1. A


    A contact lens manufacturer is considering replacing its polisher . It requires that the new polisher , which is very expensive , produce less than 8% of lens whose surface defects behave - if it will keep the current polisher . It will use a confidence level of 2.5 % a) It produces 380 contact...
  2. X

    variation of parameter

    For this question, when we integrate x with d(y' + 3y)= e^(-4x) +4y with x , we got y' +3y= e^(-4x)/-4 + 4yx, we are unable to get f(x) , there is 4xy, ihow to solve this question??
  3. K

    Notation : Is ln(x)² = ln(x*x) or ln(x)² = (ln(x))²

    Hi there, I'm a little confused about the problem mentioned by the title of my thread. My math teacher told my friend he was wrong when he wrote ln(x)² as a result of an equation because the parentheses were misplaced. She corrected it this way : (lnx)². The thing is, I raised my hand to say...
  4. T

    For the system of equations check whether the 2 conditions in IMF theorem are true

    For the system of equations below, check whether the two conditions in the Implicit Function Theorem are satisfied at point A = (x, y, t) = (1, 1, 0), where x and y are variables and t is a parameter. If yes, find the expression for &dx/&dt and evaluate it at A. EQ#1 xy2 − y = 5t EQ#2...
  5. M

    parametric double integral, 3 cases

    Hi everybody, I have to find for which Alpha exists \int \frac{x^2}{(x+y)^\alpha} 1) defined on y=tanx and \pi/4<x<\pi/2 2) defined on x<=1 and \frac{(x^3-1)}{x}<y<x^2 3) in the triangle (-1,0), (0,1), (1,0) with this similar integral \int \frac{x^2}{(x^2+y^2)} In the first case I can...
  6. X

    variation of parameter

    in step2 , why thw y1 not equal to Acosx ? y2 not equal to Bsinx ? for second photo , why the author assume B+1 = B ?
  7. W

    Bayesian parameter estimation via MCMC?

    Hi folks. I have the following question. I have a model M containing 20 adjustable parameters k = {k_j}. I also have 40-50 measured temporal profiles e = {e_i} at my disposal. I can use M to predict the experimental values after solving complex systems of differential equations...
  8. L

    Parameter question please help!!? ?

    Did i do this right?? If not, whats the right answer? Is it D? Please help thank you!!!
  9. S

    Eliminating the Parameter Given Cartesian and t Equations

    I just need help figuring one simple part of the problem out, everything else is already done. I was given: x=1-3sin(4piT),y=2+3cos(4piT);0<t<1/2 I worked out the Cartesian to be; T=(sin^-1((1-x)/3))/4pi, y=2+3cos(sin^-1((1-x)/3)) Then I continued to do this: 0<(sin^-1((1-x)/3))/4pi<1/2...
  10. Jason76

    Eliminating the Parameter

    Eliminate the parameter to find the cartesian equation of the curve for -7 \leq y \leq -3 x_{1} = 1 - t^{2} y_{1} = t - 5 -2 \leq t \leq 2 (y - y_{1}) = m(x - x_{1}) m = \dfrac{\dfrac{dy}{dt}}{\dfrac{dx}{dt}} m = -\dfrac{1}{2t} How to find t, so I can find x_{1} and y_{1}?
  11. S

    Differentiating the integral by parameter

    Hi, sorry for the stupid question, but how to find the following derivative?
  12. T

    variation of parameter to find second solution

    (1+t)^{3} \frac{d^{2}x}{dt^{2}}-(1+t)\frac{dx}{dt} + x = 0 i) show that x(t) = 1+t is a solution to this ODE ii) use variation of parameters to find another solution to this ode ie. write x(t) = c(t)(1+t) and fint c(t) I need help with part (ii) x(t) = (1+t) x'(t) = 1 x''(t)...
  13. A

    Finding whether or not a function has roots, depending on a parameter

    Hello, I have this very ugly function (about 6 lines in latex), which I'll call U(theta,p), which has either 0, 2 or 4 zero roots in theta (defined between 0 and 2pi) depending on the value of the parameter p. Now, I can work out these roots numerically very easily in Matlab, or get a NaN...
  14. M

    Logarithmic distribution: Find the canonical parameter

    Hi, The logarithmic's probability function is: To find the canonical parameter, one must re-express the above to the generic pdf of exponential distribution: I have managed to: 1: take log then exp: 2. apply log rules: Unfortunately, this is where I could not expand further to...
  15. Jason76

    Parameter Elimination Problem - # 3

    x = t^{2} - 2t y = t Solving for t x = t^{2} - 2t 2t = t^{2} 2 = \dfrac{t^{2}}{2t} 2 = t y = \sqrt{2} - This must be converted into an "x =" equation Ultimately this last equation needs to be converted to an "x =" thing, because it's part of a bigger area problem in terms of the y...
  16. Jason76

    Parameter Elimination Problem

    Eliminate the parameter and find the Cartesian equation. x = 1 - t^{2} y = t - 3 -2 \leq t \leq 2 When you try to solve the first equation for t, then it seems to get a negative under the square root. x = 1 - t^{2} x - 1 = -t^{2} -x + 1 = t^{2} \sqrt{-x + 1} = \sqrt{t^{2}} ??
  17. Jason76

    Parameter Elimination and Two Trig Functions

    These functions have no t variable, but they have a \theta So I'm assuming it takes the place of t. Find the Cartesian equation of the curve by eliminating the parameter. y = \sin \dfrac{1}{2}\theta and y = \cos\dfrac{1}{2}\theta and \pi \leq \theta \leq \pi
  18. M

    C4 differentiation

    A curve is given by x = 2t + 3, y = t 3 − 4t, where t is a parameter. The point A has parameter t = − 1 and the line l is the tangent to C at A. The line l also cuts the curve at B. (a) Show that an equation for l is 2y + x = 7. (b) Find the value of t at B.
  19. M

    Matlab and Defining colors by Z parameter

    Hello! I'm working a matlab project where I need to define a Beam X=-5 to 5 and Y=-1 to 1. I have successfully plotted that, no issue. Next I determined the strain on the object and successfully defined a third parameter, Call it Z. So Now I have a matrix of >150 rows and 3 columns. How do...
  20. nycmath

    Algebra 1 Parameter Changes...Changing Points

    I posted a new thread yesterday which no one has replied to. I simply want to know how to find new points using the information. Sample: Change m(x) to m(x+4) given the following two points: (-5,5)--> (0,0)--> The arrow indicates that the given points must be changed. In other...