, if written in the form Ax + By + C = 0 the slope of the line is -A/B so for #1 -2x=-10y+6 ---> 2x - 10y + 6 = 0 , slope = -2/-10 = 1/5 x+5y=3 ---- slope = -1/5 so the lines have different slope, so they must intersect in 1 ...
  82. Alegbra 1

    Bill, you have now posted this same question 7 times since yesterday. You received a variety of ways to get the answer. Ms Sue even told you not to post it again, so here it is once more
  83. Math

    this is probably a question asking for EXACT values 37.5 = 1/2 of 75 and 75 = 30+45 so find tan75 = tan(30+45) = (tan30 + tan45)/( 1 - tan30*tan45) = (1/?3 + )/(1 - 1/?3) = (1+?3)(?3 - 1) recall tan 2A = 2tan A/(1 - tan^2 A) tan 75 = 2tan37.5/(1-tan^2 37.5) let tan37.5 = x (1...
  84. Algebra 2/ Intermediate

    I will assume you mean: log4(x-6)= -1 then .. x-6 = 4^-1 x-6 = 1/4 4x-24 = 1 4x = 25 x = 25/4
  85. Math

    geeeshhh let her income be x (1/4)x + (1/12)x + (1/2)x + 10000 = x times 12 3x + x + 6x + 120000 = 12x 120000 = 2x x = 60,000
  86. Math Help

    did you notice: 12-9=3 15-12=3 so what is your verdict ?
  87. Should be the last one

    You probably did 3^2 instead of 2^3 --- neither one of which requires a calculator
  88. Should be the last one

    make sure you follow the order of operations 4 + 3(10 - 2^3) = 4 + 3(10 - 8) = 4 + 3(2) = 4 + 6 = 10 how did you get 11 ??
  89. correction - MATH

    since V = pi(r^2)h if we double r and h new V = pi(2r)^2(2h) = 8pi r^2 h so it increased 8 times or, since they gave you the volume after doubling in the second sentence, just divide 401.9/50.2 = 8.0059... or 8 times or volume of similar objects varies directly with the cube ...
  90. math

    nothing to solve, you don't have an equation. If you are simplifying .... 3loga(2x+1)-2loga(2x-1) = loga(2x+1)^3 - loga(2x-1)^2 = loga [ (2x+1)^3 / (2x-1)^2 ] not really simplifying, just changing it around a bit
  91. Mathe

    Did you make a sketch ? Draw a perpendicular from the centre to the chord and you have a right-angled triangle. h^2+ 6^2 = 8^2 h^2 = 64-36 = 28 h = ?28 cm
  92. Math again ;-;

    First you have to expand using the distributive property 5x + 2(x + 6) , remember multiplication comes before addition according to BEDMAS = 5x + 2x + 12 = 7x + 12
  93. Algebra 1

    Since the two y values must be the same .... 2/5 x- 17 7/10 = -5/2 x + 20 2x/5 - 177/10 = -5x/2 + 20 I suggest we multiply each term by 10 4x - 177 = -25x + 200 take over , (the x value is a whole number, but the y isn't)
  94. math

    Well, if n is a whole number, then 2n will always be even. When you add 1 to any even, the result will be odd. So 2n+1 is always odd by writing it as 2n^3+n^2+6n+3 = (2n+1)(n^2 + 3) I have shown that one of the factors, namely (2n+1), will always be an odd number, thus 2n^3+n^...
  95. math

    let's factor it ... 2n^3+n^2+6n+3 = n^2(2n+1) + 3(2n+1) = (2n+1)(n^2 + 3) what kind of a number is 2n+1 ??
  96. Geometry

    let the other endpoint be (a,b) recall how to find the midpoint: for the x-coordinate, add up the x's of the endpoints , then divide by 2 for the y-coordinate, add up the y's of the endpoints , then divide by 2 so for the x of the endpoint: (a+7)/2 = 2 a+7 = 4 a = -3 ...
  97. PLEASE HELP, MATH

    Alternate way: find inverse of f(x) to see if you get g(x) let y = f(x) = (7x-2)/4 the inverse is : x = (7y-2)/4 4x = 7y - 2 4x + 2 = 7y y = (4x+2)/7 which is the given g(x) so yes, they are inverses of each other.
  98. math - factoring

    the pattern for the difference of squares is a^2 - b^2 = (a+b)(a-b) so for your 25x^2 - 9 or (5x)^2 - (3)^2 , what do you see for a and what for b ? what would you get as the factors ??
  99. Math (Check Answers Please)

    You might want to "disguise" the equation a bit, so that it is not so obvious such as yours. e.g. 6x + 21 = 3(2x + 5) + 6 In your explanation, you might also want to show the results for the 3 types of condition. 1. If after solving the equation the variable ...
  100. Does anyone know how to do calculous easy?

    Assuming you know and are reasonably good at basic arithmetic, algebra and related topics .... Pay attention in class. Understand the basic concepts. Do lots of questions. Calculus will be easy.
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