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03:07

Taylor S.

Using Models Use the model given to answer the questions about the object or process being modeled. Arizonans use an average of 40 gal of water per person each day. The number of gallons $W$ of water used by $x$ Arizonans each day is modeled by $W=40 x$ . (a) Make a table that gives the number of gallons of water used for each $1000-$ person change in population, from 0 to $5000 .$ (b) If the pressure is $30 \mathrm{lb} / \mathrm{in}^{2},$ what is the depth? (b) What is the population of an Arizona town whose water usage is $120,000$ gal per day?

0:00

Kyle I.

Using Models Use the model given to answer the questions about the object or process being modeled. The distance $d$ (in mi) driven by a car traveling at a speed of $v$ miles per hour for $t$ hours is given by $$d=v t$$ If the car is driven at 70 milh for 3.5 $\mathrm{h}$ , how far has it traveled?

03:34

02:13

Using Models Use the model given to answer the questions about the object or process being modeled. A mountain climber models the temperature $T$ ( in $^{\circ} \mathrm{F}$ ) at elevation $h$ (in ft) by $$T=70-0.003 h$$ (a) Find the temperature $T$ at an elevation of 1500 $\mathrm{ft}$ . (b) If the temperature is 64$^{\circ} \mathrm{F}$, what is the elevation?

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Let's have a look at absolute value equations. Now let's before we kind of really get into absolute value equations. Let's talk about absolute value because absolute value, remember, is a distance and number is from zero. For example, the absolute value of three is three because it's three units away from zero. The absolute value of negative six is six, because even though it's negative, it's six units away from zero. So we're always trying to find how many units it is from zero. So that's really important. When we look at absolute value equations, let's look at a very simple one. So let's look at the absolute value equation. Three. X Absolute value. Three. X equals Not now. When you're solving an absolute value equation, there's a couple of rules you want to dio one you want to simplify, just as if we would do any equation you want to simplify. You want to get the absolute value by itself, though. So, for example, three exes only left side of the equation by itself. The second one is you're going to work, talked to taps, and here's where it's going to get a little different. So the first time you work it all you're going to do is basically you're going to drop the absolute value bars because now you're wanting to see what would it be if it was positive? So we're gonna leave it at three x equals not. And we would divide by three. So X could bay three for the absolute value of three times X thio equal nine x could be three. But X could also be another number. So the second time you work it, what's inside The absolute value bars will stay the same. So we're still going to use three eggs, but we're going to change everything outside. So instead of positive none, we're going to change it to negative. Not we're gonna divide by three. So X could equal negative three. So here's how why that works. So we said we're looking at the absolute value of three X, and we're saying that that would equal not so. Whatever. The absolute value of three exes is non units away from zero. So if x equals positive three, that means that three times three is none, and the absolute value of none is not. And if x equals negative three Nate three times. Negative three is negative nine. And the absolute value of negative nine is positive. None. So that is why it works. So let's look at another one. Let's look at the absolute value of negative four plus five. X equals 16. So we see a simplified because it was the absolute value section is all by itself. So now we're gonna work it twice. First time we work it, all we're gonna do is basically dropped the absolute value bar. So negative four plus five x equal 16. We're gonna add forward to both sides, so we're gonna have five x equals 20. We're gonna divide by five X is gonna equal four. So our first solution will be four. And we're gonna ride our answers in a solution set. So I'm gonna go ahead and write that one in. Then I'm gonna work it the second time. The second time I work it. I'm gonna leave everything inside the absolute value bars alone, so I'm still gonna have negative four plus five X. But this time, instead of positive 16, I'm gonna have negative 16, so we'll add four to both shots. So five X equals negative. 12. Divide by five, and that can't be simplified anymore. So X could equal negative 12 over five. So that is the second part of my solution set. Well, remember how our first rule is? We're going to simplify. Let's look at what we can't. We have to simplify. So let's look at the problem. Three. Tom's The absolute value of negative eight X plus eight equals 80. Now, what's inside the absolute value bars is negative. Eight x. I don't wanna mess with that. I want to leave that alone. I wanna move everything else away. So I wanna move this three and this plus eight. So let's start with the plus eight. So let's subtract eight on both sides. So now I have three times the absolute value of negative eight X equals 72. I still have this three over here, though, that I still need to get rid of it. So we're gonna get rid of it that by dividing both sides by three. So now I have the absolute value of negative eight X equals 24. Now, this is what I'm gonna work out twice. I'm not going to go back to my original problem because I would just have to go through these steps again. So let's work out the absolute value of negative eight X equals 24. We're gonna work it twice. First time we're gonna have negative eight X equals 24 The vibe by negative eight. So X is going to equal negative three. The second time will be negative. Eight. X equals negative. 24. The vibe. A negative eight x is going to equal positive three. So my solution set is negative three three.

Linear Equations and Functions

Linear Equations and Inequalities

Matrices and Determinants

Quadratic Equations

Applications of Trigonometric Functions

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