Math

posted by .

A) A rectangle has perimeter 64 cm and area 23 cm^2. Solve the following system of equations to find the rectangle's dimensions.
length=23/width
length + width = 32

B) Solve the system of equations
x^2+y^2=1
xy=0.5

  • Math -

    A) A rectangle has perimeter 64 cm and area 23 cm^2. Solve the following system of equations to find the rectangle's dimensions.
    length=23/width
    length + width = 32


    Let
    L = length
    W = width
    L=23/W
    L+W=32
    23/W+W=32
    W2-32W+23=0
    Solve for the quadraticequation in W.
    Find L using L = 23/W.
    You should get 0.7 and 31 approx.

    B. Solve
    x^2+y^2=1
    xy=0.5

    If you plot the two equations on sqaure paper, you will see a circle (firt equation) and two disjoint curves with asymptotes toward the 4 extremities of the axes. This will give you an idea where the roots will be, namely where they intersect, and that there should be four of them if they cut the circle, zero if they don't, and two (visually) if they are tangential to the circle.

    Substitute y=0.5/x into the equation of the circle (with unit radius).
    x2 + (0.5/x)2 = 1
    substitute u=x2,
    u+0.25/u=1
    u2 -u + 0.25 = 0
    Solving for u, we get
    u=0.5 ± 0 (meaning the intersection is tangential)
    =0.5
    x=±sqrt(0.5)
    y=0.5/x=±sqrt(0.5)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math ,correction

    Directions: Solve each of the following problems. Be sure to show the equation used for the solution. The length of a rectangle is 2in. more than twice its width. If the perimeter of the rectangle is 34 in., find the dimensions of …
  2. algebra , help

    Can someone help me set up the equations thanks. Directions: Solve each of the following applications. Give all answers to the nearest thousandth. Problem: Geometry. The length of a rectangle is 1 cm longer than its width. If the diagonal …
  3. math 209

    The perimeter of a rectangle is 44ft the length is 4ft longer than the width. Find the demensions. Write a system of linear equations and solve the resulting system. Let x be the length and y be the width.
  4. MAT 116

    The perimeter of a rectangle is 28 ft. The length is 10 ft longer than the width. Find the dimensions. Write a system of linear equations and solve the resulting system. Let x be the length and y be the width.
  5. math

    Solve each system of equations by graphing. Check each solution. The perimeter of a rectangle is 24 ft. Its length is five times its width. Let x be the length and y be the width. What is the area of the rectangle?
  6. algebra

    the primeter of a rectangle is 24ft. the length is 2 ft longer than the width. Find the dimensions. Write a system of linear equations and solve the resulting system. Let x be the length and y be the width. Is the answer for the lenght …
  7. algebra

    the primeter of a rectangle is 24ft. the length is 2 ft longer than the width. Find the dimensions. Write a system of linear equations and solve the resulting system. Let x be the length and y be the width. is the answer for the length …
  8. Math

    The perimeter of a rectangle is 42ft. The length is 7ft. longer than the width. Find the dimensions. Write a system of linear equations and solve the resulting system. Let X be the length, and Y be the width.
  9. Algebra

    A rectangle's length is 6 less than twice its width. The perimeter of the rectangle is 36 units. Set up and solve a system of equations to determine the length and width.
  10. Algebra

    A rectangle's length is 6 less than twice its width. The perimeter of the rectangle is 36 units. Set up and solve a system of equations to determine the length and width?

More Similar Questions