Posted by Christine on Sunday, June 7, 2009 at 5:12pm.
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 ħ 0 (meaning the intersection is tangential)
=0.5
x=ħsqrt(0.5)
y=0.5/x=ħsqrt(0.5)
Related Questions
algebra , help - Can someone help me set up the equations thanks. Directions: ...
Algebra/geometry - a rectangle has a width of 4 cm less than it's length. ...
algebra - The length of a rectangle is 6 cm more than four times the width. If ...
geometry - The width of a rectangle is 6 cm less than its length. If the area of...
math - The width of a rectangle is 6 cm less than the length. A second rectangle...
math - The length of a rectangle is 5 cm more than twice the width. The ...
Math - The length of a rectangle is 8 cm greater than its width. Find the ...
algebra - Perimeter of a rectangle. The width of a rectangle is three fourths of...
math - the length of a rectangle is 1 cm less than twice its width. the area is ...
Math - The length and width of a rectangle are (x+4) cm and x cm respectively. ...
For Further Reading
