1. Trigonometry

    Every point (x,y) on the curve y=log(3x)/log2 is transferred to a new point by the following translation (x′,y′)=(x−m,y−n), where m and n are integers. The set of (x′,y′) form the curve y=log(12x−96)/log2. What is
  2. Math

    Every point (x,y) on the curve y=log23x is transferred to a new point by the following translation (x′,y′)=(x+m,y+n), where m and n are integers. The set of (x′,y′) form the curve y=log2(12x−96). What is the value of m+n?
  3. Logarithms

    I'm working on logarithmic equations and I'm stuck on how my book arrives at the next step. First, they use the change of base formula on, log(sqrt(2))(x^3 - 2) (sqrt(2)) is the base,changing to base 2 log(sqrt(2))(x^3 - 2)= log2(x^3 - 2)/(log2(sqrt(2)) I
  4. Math

    1. The sequence log2 32, log2 y, log2 128, ... forms an arithmetic sequence. What is the value of y? 2. If log a^2 b^3 = x and log (a/b) = y, what are the values of log a and log b?
  5. Trigonometry

    Every point (x,y) on the curve y = \log_{2}{3x} is transferred to a new point by the following translation (x',y') =(x+m,y+n), where m and n are integers. The set of (x',y') form the curve y = \log_{2}{(12x-96)} . What is the value of m + n ?
  6. precalc

    I don't understand how to do these w/o calc. I tried to write it in a way that will make someone understand how to read it. Hope I typed it clear enough.Thanks so much for the help anyone! How to find the exact value of logarithm: 10. log5^100 -log5^4 11.
  7. Math

    The problem I have to solve is log with base 2 ^6 multiply by log base 6 ^ 8. I use the change of base formula and got log6/log2 * log8/log6 Which become log6/log2 * log2()^3/ log 6 I'm stuck here thanks.
  8. calculus

    A curve passes through the point (1,-11) and it's gradient at any point is ax^2 + b, where a and b are constants. The tangent to the curve at the point (2,-16) is parallel to the x-axis. Find i) the values of a and b ii) the equation of the curve
  9. math

    the tangent yo the curve y=x^2 +5x -2 @ the point (1,4)intersect the normal to the same curve @ the point (-3,-8) at the point P.Find the coordinates of point P.[ans: -1/3,-16/3] just give me some hint to calculate this solution.
  10. math30

    1.Use the laws of logarithms to express log2 (6) – log2 (3) + 2log2 (8)^1/2 as a single logarithm; then evaluate. 2. For logy = log(0.5x – 3) + log2, express y as a function of x.
  11. Math - Logarithmic

    Solve: 2^(5x-6) = 7 My work: log^(5x-6) = log7 5x - 6(log2) = log7 5x = log7 + 6(log2) x = (log7 + log2^6) / 5 And textbook answer: (log7) / (log2) What did I do wrong?
  12. mathematics -logs

    which three statements are true? a) if x= -10^4 then log 10 = -4 b)if x= 2^8 then log 2x = 8 c) log2 2= 4 d) if x= 3 then log10 3=x e) log 10 256-2log 10 a/log 10 b f)log 10 (a-b)= log 10 a/log 10 b g) the gradient of the graph of y= 2x^x at x= 2 is 2e^e
  13. Math

    Given that x²cos y-sin y=0 ,(0,π): a)verfiy that given point is on the curve. b)use implicit differentiation to find the slope of the above curve at the given point. c)find the equation for tangent and normal to the curve at that point.
  14. maths

    which three statements are true? a) if x= -10^4 then log 10 = -4 b)if x= 2^8 then log 2x = 8 c) log2 2= 4 d) if x= 3 then log10 3=x e) log 10 256-2log 10 a/log 10 b f)log 10 (a-b)= log 10 a/log 10 b g) the gradient of the graph of y= 2x^x at x= 2 is 2e^e
  15. maths

    which three statements are true? a) if x= -10^4 then log 10 = -4 b)if x= 2^8 then log 2x = 8 c) log2 2= 4 d) if x= 3 then log10 3=x e) log 10 256-2log 10 a/log 10 b f)log 10 (a-b)= log 10 a/log 10 b g) the gradient of the graph of y= 2x^x at x= 2 is 2e^e
  16. dynamics

    A racecar is initially travelling at 75 mph at point A as it enters the S-curve shown. In order to successfully traverse the curve, the racecar driver applies his brakes and decelerates uniformly between point A and B. Point B is located 750 ft down the
  17. DYNAMICS

    A racecar is initially travelling at 75 mph at point A as it enters the S-curve shown. In order to successfully traverse the curve, the racecar driver applies his brakes and decelerates uniformly between point A and B. Point B is located 750 ft down the
  18. Calculus

    The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve? x2 − y2 = 15 x2 + y2 = 15 x + y = 15 <- my answer xy = 15
  19. math

    which three statements are true? a) if x= -10^4 then log 10 = -4 b)if x= 2^8 then log 2x = 8 c) log2 2= 4 d) if x= 3 then log10 3=x e) log 10 256-2log 10 a/log 10 b f)log 10 (a-b)= log 10 a/log 10 b g) the gradient of the graph of y= 2x^x at x= 2 is 2e^e
  20. 12th Grade Calculus

    1. a.) Find an equation for the line perpendicular to the tangent curve y=x^3 - 9x + 5 at the point (3,5) [* for a. the answer that I obtained was y-5 = -1/18 (x-3) ] b.) What is the smallest slope on the curve? At what point on the curve does the curve
  21. Math

    Hello! Could someone please take a look at the problem below and let me know if I made mistakes in simplifying the given equation? I'm quite certain that I did make a mistake somewhere because the original equation and its simplified form give different
  22. calc

    The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (3, 1) is a point on the curve?
  23. Calculus

    The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve? x2 − y2 = 15 x2 + y2 = 15 x + y = 15 xy = 15
  24. Calculus

    The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (2, 1) is a point on the curve?
  25. calculus

    If u = log(r), where r^2 = (x-a)^2 + (y-b)^2, and (x-1) and (y-b) are not zero simultaneously, show that d^2u/dx^2 + d^2u/dy^2 = 0. I first used some of the properties of log and made u = 1/2 * log((x-a)^2 + (y-b)^2) Then made u = 1/2 * ln((x-a)^2 +
  26. algebra/please can you ck my answers

    Tell what the output value is for the function machine for the given values. log 16.9=1.23 log2^152=9 log2^1=0 log0.046=1.34 thank you
  27. surveying

    how to solve for radius of horizontal curve with coordinates(NE) for points A,B, C on the curve Point A : N1405.4018 E1256.7569 Point B : N1283.3703 E1294.7027 Point C : N1225.9373 E1286.6137
  28. math

    how to solve for radius of horizontal curve with coordinates(NE) for points A,B, C on the curve Point A : N1405.4018 E1256.7569 Point B : N1283.3703 E1294.7027 Point C : N1225.9373 E1286.6137
  29. Calculus

    The slope of the tangent to a curve at any point (x, y) on the curve is -x/y . Find the equation of the curve if the point (3,-4) on the curve.
  30. Precalculus

    More log/exponential equations log2 x + log2(x+2) =3
  31. math

    consider the curve defined by the equation y=a(x^2)+bx+c. Take a point(h,k) on the curve. use Wallis's method of tangents to show that the slope of the line tangent to this curve at the point(h,k) will be m= 2ah+b. have to prove this for tow cases: a>0
  32. maths

    1. Log10²x+log10x²=log10² 2-1 2. Log4(log2x)+log2(log4x)=2 3. X^logx+5/3= 10^5+log x 4. Log 1/2(x-1)+ log 1/2(x+1)-log1/√2(7-x)=1
  33. Math

    I don't understand how log2 √(1/2) turned into log2 2^(-1/2). Quote: You will have to know the 3 prime properties of logs 1. logk (AB) = logk A + logk B 2. logk(A/B) = logk A - logk B 3. logk (A^n) = n logk A where k is any positive number , k
  34. Math

    I don't understand how log2 √(1/2) turned into log2 2^(-1/2). Quote: You will have to know the 3 prime properties of logs 1. logk (AB) = logk A + logk B 2. logk(A/B) = logk A - logk B 3. logk (A^n) = n logk A where k is any positive number , k
  35. Math

    I don't understand how log2 √(1/2) turned into log2 2^(-1/2). Quote: You will have to know the 3 prime properties of logs 1. logk (AB) = logk A + logk B 2. logk(A/B) = logk A - logk B 3. logk (A^n) = n logk A where k is any positive number , k
  36. Please check my maths?

    How should i do this question?? it says: find the equation of the tangent to the curve y=(x-2)^3 at the point (3,1). calculate the coordinates of the point where this tangent meets the curve again. I know how to get the first part, if i'm not wrong, it's y
  37. Math

    If ln a=2, ln b=3, and ln c=5, evaluate the following: (a) ln(a^−2/b^4c^−3)= -.9524 (b) ln(√b^−4*c^1*a^−1)= -1.739 (c) ln(a^2b^4)/ln(bc)^−2= 42.39 (d) (ln(c^−1))*(ln(a/b^3))^−4= -.03507 I am getting these answers but the problem gives me an
  38. Physics

    Point A is 5 m from a loudspeaker. At point B, the loudspeaker sounds half as loud as at point A. How far is point B from the loudspeaker? I get 50 m, but the answer is supposed to be 15.8 m. I need to know what I'm doing wrong. By my (apparently flawed)
  39. Maths

    a curve ahs parametric equations x=t^2 and y= 1-1/2t for t>0. i)find the co-ordinates of the point P where the curve cuts the x-axis which i found to be P(1/4, 0) the next part i cant do ii) find the gradient of the curve at this point. So far, I have
  40. calc

    given that log2 3 = x, log 2 5=y and log 2 7 = z, express log 2 21 in terms of x,y, and z the 2 is the base
  41. Math (repost, URGENT)

    A curve is traced by a point P(x,y) which moves such that its distance from the point A(-1,1) is three times the distance from the point B(2,-1). Find the equation of the curve and identity.
  42. calculus

    1. Given the curve a. Find an expression for the slope of the curve at any point (x, y) on the curve. b. Write an equation for the line tangent to the curve at the point (2, 1) c. Find the coordinates of all other points on this curve with slope equal to
  43. Urgent math

    i need help with these two homework problems Use the Laws of Logarithms to combine the expression into a single logarithm log2 5 − 5 log2 x + 1/2 log2(x + 1) Solve the logarithmic equation for x log2(x + 2) + log2(x − 1) = 2
  44. Calculus - Damon

    Find the line which passes through the point (0, 1/4) and is tangent to the curve y=x^3 at some point. So I found the derivative which is 3x^2. Let (a, a3) be the point of tangency. 3x^2 = (a3 - 1/4)/(a-0) I'm not sure how to solve for a. Yes, the point is
  45. AP Calculus

    Consider the curve given by x^2+4y^2=7+3xy a) Show that dy/dx=(3y-2x)/(8y-3x) b) Show that there is a point P with x-coordinate 3 at which the line tangent to the curve at P is horizontal. Find the y-coordinate of P. c) Find the value of d^2y/dx^2 (second
  46. Math

    A curve is traced by a point P(x,y) which moves such that its distance from the point A(-1,1) is three times the distance from the point B(2,-1). Find the equation of the curve and identity.
  47. calc

    for the parametric curve defined by x=3-2t^2 and y=5-2t ...sketch the curve using the parametric equation to plot of the point. use an arrow to indicate the direction of the curve for o<t<1. Find an equation for the line tangent to the curve at the
  48. Calc I

    Find an equation of the tangent to the curve at the given point. y=4(sinx)^2 point: pi/6,1) So I took the derivative of the original function to get: y' = 8cosx*sinx I then chose a point to plug in to find a point for the slope. i picked pi/6 because i
  49. Logarithm help

    using logarithms to solve exponential equations. 5^1+x = 2^1-x I need exact numbers. I did one on my own already. 5^x-1 = 9 5^x-1 = 9 log(5^x-1) = log9 (log5)(x-1) = log9 x-1 = (log9/log5) x= (log9/log5)-1 x = 2.3652 Logarithm help - Joe, Friday, September
  50. Chemistry

    When looking at a titration curve, I have to determine which is not true and I have it narrowed down to two options: The initial starting point on the titration curve is where pH depends only on [HA]0 or The finial point on a titration curve the pH depends
  51. maths pls help

    1. Solve the following simultaneous equations: log2 xy = 7 log2 (x^2/y) = 5 2. If log y x =a and log z x=b where x is not equal to 1, express the following in terms of a and b: logy (yz) Solve the following simultaneous equations: y = 2 log3 x y+1 = log3
  52. Calculus Help Please!!! Check

    A curve passes through the point (0, 2) and has the property that the slope of the curve at every point P is three times the y-coordinate of P. Find an equation of the curve. dy/dp = 3y or ∫ (3/y) dy = ∫ dp or 3 ln(y) = p + c or @ (0,2) ln(2) =
  53. economics

    label a point f inside the curve. why is this an inefficient point? label a point g outside the curve. why is this point unattainable? why are pointS A THROUGH E ALL EFFICIENT POINTS?
  54. economics

    label a point f inside the curve. why is this an inefficient point? label a point g outside the curve. why is this point unattainable? why are pointS A THROUGH E ALL EDDICIENT POINTS?
  55. precalc

    Solve the logarithmic equation for x. (Enter your answers as a comma-separated list.) log2(x + 17) − log2(x − 2) = 1 2 is the base for the log.
  56. Calculus

    A curve passes through the point (7,6) and has the property that the slope of the curve at every point P is 4 times the y-coordinate of P. What is the equation of the curve? Simplify the equation as much as possible.
  57. math

    which 3 are correct a) if x= -10^4 then log10 x = -4 b)if x= 2^8 then log 2x = 8 c) log2 2= 4 d) if x= 3 then log10 3=x e) log 10 256-2log 10 16=0 f)log 10 (a-b)= log 10 a/log 10 b g) the gradient of the graph of y= 2e^x at x= 2 is 2e^2 h) the gradient of
  58. AP Statistics

    A certain density curve looks like an interverted letter V. The first segment goes fro the point (0,0.6) to the point (0.5,1.4). The segment goes from (0.5.1.44) to (1,0.6). (a) Sketch the curve. Verify that the area under the curve is 1, so that it is a
  59. calculus

    Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2 + 1 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent point is far from the
  60. Math

    The equation of a curve is y = 2x^3 + 3x^2 Find: x-intercept of the curve y-intercept of the curve b) Determine the stationery point of the curve. i) for each point in(b) above, determine whether it is a maximum or a minimum
  61. math

    find the eqt. of tangent to the curve y=-x^2+2x-10 @ the point where the curve cuts the y-axis.[ans:y=2x-10] how do i do this because they didn't give me the point...?
  62. math

    find the coordinates of the point where the tangent to the curve y=x^3 +x +2 at the point (1,4) meets the curve again. [ans:-2,-8] pls help me i don't understand the question....
  63. calculus

    Consider the curve defined by the equation y = 4x^3 +3x. Set up an integral that represents the length of curve from the point (0,0) to the point (4,268).
  64. Calculus

    Find the xy-equation of the curve that passes through (-2, -2) and whose slope at any point on the curve is equal to 5 times the x-coordinate of that point
  65. math

    Logarithm!!! Select all of the following that are true statements: (a) log(2x) = log(2) + log(x) (b) log(3x) = 3 log(x) (c) log(12y) = 2 log(2) + log(3y) (d) log(5y) = log(20y) – log(4) (e) log(x) = log(5x) – log(5) (f) ln(25) = 2ln(5) (g) ln(1) =
  66. math

    solve the equation log2(x+4)-log4x=2 the 2 and 4 are lower than the g This is what I got: log2(x+4)+log2(4^x)=2 log2((x+4)*4^x)=2 4^x(x+4)=4 x=0 is a solution???
  67. calculus

    Determine the equation of a curve in the xy-plane that passes through the point (0, 1) and has the slope x2 sin 4x at any point (x, y) on the curve.
  68. Calculas-Differentiation

    Find the coordinates of a point on the curve y=6-x^2 at which the tangent of the curve at the point is perpendicular to the line y=1/4x+1.
  69. Maths

    The tangent to the curve 2y= 2x^2 -5x +4 at the point where x=1 is parallel to the normal to the curve y= ax^2 + bx +10 at the point (-2,2). Calculate the values of a and b. The answers are a=1, b=6
  70. Chemistry

    When looking at a titration curve, I have to determine which is false and I have it narrowed down to two options: The initial starting point on the titration curve is where pH depends only on [HA]0 or The finial point on a titration curve the pH depends
  71. calculus!URGENT

    Show that the tangent line to the curve y=x^3 at the point x=a also hits the curve at the point x=-2a. Any help?! PLEASE!
  72. calculus

    The slope of a curve is at the point (x,y) is 4x-3. Find the curve if it is required to pass through the point (1,1). Work... 4(1)-3=1 y-1=1(x-1) y=x
  73. math

    A curve has implicit equation x^2-2xy+4y^2=12 a)find the expression for dy/dx in terms of y and x. hence determine the coordinates of the point where the tangents to the curve are parallel to the x-axis. b)Find the equation of the normal to the curve at
  74. calculus

    Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope -1 is tangent to the curve at point P. Find the
  75. Calc AB

    Suppose that f(x) is an invertible function (that is, has an inverse function), and that the slope of the tangent line to the curve y = f(x) at the point (2, –4) is –0.2. Then: (Points : 1) A) The slope of the tangent line to the curve y = f –1(x) at
  76. AP AB Calculus

    Linear approximation: Consider the curve defined by -8x^2 + 5xy + y^3 = -149 a. find dy/dx b. write an equation for the tangent line to the curve at the point (4,-1) c. There is a number k so that the point (4.2,k) is on the curve. Using the tangent line
  77. Calculus AB

    Could someone please help me with these tangent line problems? 1) Find the equation of the line tangent to the given curve at the indicated point: 3y^3 + 2x^2 = 5 at a point in the first quadrant where y=1. 2) Show that there is no point on the graph of
  78. calculus

    Consider the curve given by the equation y^3+3x^2y+13=0 a.find dy/dx b. Write an equation for the line tangent to the curve at the point (2,-1) c. Find the minimum y-coordinate of any point on the curve. the work for these would be appreciated i don't need
  79. Chemistry

    1. A solution is prepared such that it is 0.45 M in formic acid and 0.35 M in sodium formate. a) Where is this mixture located on a titration curve: before the buffer point, at the buffer point, or after the buffer point? b) Use the Henderson-Hasselbach to
  80. MATH

    Write as a single logarithm: 2 log 3 – log 5 +2 log2
  81. statistics

    What is the value of the z-scores if the area of the curve to this point is 0.887? How much of this are is between the peak of the curve and this point?
  82. Calculus

    Find the inverse of each relation: y = (0.5)^(x+2) and y = 3log base 2 (x-3) + 2 For the first one I got y=log base 0.5 (x+2)...but the answer in the back of the textbook says that it is not x+2, but x-2. Can someone tell me why it would end up being x-2
  83. Algebra II

    Please check answers: Use the equation of the exponential function whose graph passes through the points (0,-2) and (2,-50) to find the value of y when x= -2. My answer: -2/25 Solve 64^x<32^x+2 Answer: x<10 Write the equation log(243)81=4/5 Answer:
  84. Calculus

    Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2+7 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent point is far from the
  85. precalculus

    solve log(2+x)-log(x-3)=log2 I know the answer is 8
  86. Math

    Consider the paraboloid z=x^2+y^2. The plane 3x-2y+z-7=0 cuts the paraboloid, its intersection being a curve. What is the "the natural" parametrization of this curve? Hint: The curve which is cut lies above a circle in the xy-plane which you should
  87. Math

    Consider the paraboloid z=x^2+y^2. The plane 3x-2y+z-7=0 cuts the paraboloid, its intersection being a curve. What is the "the natural" parametrization of this curve? Hint: The curve which is cut lies above a circle in the xy-plane which you should
  88. Calculus

    The line that is normal to the curve x^2=2xy-3y^2=0 at(1,1) intersects the curve at what other point? Please help. Thanks in advance. We have x2=2xy - 3y2 = 0 Are there supposed to be 2 equal signs in this expression or is it x2 + 2xy - 3y2 = 0 ? I'll
  89. Pre-Cal

    log 3x=log2+log(x+5)
  90. math

    solve log(2+x)-log(x-3)=log2
  91. MATH--Please help!!

    I'm desperate! Find the point where the curve r(t)=(12sint)i - 12(cost)j+ 5tk is at a distance 13pi units along the curve from the point (0,-12,0) in the direction opposite to the direction of increasing arc length. Thanks for any advice...
  92. calculus

    there are two tangents lines to the curve f(x) = 3x^2 that pass through the point p =0,1 find the x coordinates of the point where the tangents line intersect the curve
  93. Calculus AB

    Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive? Negative? Zero? 2) Find an equation of the tangent line to the oven curve at the specified point.
  94. Mathematics

    Prove that log a, log ar, log ar^2 is an a.p. Is the following below correct? Log ar^2 - Log ar= Log ar - Log a hence applying laws of logarithm Log(ar^2/ar) = log(ar/a) Log and log cancels out and then cross-multiply hence a^2r^2 = a^2r^2 L.H.S=R.H.S
  95. Precalculus

    I'm studying for my precalc exam and have completed 42 practice problems. I have 3 I need to answer that I can't. Please help. What is the base of the function G(x) = log subscript b x if it's graph has points (16,4)? Using the properties of logarithms how
  96. Math (Calculus)

    A(1,0) is a point on the parabola y=2x(x−1). From point A, point P is moving along the curve towards the origin O(0,0). As P → O, sec^2∠APO → N, where N is a positive integer. What is the value of N?
  97. Math (Limits)

    (1,0) is a point on the parabola y=2x(x−1). From point A, point P is moving along the curve towards the origin O(0,0). As P→O, sec^2∠APO→N, where N is a positive integer. What is the value of N?
  98. Calculus

    A point is moving along the curve xy=12. When the point is at (4,3), the x-coordinate decreases at the rate of 2cm/sec. How fast is the y-coordinate changing at that point?
  99. AP Calc for Reiny

    You did just fine and your second derivative is correct, if you meant (6y^2 - 4x^2)/(9y^3) except they took it a bit further. notice your numerator is -4x^2 + 6y^2 from the original 2x^2 - 3y^2 = 4 , then 4x^2 - 6y^2 = 8 , and -4x^2 + 6y^2 = -8 to get
  100. AP Calc for Reiny

    You did just fine and your second derivative is correct, if you meant (6y^2 - 4x^2)/(9y^3) except they took it a bit further. notice your numerator is -4x^2 + 6y^2 from the original 2x^2 - 3y^2 = 4 , then 4x^2 - 6y^2 = 8 , and -4x^2 + 6y^2 = -8 to get