Posts by Steve

Total # Posts: 56,195

  1. Math

    well, 10/2 = 5 (x+5)^2 = ?
  2. math

    1/4 spent leaves 3/4 2/3 * 3/4 = 1/2 (a) 1/4 + 1/2 = 3/4 (b) duh
  3. math

    16 * 15C10
  4. math

    There are 11 players who can be chosen at will If no triplet is chosen, you have 11C6 ways to do it If 1 is chosen, you have 11C5*3C1 ways to do it If 2 are chosen, you have 11C4*3C2 ways to do it so add them up
  5. math, calculus

    well, just plug and chug sin(?t + ?) = sin?t cos? + cos?t sin? so, you have Csin ?t + C(sin?t cos? + cos?t sin?) = Csin ?t + Csin?t cos? + Ccos?t sin? =(C+cos?)sin?t + (Csin?)cos?t Now, since ksin(?t + ?)=ksin?t cos? + kcos?t sin? you want to find k and ? such that (C+cos?) = ...
  6. Data

    p(1st ace)=4/52 p(2nd ace)=3/51 ... p(all 4 aces)= (4*3*2*1)/(52*51*50*49) = 4!/(52P4) = 1/(52C4) = 1/270725 so, the odds are 1:270724
  7. math

    no, because 4 has two images. f(4) cannot be both -6 and -3.
  8. math

    8.61/123.00 = 0.07 = 7%
  9. geometry

    sorry - no tool here. I assume your software has a user guide you can probably also find examples online.
  10. math

    Don't let all the words scare you. Just write it down as math. d=2n n+d+q=63 5n+10d+25q=575 now crank it out.
  11. Calculus

    so, have you tried drawing such a curve and trying them out? How about y=x^2 where 0 <= a <= b
  12. AP Calculus

    you have the values. Just compute the area of the kth trapezoid using ak = (f(xk)+f(xk+1))/2 * (xk+1-xk) for k=1..6 For example, a1 = (4+8)/2 * (3-1) = 12
  13. Calculus

    see "Bryan's" post
  14. Calculus

    I is true sometimes -- e.g., at (2,5) II is true sometimes -- e.g., at (1,1),(-1,5),(-1,1),(1,-5) III is clearly false. In a column at x=h, the tangents will get more negative as y increases. I think the question is poorly worded.
  15. Math

    sinØ (1+ tanØ) + cosØ(1+ cotØ) sinØ(sinØ+cosØ)/cosØ + cosØ(sinØ+cosØ)/sinØ tanØ(sinØ+cosØ) + cotØ(sinØ+cosØ) (tanØ+cotØ)(sinØ+cos&...
  16. algebra

  17. Algebra 2

    C Clearly you need to review the topic.
  18. math

    1400(1+(8 5/12)*.06) = 2107 makes sense, since 8 1/3 * 6% = 50%
  19. Geometry

    even better: learn to do the exercises! Since all the sides are equal, 5x+18 = 4x+22 Now just find x and you're almost done.
  20. Geometry

    since the congruent sides have equal lengths, 5x+23 = 2x+32 Find x and let 'er rip.
  21. Calculus

    the height y is given by y = -16t^2+64t as with all y=ax^2+bx+c the vertex (max in this case) is at -b/2a = 2
  22. Calculus

    s(T) = ?[0,T] v(t) dt you want s(2) = ?[0,2] -3t^2+5 = (-t^3+5t) [0,2] = 2
  23. AP Calculus

    v(t) = ? a(t) dt = ? cost-sint dt = sint+cost+C Now plug in (0,3) to find C
  24. Math

    P(even) = 1/2 P(not 2) = 5/6 so just multiply them
  25. MATH

    hard to say, since there is no "x" involved. However, solving the 2nd equation for y, we get x=R-((R-r)/h)y ((R-r)/h)y = R-x y=(R-x)/((R-r)/h) = (R-x)h / (R-r) so maybe you can figure out what to do the other way.
  26. Math

    (F-G)(-6) = F(-6) - G(-6) Now just plug and chug.
  27. Math

    (f*g)(x) = f(x)*g(x) = (44x-22)(22x^2-11) = 22(2x-1) * 11(2x^2-1) = 242(2x-1)(2x^2-1)
  28. Math

    y = 2x^2+12x+14 y = 2(x^2+6x+9)-4 y = 2(x+3)^2-4 so, the vertex is at (-3,-4) the y-intercept is at (0,14) the x-intercepts are at (-3±?2,0)
  29. Math

    you are.
  30. English

    Hmmm. I think it is clear that the are all adverb phrases. They answer the question "where?"
  31. Calculus

    hmmm. Didn't think of solving for x? y+4x=0 means y = -4x. So, 3x^2-8x = -4x 3x^2-4x=0 x=0 or 4/3 But that is not the problem. You don't care where the two graphs intersect. You care where the slopes are equal. so, you really want 3x^2-8x = -4 3x^2-8x+4 = 0 (3x-2)(x-2...
  32. calculus2

    I assume you have sketched the region and found it to be a triangle with vertices at (1,0), (8,0),(8,7) So, consider the volume as a stack of thin discs of thickness dx. Then v = ?[1,8] ?r^2 dx where r = y = x-1 v = ?[1,8] ?(x-1)^2 dx = 343?/3 Or, consider it as a set of ...
  33. Math

  34. Math

    As for the parabola, recall the properties of the parabola y^2 = 4px Yours is shifted a bit, making it (y+7)^2 = 1(x+51)
  35. Math

    the domain is clearly not all real numbers. Suppose x=0. No way can -9y^2 = 900 The hyperbola is x^2/900 - y^2/100 = 1 The vertices of the hyperbola are at (±30,0) So, the domain is (-?,-30]U[30,?) Using what you know of the shape of hyperbolas, the range is clearly all...
  36. math

    just multiply the two numbers 215*449 = ?
  37. Calculus

    If it has vertical asymptotes at x=1,4 then that means that x^2+cx+4 = (x-1)(x-4) So, c = -5
  38. calculus

    f(0)=1 f'(x)=5e^(5x) So, f'(0)=5 Now we have a point and a slope, so the line is y-1 = 5(x-0) or y=5x+1 See the graphs at,y%3D5x%2B1
  39. Math

    Feels good, don't it?
  40. Math

    You know that f(8) = -4 So, if you want f(x/2), you need x/2 = 8, so x = 16 g(16) = 3f(8)+11 = 3(-4)+11 = -1 So the point (16,-1) is on the graph of g(x)
  41. Math

    the 4th and 6 terms differ by 2d so, 2d=10 and the rest is a cinch. . . . right?
  42. math

    4+3+3=10 4+2+2+2=10 2+2+3+3=10 So figure out the ways to make those combinations. I get 1+1+3=5 ways to do it (3C2=3)
  43. Math

    (7.5*8)/(15*26) * $348 = $53.54 Typo somewhere?
  44. calculus2

    tan ?/3 = ?3 tan ?/6 = 1/?3 One of those "standard" values. learn it, love it.
  45. Algebra

    9^2+x^2=(x+1)^2 81+x^2 = x^2+2x+1 x=40 So, the ladder is 41 ft long. That's some ladder!
  46. Maths

    There are lots of solutions to this problem. One of them is H=11 T=7 B=0 H&T=2 H&B=1 T&B=1 H&T&B=2 So, 4 play exactly two games. But there is so much unspecified, the numbers can be juggled in many ways. Draw a Venn diagram and fill in the center value of 2, and you can see ...
  47. math

    today you are 42. So, clearly the daughter is 7.
  48. Math

    No idea where A,B,C,D are, but let's just assume they are the ends of the 1/4 circle at the corner. Any distance along the straight portions will be the same for both people. Since C=2?r for a whole circle, and we are only using a 1/4 circle, then the difference in ...
  49. Maths

    but surely not "each and every" number There are many exceptions, such as ?, ?2, etc. If by "number" you just mean integers, then yes, they are all rational numbers, with a denominator of 1.
  50. Math

    since C=?d for a whole circle, you have 1/2 * 20? = 10? meters
  51. Maths

    assuming you meant 1.5 m/s^2, then it will of course take (30m/s)/(1.5 m/s^2) = 20 s Think about it. If it loses velocity by 1.5 m/s every second, wit will take 20 s to lose all 30 m/s.
  52. math

    since 4 inches is 1/3 foot, that will be 5 2/3 feet left.
  53. Math

    I looked at this link and still cant get it
  54. Math

    A biased coin lands heads with probabilty 2/3. The coin is tossed 3 times a) Given that there was at least one head in the three tosses, what is the probability that there were at least two heads? b) use your answer in a) to find the probability that there was exactly one head...
  55. Maths

    consider the girls as one person. Then there are 4 people to arrange. They can be arranged in 4! ways. Now, within the group of 4 girls, there are 4! ways to shuffle them. So, the total is 4!4! = 576
  56. math

    well, work = force * distance so, plug in your numbers
  57. math

    prove that (n choose k) = (n-1 choose k-1) (n-1 choose k) a) By using formula of (n choose k) b) by breaking subsets of size k into two mutually exclusive classes, one class comprising all those subsets which contain a given element and the other all those which dont
  58. science

    since the sines are directly proportional, with the index as the constant of variation, as the index increases, so does the angle of refraction. Take a look at Snell's Law and it should be clear.
  59. Math

    a=5 and d=4, so the graph is just the line y=5+4(x-1)=4x+1 all arithmetic sequences are just straight lines, because of the constant d (the slope of the line)
  60. Math

    clearly, a=-7 and d=3 -7+(n-1)*3=44 Now just find n.
  61. geometry

    Looks like you have the instructions. Where do you have a problem? I'm sure you can find videos online of the constructions you want.
  62. geometry

    values on the number line can be measured in either direction. So, it makes a difference which one is subtracted. The distance though, is always positive. In the xy distance formula, the differences are squared, so that always gives a positive result. If you think about it, ...
  63. Pre-Calc

    v = 1/3 ? r^2 h Now, h = 2/3 d = 4/3 r, so r = 3/4 h v = 1/3 ? (3/4 h)^2 h = 3?/16 h^3 Since v increases at a constant 10 yd^3/min, v(t) = 10t = 3?/16 h^3 h^3 = 160t/3? h(t) = 2?(20t / 3?)
  64. geometry

    (90-x)=2x-24 Looks like (a) to me
  65. geometry

    y = 6+3(180-y) now just solve for y
  66. geometry

    well, we know that AXB=4 AXB+CYD=90 So, both CYD and FZE = 86 and their sum is 172
  67. Math

  68. Math

    prove (n choose k) = (n choose n-k)
  69. Math

    #1 they will be 240m apart. 60m per 5 min They would be 180m farther apart than they were at 1:05 #2 There are 20 pencils which are not green. So unless you take 21, you cannot be sure of a green. #3 ok
  70. Math

    The first train has a lead of 150 miles The 2nd train catches up at a rate of 125-75 = 50 mi/hr so, it will take 3 hours. In that time, the 2nd train will have gone 375 miles The first train will have gone 150+3*75 = 375 miles
  71. Math

    A biased coin lands heads with probabilty 2/3. The coin is tossed 3 times a) Given that there was at least one head in the three tosses, what is the probability that there were at least two heads? b) use your answer in a) to find the probability that there was exactly one head...
  72. Maths

    1/2 + 1/4 + 1/5 = 19/20 So, 1/20 x = 25k x = 500k
  73. Maths

    Hmmm. It sounds like they are providing a set of only 6 digits to choose from. In that case, there would indeed be only 6! combinations. 10P6 appears to be the correct answer, however.
  74. Science

    no calculation needed. The new liquid is heavier than the water. Only one of the choices is heavier than water. It would have been a better question if several heavier liquids had been offered.
  75. math

    for the focus, c^2=a^2-b^2 The distance between the foci is 2c
  76. Math

    A biased coin lands heads with probabilty 2/3. The coin is tossed 3 times a) Given that there was at least one head in the three tosses, what is the probability that there were at least two heads? b) use your answer in a) to find the probability that there was exactly one head...
  77. calculus1

    If F(x) = ?[u,v] f(t) dt where u and v are functions of x, then F'(x) = f(v)*v'(t) - f(u)*u'(t) This is just the chain rule in disguise. So, for your function F'(x) = tan(cos x)*(-sin x) - tan(sin x)*(cos x)
  78. algebra

    Oh, well, in that case, we can proceed. I misspoke. The way I rotated the axes, I should have said x' = 8?10 y'^2 I'd rather have y=ax^2, so I should have said x'^2 = 8?10 y' or y' = 1/(8?10) x'^2 I'll get back to you on how that works with the ...
  79. algebra

    Recall that the parabola x^2=4py has vertex at (0,0) focus at (0,p) Clearly your parabola has been rotated through an angle ? where tan? = 6/2 The distance from (0,0) to (2,6) is ?40=2?10. So, in the rotated coordinate system (x',y') we have y' = 8?10 x'^2 Now...
  80. math

    so did I
  81. Maths

    each side is 17, so the height h = 240/17 So, if the angle subtending the height is x, then the diagonals are 17?(2±2cosx) and sinx = h/17 = 240/289
  82. Math

    P*1.06^25 = 400000 Now just solve for P
  83. science

    so, have you done any research yet?
  84. math

    Since tan(theta)=y/x, y/x = tan210° = 1/?3 y = x/?3
  85. algebra

    y=x y=x^2 x^2=x x^2-x=0 x(x-1)=0 x=0,1
  86. Math

    multiply the 2nd equation by 4^2=16 and you have 64n=(12-4m)² 64n=(12-(9-n)²)² Now just expand that out and solve the 4th-degree equation for n. Then you can get m. Sorry, it has no rational roots, so you'll have to use numeric or graphical methods.
  87. Maths

    review permutations with duplicates. 10!/(5!5!) That is, for each of the 10! permutations, the 5 beads of the same color cannot be distinguished, so you need to divide by the 5! ways they can be shuffled about. Of course, permutations in a circle are a little more involved, ...
  88. Maths

    the first digit cannot be zero. That leaves 9*9*8*7 = 4536
  89. Algebra

    time = distance/speed, so t = 5/s + 1/(2s) + 2/(2s-12) = (13s-66)/(2s^2-12s)
  90. Algebra

    You want to maximize p = 0.11x + 0.16y subject to x+y = 500000 y <= 0.40(x+y) So, graph the region and pick the vertex which maximizes the income. I get (in 10,000's) p(30,20) = 6.50
  91. math

    there are several handy calculators for this. You can see the details at
  92. Programming

    which language? That is the first place to start. Each has its own syntactical peculiarities. There are many code snippets online to look at. I assume you know how to format a for loop. So, write that out first. Then, place a switch statement inside the loop. Google is your ...
  93. Math Probability

    there are 4 choices for each knob. Since each knob is independent of the others, that gives 4*4*4=64 choices. 24 would be correct if no duplicate digits were allowed.
  94. Math

  95. Math

  96. Algebra

    Label the various points P,K,F,L using similar triangles, PL/4 = 10/PL PL=2?10 10/PF=PF/14 PF=2?35
  97. Maths

  98. Math

    The discriminant must be zero, so (c-a)^2-4(b-c)(a-b)=0 c^2+a^2?2ac?4(ab?b^2?ac+bc)=0 c^2+a^2?2ac?4ab+4b^2+4ac?4bc=0 c^2+a^2+2ac+4b^2?4ab?4bc=0 (c+a)^2?4b(a+c)+4b^2=0 (c+a)^2?2?(c+a)?(2b)+(2b)^2=0 [(c+a)?(2b)]^2=0 c+a?2b=0 2b = a+c
  99. math probability

    Laura and Adrian attend a dinner party. The 12 guests are seated at random around a round table, with all seating arrangements equally likely. (a) What is the probability that Laura and Adrian sit next to each other. (b) Explain your answer by giving a clear description of an ...
  100. Math

    since KL and KM are the same distance, triangle KLM is isosceles. Angle K is 110° Thus angles L and M are each 35° The bearing of K from L is 330-180=150° Add to that the 35° at angle L and M's bearing from L is 185°
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