Posts by steve

Total # Posts: 56,000

  1. Algebra

    12! ways
  2. math

    all look good to me
  3. math

    Clearly false.
  4. Math

    3-4sin^2a = (3sec^2a-4tan^2a)*cos^2a = (3(tan^2a+1)-4tan^2a)*cos^2a = (3-tan^2a)*cos^2a 1-3tan^2a = 1-3(sec^2a-1) = 4-3sec^2a = (4cos^2a-3)/cos^2a now just multiply and the cos^2a factors cancel
  5. Math

    For Q7, I disagree. Vertical angles share only the intersection. I don't have the diagram, but I can't see how CED and BED can be vertical angles, since D is on both of them. Q9 looks like a better possibility.
  6. math

    1/2 * 3/6 = 1/4
  7. Physics

    step1: v=0+2a=1, so a = 1/2 km/min^2 s=0+1/4*2^2=1 step2: s=1*10 step3: a = -1/3 km/min^2 s = 1*3 - 1/6 * 3^2 = 3/2 PQ = 1 + 10 + 3/2 = 25/2 avg speed = (25/2)/(2+10+3) = 5/6 km/min there are two different accelerations, shown above. I assume you can convert to m/s^2
  8. Algebra

    looks like y=5x so, what is that?
  9. Math

    No. how did you get that? Just a guess? (8+11+12+16+n)/5=12
  10. Math

    the average of 5 numbers is their sum/5 So, now you know that (sum)/5 = 12
  11. Math

    two ends at pi*2.1^2 each is 27.71 cm^2 the curved side is 2 pi*2.1*8.8 = 116.11 cm^2 I agree with your answer, but it does not seem like quite enough.
  12. Trigonometry

    just use the parametric formulas... r = 2/(1+sin?) r+rsin? = 2 r+y=2 r = 2-y r^2 = (2-y)^2 x^2+y^2 = y^2-4y+4 x^2 = 4-4y y=1-x^2/4 check the polar form for conics and you will see that the curve is a parabola, since e=1 y=3 rsin? = 3 r = 3csc? 3x^2+3y^2-6x=0 3r^2 = 6rcos? r=2cos?
  13. math

    assuming you mean to cover the entire board, then since GCD(50,70)=10 The largest square which will work has side 10
  14. science/math

    work = force * distance 140N * 7.0 m/s * 40s = 39200J
  15. math

    the given line has slope 5/2 so, our new line will have slope -2/5 Now, we have a point and a slope, so using the point-slopr form, our new line is y-8 = -2/5 (x+7)
  16. Math

    ?(3974^2-492^2) ? 3943 ft love your creative spelling ... not!
  17. calculus

    I guess you could use the law of cosines. Draw a diagram and you will see that |3a-5b|^2 = 3^2+5^2-2*3*5*cos120° do the same for the other
  18. Physics

    You might start here: http://www.dummies.com/education/science/physics/how-to-calculate-rotational-kinetic-energy/
  19. Math

    total points so far is 196 so, the mean for those 4 games is 196/4=49 They need 49 in the next game to keep the same mean.
  20. math

    add up the total points and divide by 4.
  21. trig

    in QIV, y = -2 r = 3 x = ?5 cos? = x/r = ?5/3
  22. calculus

    Let a=<1,0> Then b=<1/2,?3/2> Now you just add the components. For example, 2a+3b = <2,0>+<3/2,3?3/2> and |2a+3b|=?((2+3/2)^2+(0+3?3/2)^2) = ?(49/4 + 27/4) = ?76/2 = ?19
  23. Math

    (7-6)/0.65 = 1.538 std so, look that up in your Z table to see how much lies in the right tail.
  24. MATH

    you're kidding, right? Why not show your work, so we can see whether you did it right... 41*41 = 1681 ...
  25. Math

    ln(3x)-ln(x) = ln(3x/x) = ln3 is constant
  26. Math

    The revenue must be positive, so if there are x price increases, the revenue is (4000-40x)(2.00+0.15x) So, they need -6x^2+520x+8000 >= 10450 5 <= x <= 81.67 So, the fare must be between $2.75 and $14.25 The maximum revenue of $19270 will be achieved at a price of $8.50
  27. trigonometry

    cosine is not a quadrant. With x positive and y negative, that is QIV cosine = x/r
  28. math

    ooops - my bad. So, divide the circumference by the plant's diameter. If you knew enough to catch my mistake, you should know enough to figure the correct answer. What did you get?
  29. math

    the obvious answer, though probably not technically correct, is gotten by dividing the total area by the area required by each plant. That would be ?*140^2 / ?*0.5^2 = (140/0.5)^2 = 78,400
  30. C++ Programming

    so, what have you done so far? I assume you know how to declare the (main) function, and define a structure... Presumably you have covered these topics, and many code samples can be found online.
  31. Math

    I assume by "one with the smallest ratio" you mean the one who received the smallest amount. In that case, multiply everything by 25/2 and the ratios become 125/2 : 75/2 : 25 But that requires some split mangoes. The total is 125 mangoes.
  32. math

    sinB/6 = sin50/6.188 2.82^2 = g^2+7^2-2*6*7 cos(CAD) area of ACD = 6*(7*sin(CAD))/2
  33. Maths

    draw a diagram. Clearly the distance x is found using 86/x = sin 36°
  34. Algebra

    y=x y=x^2
  35. Maths

    I think you have left out some important parts of the description.
  36. Pre Calculus

    Looks like (c) to me. Just set u=2t and you have x(t)=2cos2u y(t)=sin3u The names have been changed to protect the innocent parameters.
  37. 12th math

    c'mon, guy -- you're not in Algebra I any more. Just plug in t=(x+1)/4 and you have y = 2((x+1)/4)^2+3(x+1)/4-4 Now just expand that out
  38. Math

    Ummm. Did you ever think of describing the designs? I don't mind working on an answer, but I refuse to provide the question as well!
  39. Pre-Calculus Help?

    looks like B to me
  40. Science

    it's one mole So, add up the atomic weights of all the atoms, and that's how many grams of CaCO3 there are.
  41. Pre-Calculus Help?

    work = force * distance so, how far between the points?
  42. Math

    42
  43. Trig

    got to know how high the pulley axles are. Also, where on the circumference of B is the drop of paint at time t=0? Then it's just a matter of knowing that A rotates twice as fast as B.
  44. Chemistry

    PV=kT If P is constant, then V/T is constant (k/P) So, you want V such that V/(72+273.15) = 62/(-15+273.15)
  45. Chemistry

    °K
  46. geometry

    The altitude of the large yellow area is 12, the side of the square. So, if you folded the small triangular area which includes the blue, the area outlined by the large yellow triangle would be 12*12/2 = 72 subtract the blue twice (once in its present location, and again after...
  47. geometry

    v = ?r^2h, so h = v/(?r^2) a larger r means a smaller h, so 315/(?*7^2) <= h <= 315/(?*6.5^2) 2.05 <= h <= 2.37
  48. Math

    1st step: subtract two from each side to get 5x = 60 Now what, do you think?
  49. math;)

    |u| = ?(9+4) = ?13 So, divide u by its length to get a unit vector (length=1) so, (a) If you've advanced to the point where you're studying vectors, your teacher should stop insisting on rational denominators. I much prefer 1/?13 to the cumbersome ?13/13 just sayin'...
  50. Math

    yes
  51. Geometry

    the areas scale as the square of the ratio the volumes scale as the cube of the ratio so, volumes scale as the 3/2 power of the area ratio So thar larger pyramid's volume is 8*(40/25)^(3/2) = 8 * (9/4)^(3/2) = 8 * 27/8 = 27
  52. Math

    you need a compass to do it right. Pick a point A on the circle. Set the compass to reach to the center, then use that radius to mark where the arc intersects the circle at B. Since all 3 sides of the triangle are the same, the angle is pi/3. The arc s = pi/3 * r
  53. Calculus

    F' = (1/(3x))*3 - (1/x)*1 = 1-1 = 0 so, F is constant
  54. Geometry

    the center of the circle is the midpoint of the diameter: (-3,2) The length of the diameter is ?(14^2+8^2) = ?260 = 2?65 so, the radius is ?65 That means the equation is (x+3)^2 + (y-2)^2 = 65
  55. Calculus

    using shells, v = ?[0,2] 2?rh dx where r = 5-x and h=x-0.5x^2 or, using discs, v = ?[0,2] ?(R^2-r^2) dy where R=5-y and r=5-?(2y)
  56. Calculus

    time to post your answer. Remember the 2nd FTC. If F(x) = integral[a,u(x)] f(t) dt then F'(x) = f(u(x))*du/dx
  57. Calculus

    for each trapezoid number i the area is (f(x_i)+f(x_i+1))/2 * (x_i+1 - x_i)
  58. Calculus

    By the 2nd FTC, F' = -cos((x^3)^4)(3x^2) = -3x^2cos(c^12) why minus?
  59. Trig

    the curve is an ellipse with semi-axes a and b. If a=b it is a circle.
  60. maths

    The volume of a thin slice of water is the area of the slice times its thickness, dy At a depth of d, with d<r, we have the radius of the surface of the water is x = ?(r^2-y^2) v = ?[-r,d-r] ?(r^2-y^2) dy Now you can answer the last part by subtracting the volume from the ...
  61. math

    infinitely many try it - pick any value you want for x, and the equation will balance.
  62. calculus

    actually, F' = 2tan((2x)^2) = 2tan(4x^2) F' = 2sec^2(4x^2)(8x) = 16x sec^2(4x^2)
  63. English

    odd. I gave the phrase to google and the very first link explained it. Maybe you can start here: https://blog.udemy.com/imagery-in-literature/
  64. Trigonometry

    since the height h is the same on both ends, and the extra length of the long base is 143.47, then h = x tan 68°39.2' = (143.47-x) tan 72°6.0' solve for x. Now, one diagonal d is seen to be d^2 = (x+254.15)^2 + h^2 and the side s nearest that vertex is s^2 = h^...
  65. Math

    since the ratio of weights is constant, x/7 = 18/15
  66. Calculus

    A. The volume of a spherical cap of height h of a sphere of radius r is V = ?/3 h^2(r-h) This is a known formula, but you can always verify it by finding the volume made by rotating a circular segment. For example, V = ?[h,r] ?(r^2-y^2) dy B. The mass of any small disc of ...
  67. math

    well, how much has he saved so far? 3*.50 + 4*.20 + 1*.10 = 1.50+0.80+0.10 = 2.40 so, what do you think?
  68. Math

    all correct
  69. analytic geometry

    you have b=6 c=8 so, a=10 and e=4/5
  70. calculus

    yes. the height of each rectangle is the distance between the curves: x-x^3 or, you can consider finding the area below y=x and then subtracting from that the area below y=x^3
  71. maths

    the average of n numbers is the total divided by n.
  72. Math

    f(6) = f(3*2) = 3f(2) so, 12 = 3f(2) f(2) = 4 you are correct
  73. maths

    yes, I can do it.
  74. Math

    just plug your numbers into the annuity future value formula, which you must have.
  75. Math

    even integers differ by 2, right? So, if the width is w, then the length is w+2 Now just figure the perimeter and find w: 2(w + w+2) = 196
  76. algebra

    Nope. You divided the coefficients, but you also have to subtract 3 from each power. (c)
  77. math

    geez - impatient much?
  78. math

    The slope of the line is (5+23)/(6+8) = 2 So, using the point-slope form of a line, y-5 = 2(x-6) y-5 = 2x-12 y = 2x-7 Or, you could go through the hassle of solving 6a+b = 5 -8a+b = -23 subtract to get 14a = 28 a=2 so b = -7
  79. algebra

    1/x - 6/x^2 = -12 multiply by x^2 and you have x-6 = -12x^2 12x^2+x-6 = 0 (3x-2)(4x+3) = 0 x = 2/3 or -3/4
  80. Physics

    The initial 25 m/s is upward The acceleration is downward: -3.7 m/s^2 The final impact speed is also downward. 25 - 3.7t = -75 3.7t = 100 t = 27.03 seconds
  81. Algebra

    let x be the amount invested at 2½% Then the rest (23456.78-x) was invested at 1¾% So now, just add up the interest to find x. 0.025x + 0.175(23456.78-x) = 368.50 once you have x, you know the two amounts.
  82. maths

    as always draw the diagram. If you review your basic trig functions, you will see that h (in feet) can be found using h cot43° - h cot68° = 70
  83. math

    this is just an arithmetic sequence with a=2 d=3 So, S15 = 15/2 (2*2+14*3) If you really wanted a geometric sequence, the I assume you meant ?3^(n-1) In that case, a=1 r=3 so S15 = 1*(3^15-1)/(3-1)
  84. math

    S6 = 200(1.09^5 - 1)/(1.09-1)
  85. maths

    impatient much? reposting after 3 minutes?
  86. math

    #1 is indeed 30% for #2, just substitute values 1,2,3,4 for n. The terms are seen to be 2*1+3=5 2*2+3=7 2*3+3=9 2*4+3=11
  87. multimedian

    so, what have you done so far?
  88. Science

    The ISU provides handy names for various combinations of units. For example 1N = 1kg-m/s^2 You could just as easily have used slug-chains/year-weeks (a) most people would not have the slightest feel for what that means (b) you'd have to carry around that cumbersome ...
  89. Calc

    so, assuming that you have the linear function 1+x/5 root(0.95) = root(1-.05) ? 1+(-.05)/5 = 1-.01 = 0.99 root(1.1) = root(1+0.1) ? 1+0.1/5 = 1.02
  90. Calc

    since ln(sqrt(u)) = 1/2 ln u y = 1/2 ln(4+t^2) dy = 1/2 * 1/(4+t^2) * 2t dt = t/(4+t^2) dt
  91. Calculus

    Note that x=4siny and you want the area "above" the curve a = ?[0,pi/2] 4-4siny dy = 4y+4cosy [0,pi/2] = 2pi-4
  92. Maths

    ok. now what?
  93. Calculus

    f(0)=0 f(9)=0 So, that satisfies the theorem f is continuous and differentiable. So, we just have to find c such that f'(c)=0 f'(x) = 1/(2?x) - 1/9 1/(2?c) - 1/9 = 0 1/(2?c) = 1/9 2?c = 9 c = 81/4 which is in [0,81]
  94. Science

    could be the same, if the mug is the same metal. Otherwise, they will probably be different.
  95. math

    come on -- just add them up. S1 = 9 S2 = 9+12 = 21 ...
  96. Calculus

    clearly you must have meant C(t)=15t/(80+t) which --> 15 I am troubled by the fact that the equation for C(t) does not reflect the data given in the words. Also, at some point the tank will overflow, so having t unbounded is not realistic.
  97. Calculus

    come on -- this is Algebra II How far do you get?
  98. Calculus

    clearly, after 1 hour, the population has increased by 6000
  99. Calculus

    geometrically the argument makes sense. But algebraically, ?[a,b] f(x) dx = -?[b,a] f(x) dx
  100. Math

    you know that log_3(3)=1 so, log_3(x)+c = 1+c when x=3
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