Expert: Sherry Wallin - 6/10/2009

Question
QUESTION: Hi, I am having difficulties with some math problems and was wondering if you could help me.  I would appreciate any help.  Thankyou!  

1. Does the vertex of the graph of y = -99(x - 7)2 - 2 is a minimum value?

2. Solve the system, y^2 - 4x^2 = 4 and y = 2x.

3. Is there a solution to x^2 - y^2 = 3 and y^2 - x^2 = 3

4. Which quadrant is the terminal side of a -191° angle in?

5. What is the coterminal of a 230° angle?

6. Solve 8^x < 25.  
 




ANSWER: Hi Kelly~
    I'm not sure what your goal is. Were you looking for answers or ways to learn how to do these problems yourself? I will give you some instruction and hints, okay?

1)  Recall that parabolas open up when a>0 and open down when a<0. When a>0 the graph has a minimum and when it opens down it has a maximum therefore a graph with a>0 has a minimum because the parabola opens up and vice versa for when a<0. So merely determine the sign on a and answer. By the way you wrote:  y = -99(x - 7)2 - 2 and I believe you meant y = -99(x - 7)^2 - 2, yes??

2)  The easiest way to do this problem is to substitute y = 2x into y^2 giving you (2x)^2 -4x^2 = 4 so that you now have 4^2-4x^2 = 4. What do you think the solution is??

3)  Here you can try substitution but notice that the second equation is the opposite of the other on its left, i.e, y^2-x^2 = -1(x^2-y^2)
= 3. Multiply the whole 2nd equation by -1 getting x^2-y^2 = -3. But from the first equation you know that x^2-y^2 = 3. How can it be both 3 and -3????

4)  Remember we measure positive angles counter clockwise so we measure negative angles clockwise. So traverse 191 degrees going clockwise to see where you are.

5)  Here you need to be thinking about the definition of coterminal:
Two angles are said to be coterminal if they have the same terminal side. This means you want to take another lap around the circle sort to speak, which means another 360 degrees, right?

6)  Hmmm...8^x = 25. How about taking the natural log of both sides?
ln 8^x = ln 25 and then x*ln 8 = ln 25 so that x = [ln 25]/[ln 8]??

Math Prof

---------- FOLLOW-UP ----------

QUESTION: I usually find that both the answer and the explanation on how to do the problem is of the most help.  I am a homeschooler working with an online high school, so when I don't understand a question, I'm stuck.  It usually takes 1-2 days for my teacher to respond to my questions so I turn here for help.  These are all problems that I have already solved, (and ones that aren't being graded either, I don't cheat) I just wanted to make sure I was doing the problems correctly.  If you could give me the answers, that would be great.  If not, thanks anyway, you've already been a great help.

Answer
1) -99<0 so the parabola opens down and has maximum
2) 4x^2-4x^2 = 4 is never true, i.e., 0 = 4 is never true so no solution
I made a typing mistake above, it should read 4x^2-4x^2 = 4 not 4^2-4x^2 = 4, so you see 4x^2-4x^2 = 0 !=4 ever
3)  no solution
4)  360 - 191 = 169 degrees in the second Quadrant
5)  230 + 360 = 590 which is just one of an infinite of coterminal angles
6) put into your calculator if you want a numerical value different from
[ln 25]/[ln 8] approx 1.55

Happy mathing!

Math Prof