math/calc

posted by .

The hypotenuse of a right triangle has one end at the origin and one end on the curve y+x^2e^(-3x), with x > or = 0. One of the other two sides is on the x-asis, the other side is parallel to the y-axis. Find the maximum area of such a triangle. At what x-value does it occur?

  • math/calc -

    Your curve
    y+x^2 e^(-3x)
    what is that equal to ? A curve has to follow an equation.
    If you mean the curve
    y=x^2 e^(-ex)

    then the area is yx/2 which is equal to
    1/2 x^3 e^(-3x). Right?

    dArea/dx= 3x^2e^(-3x)-3x^3e^(-3x)=0
    solve for x.
    x=1 check that I did it in my head. Mornings is not a great time for me to try that.

  • math/calc -

    You appear to have a typo,
    I will assume your curve is y = x^2e^(-3x) or y = x^2/e^(3x)

    let the point of contact of the hypotenuse be (x,y) on the curve.
    Then the right angle will be at (x,0)
    and the
    Area = xy/2
    = (1/2)(x)x^2e^(-3x)

    2A = (x^3)(e^(-3x))
    2dA/dx = x^3(-3e^(-3x)) + 3x^2(e^(-3x))
    = -3x^2(e^(-3x))[x - 1}
    = 0 for a max of A
    3x^2 = 0 --->x=0, little sense, since no triangle
    or
    e^(-3x) = 0 ---> no solution
    or
    x = 1, yeahh!

    if x = 1 then
    A = (1/2)1^3(e^-3) = .0249

    ( I tested for the area with x = .99 and x = 1.01 and they were both smaller than .0249 by a "smidgeon")

  • math/calc -

    thank you and yes i had atypo i apologized it was y = x^2e^(-3x

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    The hypotenuse of a right triangle has one end at the origin and one end on the curve y=x^(7)e^(-7x) , with x greater than or equal to 0. One of the other two sides is on the x-axis, the other side is parallel to the y-axis. Find the …
  2. Math

    The hypotenuse of a right angled triangle is 65cm. One side is 10 cm shorter than twice the other side. Find the lengths of the 2 sides (provide a little of steps if available)
  3. math/calc

    The hypotenuse of a right triangle has one end at the origin and one end on the curve y+x^2e^(-3x), with x > or = 0. One of the other two sides is on the x-asis, the other side is parallel to the y-axis. Find the maximum area of …
  4. math

    one side of a right triangle is 8 cm.the hypotenuse is 3 cm.more than twice of the other side.what is the measure of the other side?
  5. calculus

    The hypotenuse of a right triangle has one end at the origin and one end on the curve y = (x^4)(e^-7x), with x > 0. One of the other two sides is on the x-axis, the other side is parallel to the y-axis. Find the maximum area of …
  6. calculus

    The hypotenuse of a right triangle has one end at the origin and one end on the curve y = (x^4)(e^-7x), with x > 0. One of the other two sides is on the x-axis, the other side is parallel to the y-axis. Find the maximum area of …
  7. Algebra 1

    1) Find the possible values of a, if the distance between the points is 5, and the coordinates are (1, 1) and (4, a). I don't know how to solve this one. 2) in a right triangle the length of the hypotenuse is 14 and the length b of …
  8. geometry (check answers)

    Determine whether you can construct many, one, or no triangle(s) with the given description. a) a triangle with angle measures of 50°, 70°, and 100° no b) a triangle with one angle measure of 60° and one 4-centimeter side no c) …
  9. Math

    In a right angled triangle, the length of a hypotenuse is 10 cm. Of the two shorter sides, one side is 2 cm longer than the other side. i) Find the lengths of the two shorter sides. ii)Hence, find the area of the triangle.
  10. Math

    the length of the hypotenuse of a right angled triangle is one unit more than twice the length of shortest side and the other side is one unit less than twice the length of the shortest side. find the lengths of other two sides.

More Similar Questions