Posts by Reiny

Total # Posts: 40,197

  1. Algebra

    number correct --- x number wrong ---- 30-x 9x - 5(30-x) = 18 solve for x
  2. Calculus

    look at the graph http://www.wolframalpha.com/input/?i=y+%3D+x%5E2+-+1+and+y+%3D+cos(x) and notice the symmetry. So we need the intersection cosx = x^2 - 1 which you found correctly as ± 1.177 correct to 3 decimals area = 2[integral] (cosx - (x^2 -1)) dx from 0 to 1.177...
  3. Math

    original: boys: 80 girls : 95 now: boys = 1.15(80) = ... girls = .8(95) = ... add them up to get the new total. take the difference, percent change = difference/175 , interpret the positive vs negative answer.
  4. Math

    solve for x , the price of the car .15x = 247.50
  5. Math

    or, you could do it using decimals .... 2 1/5 subtract 1 1/5 = 2.2 - 1.2 = 1
  6. Algebra 1

    let the part invested at 10% be x let the part invested at 14% be 10000-x solve for x .1x + .14(10000-x) = 1280 let me know what you get, so I can check it
  7. Math

    Are you solving 3tanA.tanA-4?3TanA+3=0 ? What does the . in 3tanA.tanA mean? Is it multiplication? I have no clue what TanA=n,3n.n-4?3n+3=0 in the second part of your post means.
  8. Algebra

    You need 2 numbers which have a sum or difference of 3, c will be their product e.g. 1,2 , product = 2 , c = 2 ----- (x+1)(x+2) = x^2 + 3x + 2 5, -2, product = -10 , c = -10 ----- (x+5)(x-2) = x^2 + 3x - 10 7, -4 , product = -28 , c = -28 ----- (x+7)(x-4) = x^2 + 3x - 28 -1, 4...
  9. maths

    number at the beginning ----- x Paul took (1/3)x - 4 number left after Paul's turn = x - (x/3 - 4) = 2x/3 + 4 after Sarah ate 6, number left = 2x/3 + 4 - 6 = 2x/3 - 2 took 1/4 of that, so remaining = (3/4)(2x/3 - 2) = x/2 - 3/2 Kate took 1/3 of that plus 4 = (1/3)(x/2 - 3/...
  10. Trigonometry

    you can't show graphs in this format
  11. Math

    Just did that
  12. MATH

    max - min = 1 - (-7) = 8 so a = 4 , could be any of the first 3 from 3? to ? = 2? , so the period is 4? 2?/k = 4? 4?k = 2? k = 1/2 so we should see either sin(x/2) or cos(x/2) so it has to be either a) or b) test a) if x = ? , y = 4cos(?/2) - 3 = 4(0) - 3 = -3 ? 1 , that is ...
  13. Trigonometry

    If R is the resultant vector, then R = (24cos42,24sin42) + (9cos312,9sin312) = (17.8355, 16.059) + (6.02218, -6.6883) = (23.85766, 9.3707) magnitude = ?(23.85766^2 + (9.3707)^2) = appr 25.63 km/h direction: Ø = tan^-1(9.3707/23.85766) = appr 21.44° or make a sketch ...
  14. math

    number of school days ----- x walking to school = (3/5)x = 3x/5 getting ride = (7/8)(2x/5) = 7x/20 walking plus riding = 3x/5 + 7x/20 = 19x/20 staying home --- 1 day 3x/5 + 7x/20 + 1 = x 19x/20 + 1 = x times 20 19x + 20 = 20x x = 20
  15. Math

    Recall what I just said in the previous post? This time I will reverse that idea to avoid fractions, start with the largest. Also I noticed that the LCD for 1/3 and 3/4 is 12, so .... let Mary's amount be 12x then Sally has (1/3)(12x) or 4x and Jane has (3/4)(4x) or 3x 12x...
  16. MATH!!!!

    Start with the smallest amount, usually that avoids fractions ... Let Ryan's amount be x then David has 3x , and Henry has 4(3x) or 12x now it is easy: x + 3x + 12x = 128 etc
  17. precalc

    here is one version https://socratic.org/questions/how-do-you-solve-the-identity-cos3x-4cos-3x-3cosx
  18. algebra 2

    f(x)= (x^2-2x-8)/(x+6) to have a point discontinuity, (x+6) should have been a factor of the numerator and cancelled out. e.g. if g(x) = (x^2 - x - 12)/(x-4) g(x) = (x-4)(x+3)/(x-4) = x+3, x ? 4 There would have been a discontinuity at the point (4,7) So in your question , we ...
  19. Math

    y = rsinØ, x = rcosØ y^2 - 8x - 16 = 0 r^2 sin^2 Ø - 8rcosØ - 16 = 0
  20. Math

    Make a sketch of the right-angled triangle with angle 45° and hypotenuse of 4 sin45 = y/4, cos45 = x/4 y = 4(?2/2) , x = 4?2/2 new point = B(2?2 , -2?2)
  21. geometry

    areas ... the areas of similar figures are proportional to the square of their corresponding sides. so 4^2 : 3^2 or 16 : 9
  22. Math

    let the third side be x , where x > 0 then x+15 > 27 ---> x > 12 and x+27> 15 ---> x > -12 so far we have x > 12 and 12+27 > x x < 39 so : 12 < x < 39
  23. Advanced Algebra

    Even though you don't say, I will assume the time was 1 year. so look at this way: you started with 8750 and at the end of the year you had 10,000+ 1,000 or 11,000 8750(1+r) = 11000 1+r = 1.25714.. r = .25714 or 25.71%
  24. GEOMETRY helpppp

    arc length = ? r Ø where r is the radius, and Ø is the central angle measured in radians You have all the data.
  25. Advanced Algebra

    I agree
  26. math

    x+y = 30 or y = 30-x let S = 2x^2 + 5y^2 = 2x^2 + 5(30-x)^2 = 2x^2 + 4500 - 300x + 5x^2 = 7x^2 - 300x + 4500 dS/dx = 14x - 300 = 0 for a max/min x = 300/14 , sub into y = 30-x
  27. Maths

    sin²_cos²/2sin2cosx1/tan² re-enter in proper form e.g. sin = 12/13 is meaningless, "sin" is an operator and needs an operand did you mean : sinØ = 12/13 or sinx = 12/13 ?? that is like saying ? = 3 , or log = 1.3
  28. Geometry

    change your 604 ft to inches, then set up the ratio
  29. Precalculus

    Only B is correct in your choices. What are your resources for this major topic if you don't have a textbook ?
  30. Precalculus

    The correct relations are listed in your textbook or in your notes. They are easy to look up Let me know which ones you think do apply.
  31. Geometry

    In a ratio, you need the same units. Change your 5 ft to inches, and set up the ratio.
  32. Math

    total number of outfits = 12 total number of outfits with blue skirt = 3x1x2 = 6 prob of outfit with blue skirt = 6/12 = 12 prob of outfit without blue skirt = 1 - 1/2 = 1/2
  33. maths

    speed of rocket = (2.99x10^8 m/s)/5 = 5.98 x 10^7 Wow, somebody has been watching Startrek.
  34. Probability

    prob(yellow, then red) = (2/5)(3/4) = 3/10 prob(red, then yellow) = 3/5(2/4) = 3/10 so prob(your event) = 6/10 = 3/5
  35. Geometry

    vector PQ = (2-(-6), 4-0) = (8,4) magnitude = ?(64+16) = ?80 = appr 8.9 , ruling out c. angle = tan^-1 (4/8) = 26.57° from the x-axis what angle description describes that ?
  36. math

    correct
  37. Maths

    Since they right-bisect each other, you will have 4 congruent right-angled triangles, with legs of 5 and 12. Perhaps you recognize the 5-12-13 right-angled triangle, if not use Pythagoras to find the hypotenuse to be 13 So the perimeter is ......
  38. algebra 2

    did you mean? 4 ^(3?(3x-3)^2)+2=38 or 4^3(?(3x-3)^2 + 2 = 38 ??
  39. Trigonometry

    drift angle is clearly 12° Make a sketch to have a triangle with sides 500 and 580 with 12° as the contained angle. Using cosine law, let the third side be R (the wind speed) R^2 = 500^2 + 580^2 - 2(500(580)cos12° R = .... then use the Sine Law to find one of the ...
  40. @ Scott - Math

    Thanks, why didn't I see that ?
  41. Math

    I hope you weren't trying to expand all of this. let's look at the last part first, by looking at a some patterns (1+x)^2 = 1 + 2x + x^2 , 3 terms, coefficients run 1,2,1 (1+x+x^2) = 1 + 2x + 3x^2 + 2x^3 + x^4, 5 terms, coefficients run 1,2,3,2,1 (1+x+x^2+x^3)^2 = 1 + ...
  42. Math

    Now: daughter ---- x mother ------ 2x 2 years ago: daughter = x-2 mother = 2x-2 x-2 + 2x-2 = 56 solve for x
  43. math urgent

    I saw this question when you posted it yesterday. I did not answer it since it wasn't quite clearly stated. Is the 30 million split into 25 equal annual payments?? I will assume that. In that case we are simply finding the present value of those payments payment = 30 ...
  44. Advanced Algebra

    I answered your last post for this kind of problem. How about giving me your thoughts on how to start with this question ? It is a straightforward problem.
  45. Advanced Algebra

    Method1 Since the basic formulas for annuity assume payments at the end of a period, a slight adjustment is needed. PV = 9400 +9400(1 - 1.034^-9)/.034 = 81243.05 method 2. look at the geometric series 9400 + 9400(1.034^-1) + 9400(1.034^-2) + ... + 9400(1.034^-9) here a = 9400...
  46. Math

    25a^2+ ? + .25 b^2 You know it must look something like: (5a ± .5b)^2 , expand to see the middle term take your pick
  47. Math

    35 minutes is 35/60 of a ration, so the central angle of the sector covered = (35/60)(2?) radians = 7?/6 radians arc length = radius * angle , where the angle is in radians or circumference = 2?r = 2?(6) = 12? so the hand covered 35/60 of that, so .....
  48. Math

    polynomials have factors, not factories .... we could write the factors of p(x) as 2*2*3*(x-5)*(x+4) any combination of these will also be a factor. How about 2*3*(x-5)(x+4) expand it and see what you get 2) correct 3) x^2 - x = .24 x^2 - x -.24 = 0 solve for x using the ...
  49. Math

    the sides would be ?3x and 2x , then (?3x)^2 + (2x)^2 = 10^2 3x^2 + 4x^2 = 100 solve for x and you have the two sides. area = (1/2)(side1)(side2) = ....
  50. Math

    16 men and 12 women A - you want 4 from 28 , so C(28,4) B - 3 men, must be 1 woman, so C(16,3)*C(12,1) C - at least 2 men ---> 2men-2women , 3men1woman, 4men , add up the 3 cases D - your turn
  51. Math

    nope, not what I got show me your steps to catch the error
  52. Math

    steph;s wage = x/10 eve;a wage = y/29 but you said: x/10=y/29 10y=29x y = 29x/10 sub that into x+y=60 and solve 2. area of large circle = ?(r+3)^2 area of small circle = ?r^2 ?(r+3)^2 - ?r^2 = 21? divide by ?(the r^2 drops out) 3. make a sketch and really think about it Hint: ...
  53. Pre-Calc

    you have one complex root, but they always come as conjugate pairs The other must be 2-2?2i You also know that one factor is (x+2) the sum of the complex roots = 2+2?2i + 2-2?2i = 4 product of the complex roots = (2+2?2i)(2-2?2i) = 4 + 8 = 12 So the quadratic factor is x^2 - ...
  54. Math

    original fraction -- n/d new fraction formed = (n+d)/2d you want: (n+d)/2d = 4(n/d) 8nd = nd + d^2 7nd = d^2 7n = d it looks like we can find an infinite number of cases like that. e.g. let n = 1, then d = 7 then the original fraction was 1/7 and the fraction formed by your ...
  55. algebra

    If arithmetic, you know that d=6 and a=6 a+(n-1)d = term(n) 6+(n-1)(6) = 1536 6 + 6n - 6 = 1536 6n = 1536 n = 256 If GP,then a=6, r=2 In the same way, use the definition of term(n) to solve the second part
  56. Mathematics

    Let the radius of the base be r and the height be h (1/3)? r2 h = 5 ?r^2 h = 15 The new cone will be similar to the original cone, the new height i h/3 and the new radius is r/3 volume of top cone = (1/3)?(r^2/9)(h/3) = (1/9)?r^2 h = 15/9 = 5/3 the bottom fulcrum will be 15 - ...
  57. math

    yes, you want: |k-21| = 48 so, k-21 = 48 OR -k+21 = 48 k = 69 or k = -27 think of a number line and place a dot at 21 now count 48 places to the right ---> 69 and count 48 places to the left -----> -27
  58. Math

    Not silver ----> gold coin you have 123 golds out of a total of 323 prob(not silver) = 123/323
  59. MATH

    I don't have the foggiest idea. my calculator says: (2360448/(2?))² = 1.4113318 x 10^11 , (notice the change in the division by 2?) don't know how the R³/3.98x10^14 fits in
  60. Math

    20 < T < 80 , where T is temperature in Fahrenheit Since C = (5/9)(F - 32) , I will let you do the conversion
  61. Math

    correct
  62. math

    number passed ---- x number failed ------ 36-x sum of scores of passers = 78x sum of scores of failures = 60(36-x) 78x + 60(36-x) = 71(36) solve for x
  63. math

    48/x - x = 2 multiply each term by x to get the quadratic 48 - x^2 = 2x x^2 + 2x - 48 = 0 (x - 6)(x + 8) = 0 x = 6 or x = -8 btw, What she was told to do should have been: (48-x)/x if x = 6, (48-x)/x = (48-6)/6 = 7 if x = -8, (48-x)/x = (48 + 8)/-8 = -7
  64. math

    What she was told to do: (x-48)/x what she did: 48/x - x = 2 solve for x, then plug into "what she was told to do" btw, there are two values of x.
  65. math

    My money is definitely on Damon ! Annabelle just tossed some number salad.
  66. Math

    You just told me that Maya was m years old. Why are you asking how old Maya is ?
  67. Math

    3(3/7)^-2 + 2/3 = 3(7/3)^2 + 2/3 = 3(49/9) + 2/3 = 49/3 + 2/3 = 51/3 = 17
  68. Math

    By definition: 2? radians <-----> 360°
  69. Trig

    correct
  70. Math

    The easy part is to find the areas of the 3 rectangles, they are: 2x7, 3x7, and 4x7. The hard part is to find the area of the triangular base. Since it is not right-angled, 2^2 + 3^2 ? 4^2, we need more complex methods. method one: Heron's formula area = ?(s(s-a)(s-b)(s-c...
  71. Calculus

    a = -32 ft/sec^2 v = -32t + c when t = 0 , v = 64 64 = 0 + c , so c = 64, and v = -32t + 64 d = -16t^2 + 64t + k, but when t=0 , d = 0 0 = 0 + 0 + k k = 0 d = -16t^2 + 64t The vertex of this parabola will tell you the maximum height, and the t when that max occurs. I assume ...
  72. Math

    1/12(cos8t-3sin8t) = 0 cos8t-3sin8t = 0 3sin8t = cos8t sin8t/cos8t = 1/3 tan 8t = 1/3 8t = .32175 or 8t = ?+.32175 t = .0402 or t = .4329
  73. Alegbra 1

    Easiest way: An equation perpendicular to 2x - 5y = 3 must have the form 5x + 2y = c plug in our given point on this line: 5(-2) + 2(7) = c = 4 5x + 2y = 4
  74. math

    distance straight across = 120 m distance half-way around the circumference = 60? = .. compare them.
  75. Math

    average is 84, so the total is 20(84) or 1680 points points of 6 students at 100 = 600 points of 4 students at 50 = 200 remaining points = 1680 - 600 - 200 = 880 average of those 10 students = 880/10 = 88
  76. math

    5 machines 5 minutes to make 5 widgets 100 machines 5 minutes to make 100 widgets - you have 20 times as many machines, so 20 times as many products in the same time of 5 minutes
  77. MATH HELP ASAP

    change all numbers to decimals and it will be easy to tell
  78. Pre- Algebra

    (218/245)*360° will be the angle of the larger part.
  79. Algebra

    larger angle --- x smaller angle --- x/4 x + x/4 = 180 solve for x, and sub in my definitions. or smaller angle ---- y larger angle ---- 4y y+4y = 180 solve for y, y will be the smaller angle, since I defined it as such
  80. Algebra

    contributions in 2002 ---- contributions in 2003 ---- 1.15x contributions in 2004 ---- (1.1)(1.15x) (1.1)(1.15x) = 8855 solve for x
  81. Maths

    take the derivative of the ellipse equation using implicit differentiation. The slope of 3x+2y - 5 = 0 is -3/2 so the slope of the perpendicular will be +2/3 set your derivative of the ellipse equal to 2/3 . You will get a linear equation in x and y Solve that with the ...
  82. Math (Word Problems)

    Just set up a simple ratio x/9 = (3/4) / 6 6x = 9(3/4) 6x = 27/4 x = 27/24 = 9/8 or 1 1/8 cups of sugar
  83. extended mathematics

    You can't post diagrams in this forum
  84. Math

    Arora, nicely done, impressive!
  85. Maths

    In these kind of questions, when they state that 30% workers are BTeach holders, we don't assume that it is 30% exclusively. e.g. When I say, that 8% of boys play football, that doesn't mean that they can't play some other sport as well. In a Venn diagram for this ...
  86. Maths

    I disagree .. number(BT or MBA) = 30%+25% - 20% = 35% (we can't count the 20% twice ) so 65% are without degrees .65x= 325 x = 500
  87. geometry

    by basic geometry: CP:PD = 30:48 = 5:8 let CP=5x, and PD = 8x let the height between AB and CD = h so area of BCP + area of ADP = 5xh +8xh = 13xh = 78 area of ABC = 13xh = 78 area of whole thing = 78+30+48 = 156
  88. algebra

    Scientific notation consists of a number between 1 and 10, multiplied by a power of 10. I see only one that fits this.
  89. Maths

    I am sure DrBob meant: 600 = r*4 + 2r*3
  90. Maths

    Guessing that the question is to find the sides. x^2 + (3x-1)^2 = (3x+1)^2 x^2 + 9x^2 - 6x + 1 = 9x^2 + 6x + 1 x^2 - 12x = 0 Use your favourite method to solve this quadratic, remember that x > 0
  91. Maths

    from 4x – 3 = 3x + y y = x - 3 ** plug ** into 3x + y = 2y + 5x – 12 3x + x-3 = 2(x-3) + 5x - 12 4x - 3 = 2x - 6 + 5x - 12 4x-3 = 7x - 18 -3x = -15 x = 5 then y = 5-3 = 2
  92. Math

    I really don't understand what part of my analysis you don't get. Volume is (base area) x (width) So if you consider the sideview as the base, you have rectangle = 44(3) = 132 ft^2 triangle = (1/2)(44)(6) = 132 ft^2 total area of sideview = 264 ft^2 volume = that total...
  93. Math

    The top view is a rectangle It is the side view that illustrates the shape of the pool, it will be the trapezoid. Do you know what a trapezoid looks like ?
  94. Math

    Draw a side-view of the pool to see the trapezoid, the two vertical ends are your parallel sides. draw a horizontal from the short vertical to meet the longer vertical. You now have a rectangle and a right-angled triangle. The rectangle is 44 by 3 and the triangle is 44 by 6 ...
  95. Pri 5 maths

    3s = 2b s = 2b/3 5b + 6s = 108 5b + 6(2b/3) = 108 5b + 4b = 108 b = 12 then s = 8 6 skirts = 48
  96. pre algebra

    amount of pretzels ---- x lbs amount of cereal ----- 12-x lbs 1.5x + 3(12-x) = 2(12) continue
  97. math

    You just asked the same question 5 minutes ago!
  98. math

    The volume of a pyramid = (1/3)(area of base)(height) test them, I see two of them
  99. math

    since it is parallel, it will differ only in the constant, so new equation is x - 4y + c = 0 plug in the given point to find c.
  100. Math

    No, it can't be W=15, since 15/36 ? 5/18 but 10/36 = 5/18
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