Posted by Lucy on Saturday, February 23, 2008 at 5:11pm.
but it does factor to
(x^2 - 100)(x^2 - 2) = 0
so x = ± 10 or x = ± √2
BTW, check your typing
in the first you have a negative in front,
in the second you don't have an exponent on your first term
I assumed it was x^4 - 102x^2 + 200 = 0
It looks to me like the rearranged equation should be
x^4 + 102 x^2 -200 = 0, That is not what you wrote.
The answer is x2 = -51 +/- 52.924,
= 1.924 or -103.924
The only real solution for x is +/- sqrt 1.924
= +/- 1.387
In your second problem, the highest point is where
dh/dx = -.06x + 3 = 0
It occurs at x = 60 m
The height there is -.03*60^2 + 3*60 = 72 m
For the second one, I am going to use Calculus
h(x) = -.03x^2 + 3x
h'(x) - -.06x + 3
= 0 for a max of h
-.06x = -3
x = 50
so h(50) = -.03(2500) + 3(50)
I made a math error on the second one. I can't even punch a calculator anymore. Go with Reiny's answer. On the first problem, I assumed your first equation was correctly typed. If the minus sign should not have been in front of x^4, as Reiny assumed, you get an easly factored equation and Reiny's answers
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