Pre-Calculus Help?

Rewrite the following parametric equations by solving for y

x(t) = e^-t

y(t) = 3e^2t

a) y=1/3x^2,x>0

b)3/x^2, x>0

c) y= 3e^t, x>0

d) y=4e^t, x>0

  1. 👍
  2. 👎
  3. 👁
  1. x(t) = e^-t

    x^-2 = (e^-t)^-2 = e^2t

    3 x^-2 = 3 e^2t = 3/x^2 = y

    1. 👍
    2. 👎
  2. x(t) = e^-t

    ln x = - t

    t = - ln x

    y = 3 e ^ ( 2 t )

    y = 3 e ^ [ 2 ∙ ( - ln x ) ]

    y = 3 e ^ [ - ( 2 ∙ ln x ) ]

    ______________________
    Remark:
    e ^ [ ( 2 ∙ ln x ) ] = x ^ 2

    e ^ [ ( - 2 ∙ ln x ) ] = 1 / x ^ 2
    ______________________

    So:

    y = 3 e ^ [ - ( 2 ∙ ln x ) ]

    y = 3 / x ^ 2

    x > 0

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus 3

    Find the parametric equations of the line through the points (1, 3, 2) and (4, -1, 1).

  2. algebra

    1. is -7+9=-9+7 true, false, or open? This is Lesson 1 introduction to equations unit 3 solving equations.

  3. Calculus

    Find the parametric equations for the line of intersection of the planes x+y+z=3 and x-y+2z=2 I took the cross product of the 2 equations and got 3i-j-2k I then set z=0 and got x=5/2 and y=1/2. I got: x=5/2 +3t y=1/2-t z=-2t

  4. Physics

    You are given vectors A = 5.0i - 6.5j and B = -2.5i + 7.0j. A third vector C lies in the xy-plane. Vector C is perpendicular to vector A and the scalar product of C with B is 15.0. Find the x and y components to vector C. Here's

  1. Mathematics

    Q/ Find the parametric equations of the line joining the points P1( 1, 1, -1) and P2( 1, 2, 0)?

  2. Calculus

    A curve is defined by the parametric equations: x = t2 – t and y = t3 – 3t Find the coordinates of the point(s) on the curve for which the normal to the curve is parallel to the y-axis. You must use calculus and clearly show

  3. mathematics

    7.3.6 - Quiz: Solving Multi-Step Equations Quiz Algebra Readiness (Pre-Algebra) A / 7. Equations and Inequalities / 7.3. Solving Multi-Step Equations can you check my answers 1. B 8 2. A -4 3. A -5a 4. D 7a-11b 5. C 6x + 50 6. B 3

  4. Math

    Find parametric equations and symmetric equations for the line of intersection of the given planes. x + y + z = 2, x + z = 0 X=1 y = Z= x=, y=

  1. calc 3

    Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 7x2 + 2y2 + 6z2 = 33 at the point (−1, 1, 2). (Enter your answer as a comma-separated list of equations.

  2. math

    Lesson 7: Solving Equations with Two Steps Math 6 B Unit 5: Graphing, Equations, and Inequalities the practice 1.b 2.c 3.b 4.b 5.c Lesson 7: Solving Equations with Two Steps Math 6 B Unit 5: Graphing, Equations, and Inequalities

  3. math

    Find a set of parametric equations for y= 3x + 7, given the parameter t= 5 – 5x

  4. Calculus

    Graph the parametric equations: x=cos(t) y=sin(t) z=cos(2t) How would I go about solving this problem? thanks!

You can view more similar questions or ask a new question.