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1 Last checkud at 18Post-TestPre-Test 8 9 Thefollexingdata Subject...

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1 Last checkud at 18Post-TestPre-Test 8 9 Thefollexingdata Subject

1 Last checkud at 1 8 Post-Test Pre-Test 8 9 Thefollexingdata Subject



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The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. $$ \begin{array}{|c|ccccccc|}\hline x & {-3} & {-2} & {-1} & {0} & {1} & {2} & {3} \\ {f(x)} & {11} & {9} & {7} & {5} & {3} & {1} & {-1} \\ {g(x)} & {-8} & {-3} & {0} & {1} & {0} & {-3} & {-8} \\ \hline\end{array} $$ $$ \begin{array}{ll}{\text { (a) }(f \circ g)(1)} & {\text { (b) }(f \circ g)(2)} \\ {\text { (c) }(g \circ f)(2)} & {\text { (d) }(g \circ f)(3)} \\ {\text { (e) }(g \circ g)(1)} & {\text { (f) }(f \circ f)(3)}\end{array} $$

Okay. So now let's factory uh this expression. Okay so I want to first write this as five p cube minus two P squared. Uh Sorry to q squared cube. Okay so I can't use the formula for the cube. Uh Subtraction, You know A a cube. My minus B cube. Okay. I can use that formula. So I have a minus B. Times a squared plus a B plus b squared. Okay. Okay. So the next step I want to do is I want to continue factoring out this. Okay, so I have five p -2, cute and squared time. Five P plus mm hmm Two Q squared squared. Okay. Okay. So maybe we cannot do that because we lacked one B. Okay. We only have one. Will be but we need to uh be right so two plus two times a times B. But we'll only have plus A times B. Okay? So what what do we do now? Uh it's any further simplification or further factory process? We can do okay. uh maybe it's just leave it here. Okay, We cannot do further simplification or further factoring out, so this is a firm after a factory out.

So you're for the given values. But on a he wants a person type of your value. How Marie possible when I go So I got on the upper deck it toe act Dwayne de it percentile on Wayne Be 50 person day value Gioia Hamadi past one cable robbery Go Cassie Bahamas. Calculate cars at that point even replied with 20 divided by 100 is basically do full. I know 25 multiplied by. This will be do NT This will be basically 20 my multiplied by 25 by 100 2500 And this is going to be basically five. OK, so you can see that the value is going to be up fourth and the fifth, but so that's t on so

This exercise is all about going through survey questions to see if there's a floor in them. If there is one we're gonna identify on, rewrite the question more appropriately on the left. As with previous exercises in this chapter, I've read in the five most common mistakes. Just kind of give us some guidance. So this question So Exercise five asks, how long have he studied for this examination? So opens his bayous. But if you look at this bit here is asking how long Now, if you were the person collecting all the data for this survey saying how long is almost too too vague, it doesn't really. You don't know what you're saying in minutes in our than days. Um, so this is not specific enough. No specific. So I'm saying that friends in that sense is leads quite confusing question because you don't know if you don't know how to answer. A question in itself lies confusing for the person answering the survey. Um, so to rewrite this more appropriately, we're gonna happen. We're gonna be more specific when asking them How long So we could say how many hours or how many minutes in your hours. Have you spent? How many hours have you spent swelling for this? Exact On the sign of a good survey. Question is it's really clear what you're gonna put The answer is really easy. You just say, Oh, I've spent six hours studying. Well, I spent 40 hours studying, whereas with this top one, the original one, if you have to.

In this problem we're giving this polynomial one third X cubed or x squared minus two. X plus nine equals zero. And asked to solve this. So to solve this means to find what values of X. Make this true. Okay, well, first of all, Let's multiply by three so that we get rid of that fraction here. So we have X squared minus six. X plus 27 equals zero. Okay. Yeah, It's kind of hard to find factors of 27. They give us -6 by difference. So trying to factor this into two factors is kind of hard to do. So let's use the quadratic equation to find the solutions to this polynomial here. So by the quadratic equation X equals minus B. Let's plus six plus or minus the square root B squared -6 square deaths 36 -4 times a is one. C is 27 All That's over to a blaze once. That's too All right, so this is six plus or minus. Let's see the square root of what? Of course all this will be over to now. Four times 27. So that's 80 That's 108 That's negative. And we had 36 to it. And so I'm left with -72. All right. Well, I could take the negative. I'm gonna make this isn't square with a negative one, which is I are complex number. So this is six plus or minus the square root 72 times I all over to. Okay, 72. Well, I could factor a 36 out of that and take the screw to 36 which is six. So this is six plus or minus six times the square root of two. I was gonna take 36 out. I'll leave it to underneath there. Well, that's over too. So that means x is our solutions in our X equals two, goes into 6 3 times. That's three. Well, sir, minus 2006. 3 times square to to I. And there are two solutions to complex numbers. Complex college. He gets there for this problem.


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