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put this solution on YOUR website!Hello, I'm Alex, and having some difficulty with "American School" Homeschool work that I need in order to graduate high school. If you could please assist me in my attempt to complete it, I would be most gracious.
Here are a few of the problems:
1.Solve: 3(x-2)^2 =48
(X-2)^2=48/3=16
X-2=4...OR...-4
X=6....OR.....-2
2.If y varies directly as x and inversely as z^2, and y=3 when x=2 and z=4, what is the value of x when y=9 and z=4?
Y=KX/Z^2.AT X=2,Y=3,Z=4
3=K*2/4^2=K/8
K=24
Y=24X/Z^2
9=24X/4^2
24X=9*16
X=144/24=6
3.Solve the equation x^3 + 2x^2 + x + 2 = 0, if -2 is a root
-2|1+2+1+2
..|0-2+0-2
---------------
...1+0+1+0
X^2+1 IS THE QUOTIENT.
HENCE F(X)=(X^2+1)(X+2)
ROOTS ARE X=i,-i,-2
4.Given the equation x^3 - 2x^2 + x - 3 = 0, what are the possible rational roots?
POSSIBLE RATIONAL ROOTS ARE FACTORS OF -3/1....THEY ARE
-1,1,-3,3
5. Find the dimensions of a rectangle "a" with the greatest area whose perimeter is 30 feet.
P=2(L+B)=30
L+B=15
A=LB=L(15-L)=15L-L^2=-[L^2-2(L)(7.5)+7.5^2-7.5^2]
A=7.5^2-(L-7.5)^2
A IS MAXIMUM WHEN L=7.5
HENCE THE RECTANGLE WITH MAXIMUM AREA HA L=B=7.5
6. Given the equation x^3 - 4x^2 + 2x + 1 = 0, find the irrational roots? (Use the quadratic formula to solve the depressed equation.
X=1 IS A ROOT SINCE F(1)=1-4+2+1=0...HENCE DIVIDING WITH X-1
1|1-4+2+1
.|0+1-3-1
-------------
..1-3-1+0
X^2-3X+1 IS THE QUOTIENT...
X=[3+ OR - SQRT(3^2-4*1*1)]/2
X={3+SQRT(5)}/2.............{3-SQRT(5)}/2
7. Approximate to the nearest tenth, the real root of the equation f(x) = x^3 - 4 = 0
X^3=4
X=CUBE ROOT OF 4=1.59=1.6
