Posts by Reiny

Total # Posts: 40,239

  1. 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
  2. Math

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

    correct
  4. 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
  5. 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
  6. 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.
  7. math

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

    You just told me that Maya was m years old. Why are you asking how old Maya is ?
  9. 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
  10. Math

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

    correct
  12. 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...
  13. 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 ...
  14. 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
  15. 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
  16. math

    distance straight across = 120 m distance half-way around the circumference = 60? = .. compare them.
  17. 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
  18. 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
  19. MATH HELP ASAP

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

    (218/245)*360° will be the angle of the larger part.
  21. 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
  22. Algebra

    contributions in 2002 ---- contributions in 2003 ---- 1.15x contributions in 2004 ---- (1.1)(1.15x) (1.1)(1.15x) = 8855 solve for x
  23. 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 ...
  24. 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
  25. extended mathematics

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

    Arora, nicely done, impressive!
  27. 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 ...
  28. 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
  29. 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
  30. algebra

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

    I am sure DrBob meant: 600 = r*4 + 2r*3
  32. 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
  33. 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
  34. 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...
  35. 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 ?
  36. 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 ...
  37. 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
  38. pre algebra

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

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

    The volume of a pyramid = (1/3)(area of base)(height) test them, I see two of them
  41. 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.
  42. Math

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

    number of wrong --- x number of rights ---- 5x 25(5x) - 50x = 450 solve for x
  44. Math

    larger ---- x smaller --- x-8 x + x-8 = 90 continue ...
  45. Math calculus 2

    assuming profit = revenue - cost P(x) = 15*e^(0.08*t) - 12*e^(?0.04*t) P'(x) = 1.2e^(.08t) + .48e^(-.04t) = 0 for a max of P(x) 1.2 e^ .08t + .48e^-.04t = 0 divide by .48 2.5e^.08t + e^-.04t = 0 e^-.48t( e^.56t + 1) = 0 I get no real solution for this, neither does Wolfram...
  46. Math

    It isn't!
  47. Maths urgent

    Your question has been answered when you first posted this, did you not check?
  48. Math

    Volume = lwh , we know the volume, the length and the width 1440 = (15)(12)h h = 1440/180 = 8 cm.
  49. Maths

    That depends on the leap years. e.g number of Tuesdays in our leap-year cycle: 2016 -- 52 2017 -- 52 2018 -- 52 2019 -- 53 So in any leap-year cycle there are 3(52) + 53 or 209 Tuesdays and in that leap-year cycle there are 3(365) + 366 or 1460 days (ignoring the fact that ...
  50. Maths

    As well: x = 1/2
  51. Algebra

    let the number of laps needed by Jack be n then the number of laps Jill ran is n-1 Jack's distance = 800n Jill's distance = 800(n-1)= 800n - 800 Jill's speed ---- x m/s jack's speed --- x+2 m/s time for the passing = 6 min, 40 s = 400s Jill: 400x = 800n - 800 ...
  52. Maths

    I suspect a perfect square, since I noticed that the first and last terms are perfect squares, so my suspicion points to (5k ..... 2/k)^2 the middle term is negative, so I guess at (5k - 2/k)^2 check: (5k - 2/k)(5k - 2/k) = 25k^2 -10k/k - 10k/k + 4/k^2 = 25k^2 - 20 + 4/k^2 , I...
  53. Math

    let the acceleration be a m/s^2 let the velocity be v m/s let the distance be s m v = at + c when t = 7, v = 15 15 = 7a + c -----> c = 15-7a ** when t = 0, .... v = c s = (1/2)at^2 + t(15-7a) + k when t = 0, s = 0 + 0 + k = k when t = 7, s = (49/2)a + 105 - 48a + k (49/2)a...
  54. Trigonometry

    Typo? XZ=6 and ZX=7 ?? , I will assume you meant YZ=7 Use the area of the triangle formula in terms of the sine of the contained angle. Area = A = (1/2)(7)(8)sinY ---> sinY = A/28 Also A = (1/2)(6)(7)sinZ ----> sinZ = A/21 and A = (1/2)(6)(8)sinX -----> sinX = A/24 (...
  55. math

    Looks like you are studying "partial fractions" (2(4x+3))/((x-3)(x+7)) ? a/(x-3) + b/(x+7) (8x + 6)/((x-3)(x+7)) ? (a(x+7) + b(x-3) )/(((x-3)(x+7)) multiply by (x-3)(x+7) 8x + 6 ? a(x+7) + b(x-3) this must be true for all values of x let x = 3, ---> 24+6 = 10a + ...
  56. Algebra2

    for time to maximum height and that maximum height you need the vertex of this parabola. Use the method you learned finding that vertex as to hitting the ground, set -16.1t^2+73.5t+5.5 = 0 and solve the quadratic. reject any negative value of t.
  57. Algebra2

    amount invested at 6% .... x amount invested at 7.5% ----- 15000 - x .06x + .075(15000-x) = 1023 solve for x, etc notice this equation follows the same thinking as the equation I gave you in your previous post with the mixtures.
  58. physics vectors

    a+b+c = (42cos27,42sin27) + (42cos194, 42sin194) + (42cos312,42sin312) = (24.7733, -22.3052) magnitude = ?(24.7733^2 + 22.3052^2) = appr 33.335 direction angle Ø, such that tanØ = -22.3052/24.7733 I get Ø = appr -41.998° or 318.00° compare with ...
  59. Algebra2

    amount of the 25% used --- x L amount of the 50% used --- 30-x L .25x + .5(30-x) = .4(30) 25x + 50(30-x) = 40(30) ----> (don't like decimals) solve for x
  60. AP Calculus AB

    f(x) = x^5 - 10 inverse is x = y^5 - 10 y^5 = x+10 y = (x+10)^(1/5) h(x) = (x+10)^(1/5) h'(x) = (1/5)(x+10^(-4/5) h'(22) = (1/5)(32)^(-4/5) = (1/5)(2)^-4 = (1/5)(1/16) = 1/80
  61. MATH

    recall sin (2A) = 2sinAcosA so 4sin2? = 4(2sin? cos?) = .....
  62. algebra 1

    Since you are taking off 15% each year, at the end of each your you will have 85% or .85 of the previous years amount. so after 5 years: 20000(.85)^5 = ... plug in your answers where needed.
  63. Precalculus

    what is 175000(.7)^5 ??
  64. Examples on United States and Canada

    A quick comparison on gaining independence: I assume you are American, so you should be familiar with your war of independence or The American Revolutionary War from 1775-1783. In Canada 1759, the French and the British fought over that area. As a matter of fact, most of the ...
  65. Examples on United States and Canada

    I think if you had an actual question, it would help. You started by simply making a statement: United States and Canada achieved independence. ---- yes, they did, what about it? You then went on about "stew" vs "melting pot". What does that have to do with...
  66. Precalculus

    create a table (amortization table) time-interest-payment-balance now ---- 0 ------0 ------ 5000.00 1 ---- 50.00 ---300.00 - 4475.00 2 ---- 44.75 ---294.75 - 4225.00 3 ---- 42.25 ---292.25 - 3975.00 4 ---- 39.75 ---289.75 - 3725.00 5 ---- 37.25 ---287.25 - 3475.00 etc Since ...
  67. pre-alg

    I would assume that the order in the size of the dimensions would stay the same so 30 ft x 45 ft ----> 2 in x 3 in, which is a) aren't b) and d) the same ?
  68. math

    Enrico: i = .0395/52 = .000759615 , (I stored all the decimals) n = 52(3.5) = 182 E(1.000759615)^182 = 4000 E = 4000/(1.000759615)^182 = $ 3483.71 Repeat the same steps for Paul.
  69. Alegbra 1

    Jack's pay = 50 + .1(30) = $53 Clay gets .9(30) = $27 Clay just lost $26. At a profit of $30 per day, poor Clay is about to close shop.
  70. Math

    done, see your previous post
  71. Math

    They are using compound interest. amount = 1000(1.05)^6 = 1340.0956.. = $ 1340.10
  72. math

    20(.5)^(t/2.696) < 1, where t is number of days (.5)^(t/2.696) < .05 take logs of both sides and use log rules (t/2.696) log .5 = log .05 t/2.696 < log.05/log.5 = 4.3219.. t < 11.65 days So it takes just less than 12 days
  73. math

    that would be cheating you need the LCD 55 = 5*11 50 = 2*5*5 so the LCD = 2*5*5*11 = ... carry on
  74. math

    cross-multiply x^2 = 36 etc
  75. or - Algebra2

    You know that perpendicular lines have slopes that are negative reciprocals of each other. Thus the new perpendicular line is 4x+2y= c plug in your pont (9,-2) 36 - 4 = c = 32 4x + 2y = 32 2x + y = 16
  76. Algebra2

    Just did this /display.cgi?id=1517780373 give youself a name so we can identify you
  77. Algebra2

    g(x) = 17 or y =17 is a horizontal line 17 units above the x-axis G(x) is a line with slope of 5 and y-intercept of -1 they intersect when y = 17 and 5x-1=17 5x=18 x=18/5 obviously the answer is not 84
  78. Algebra2

    So clearly you have a horizontal line, slope =0 In the format you want: y - 3.3 = 0(x+4) y = 3.3 is the simplified form
  79. Math (Calculus)

    recall that sin(x) = x - x^3/3! + x^5/5! - x^7/7! for the first 4 terms so replacing x with x^2 sin(x^2 = x^2 - x^6/6 + x^10/120 + x^14/5040 ?sin(x^2) = ?(x^2 - x^6/6 + x^10/120 + x^14/5040) dx from 0 to 1 = [(1/3)x^3 - (1/42)x^7 + (1/1320)x^11 - (1/75600)x^15] from 0 to 1 = (...
  80. maths

    Make use of your "co" factor property. that is: sin 28 = cos 62, and tan38 = cot52 note that 28+62 = 90, 38+52=90 sec 30 you must know as part of your trig repertoire
  81. maths

    20 % of 5+ 8 [(7+5-3/12)-6] = .2( 5+ 8 [(7+5-3/12)-6] ) = .2(5 + 8[6 - 1/4] = .2(5 + 8[23/4] = .2(5 + 46) = .2(51) = 10.2
  82. Math

    If (a,b) and (c,d) are any two points, then the midpoint is ((a+c)/2 , (b+d)/2) )
  83. Algebra

    multiply both sides by 3 (X/3)(3) = -2(3) what happens to the 3's on the left side ??
  84. Probability of Compound Events

    prob(yellow, then green) = (18/42)(10/41) = ....
  85. Math

    smaller ---- x larger ------ x+2 (1/2)(x+2) - (1/4)x = 5 solve for x
  86. Math

    cost of helmet ---- x solve for x .07x = 3.5
  87. Calculus

    Trying the old fashioned "a bit higher and a bit lower" trick let x= 1.80 , y = 4cos(1.80/2) = 2.486 area = 4.476 < 4.49 let x=1.6, y = 2.787 area = 4.459 < 4.49 my above answer is reasonable
  88. Calculus

    Let the vertices be(x,0), (x,y), (0,y) and (0,0) then the area is xy A = x(4cos(x/2)) dA/dx = x(-4sin(x/2)(1/2) + 4cos(x/2) = 0 for a max of A x(2sin(x/2) = 4cos(x/2) sin(x/2)/cos(x/2) = 2/x tan(x/2) = 2/x no nice way to solve this, Wolfram says https://www.wolframalpha.com/...
  89. math

    What you want to do is represent 275 as powers of 7 So 7^3 = 343 ,we don't have to go that high 7^2 = 49 275/49 = 5 with remainder of 30 30/7 = 4 with remainder of 2 then 275 = 5(7^2) + 4(7) + 2 = 5427 if 21201 is a base 3 number = 2(3^4) + 1(3^3) + 2(3^2) + 0(3^1) + 1(3^0...
  90. calculus

    I will do one of them, you do the rest (iii) [1, 1.1] when x=1, y = 52-1.86 = 50.14 when x = 1.1, y = 52(1.1)-1.86(1.1)^2 = 54.72434 avg speed= (54.72434-50.14)/(1.1-1) = 45.8434 m/s
  91. Math

    I suspect a typo either 3^(2x)+3^x-1=-6 or 5^(2x) + 5^x-1=-6 As Steve pointed out, any power of 3^?? or 5^?? is always positive, so it can never be negative.
  92. @incognito --- Math

    blurting out an answer serves no purpose, especially when it is incorrect
  93. Calculus help

    You do realize that f(x) = e^(-lnx) , can be changed to f(x) = x^-1 = 1/x so area = ?(1/x) dx from 1 to 2 = [lnx] from 1 to 2 = ln2 - ln1 = ln2 or appr .6931... proof: http://www.wolframalpha.com/input/?i=%E2%88%AB(e%5E(-lnx))+dx+from+1+to+2
  94. Calculus 2

    You posted this yesterday when you were Natalie Here was my reply: /display.cgi?id=1517283368 I had asked you to check my arithmetic, which you clearly did not do, since when I checked it just now it turned out to be 76 2/3 square units, not 60 (my ...
  95. Cal 2

    Your intersection points are correct. The problem is that the second boundary value of x = 3.5 is beyond the intersection point of (2.5,0), and you have a part of the region that lies above the x-axis. So you have to find the area in two parts: from x = -1 to x=2.5, and then ...
  96. Calculus 2

    Notice the period is 2?/4 or ?/2 , (90°) so your region is 1/2 a sine curve from 0 to ?/4, plus a bit of the sine below the x-axis, so take it in two parts, from x = 0 to ?/4 then the small bit below don't forget to take ?sin4x dx from 0 to ?/4 + ?-sin4x from ?/4 to 3?/8
  97. Calculus II

    your sketch should look like this: a small "triangular shape" I would take horizontal slices, that is with respect to y you first need the intersection of 2y=5x^(1/2) and 2y+4x=9 5?x = 9-4x 25x = 81 - 72x + 16x^2 16x^2 - 97x + 81 = 0 (16x - 81)(x - 1) = 0 , wow it ...
  98. Math

    first part: replace s(t) with 100 100 = -2.7t^2 + 30t + 6.5 2.7t^2 - 30t + 93.5 = 0 This quadratic has no real solution, the discriminant b^2 - 4ac or (30^2 - 4(2.7)(93.5) is negative. So it can never reach 100 Does it reach 12 ?? Repeat the above by replacing s(t) with 12 I ...
  99. MAth

    5a/3?x = 5a/3?x * ?x/?x = 5a?x/(3x)
  100. Math

    4m/(?m - 5) = 4m/(?m - 5)*(?m + 5)/(?m + 5) = 4m((?m + 5)/(m-25) or (4m?m + 20m)/(m-25)
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