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hahajamiexlyn · Sep 4, 2007, 03:36 PM

I was assigned a 15 page math packet and here's the problems left over that my friend and I cannot figure out for our lives:

1. Solve the following by factoring and making appropriate sign charts

*this one I know has to be in radians, but I can't figure out after that*

2. Solve the equation for x

*this one seems easy, but I think maybe there's a typo because when you make a common denominator, it doesn't work out in the end so I don't know *

3. Find the exact value of the following without a calculator

* this one I just flat out don't know how to do, so if you could explain it to me, I can know how to do the other ones that are just like it*

4. Solve each equation on the interval [0,2pi)

*this one I got stuck on but I'm going to put my work up so if you could tell me what I'm doing wrong ?

THANK YOU TO ANYONE WHO HELPS ON EVEN JUST ONE OF THESE PROBLEMS :D

have a good day

galactus · Sep 5, 2007, 04:23 PM

#2:

$\frac{x}{x-2}+\frac{2x}{4-x^{2}}=\frac{5x}{x+2}$

If you multiply by the LCM: $(x-2)(4-x^{2})(x+2)$ , you can cancel and end up with:

$4x^{4}-10x^{3}-16x^{2}+40x=0$

Which factors to: $2x(x-2)(x+2)(2x-5)=0$

There are 4 solution, not all will necessarily be solutions to the given equation.

#4. $8cos^{2}(x)-2cos(x)-1=0$

Let $u=cos(x)$

Then you have a quadratic: $8u^{2}-2u-1=0$

Now solve the quadratic.

s_cianci · Sep 8, 2007, 11:09 AM

1. Set it so that the expression is > 0. Factor out the GCF. Find the roots of each factor. Plug in test values to determine the sign of each factor on each interval determined by the roots. Since the product is desired to be positive, you'll want an even number of negative factors.
2. Try it again. It's actually pretty straightforward. Hint: you may want to multiply your middle expression, 2x/(4 - x^2), by -1.
3. Simply plug in the values of sec 180 and cot 90 and do the arithmetic.
4. For this one, you really want to leave it = 0, then factor and set each factor = 0. Use a scientific calculator to determine any cosine value that isn't quadrantal or 30, 45 or 60.