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The distance a person can see on a clear day is estimated by

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the formula v is equal to 1,225 times the square root of

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a, all of that over 1,000, where v is visibility.

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So that right there is visibility in miles, and a is

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equal to altitude.

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Fair enough.

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Now, they say if Jerome can see for 150 miles-- so that's

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how far he could see; so that is the visibility, that is v--

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about how far above the ground is he?

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So they want to know what the altitude is.

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About how far off the ground is he?

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This is a.

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And this is what we don't know.

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We know that his visibility is 150 miles.

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We want to know what a is.

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So we could look at this formula for visibility as a

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function of altitude here.

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We know what the visibility is.

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It is 150 miles.

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v is 150 miles.

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So we can say that v, or 150 miles, is equal to 1,225 times

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the square root of a-- a is how far above the ground he

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is-- times the square root of a, all of that over 1,000.

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Now we can multiply both sides of this equation.

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We want to isolate this radical here, so that we can

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solve for it.

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What we can do is we can multiply both sides of this

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equation times 1,000 over 1,225.

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Let me scroll to the left a little bit.

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1,000 over 1,225.

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And the whole point of that is so that we can isolate the

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square root of a.

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This 1,000 cancels with that 1,000.

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That 1,225 cancels with that 1,225.

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And we get-- and I always like to have the variable I'm

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solving for on the left-hand side, so let's put it there.

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So let me just switch sides as well.

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So we get the square root of a is equal to all of this

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business over here, is equal to 1,000 times this 150, all

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of that over 1,225.

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And it looks like there's some simplification

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that we can do here.

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Both of these numbers seem divisible by 25.

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This number up here, 150, that's 25 times 6.

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So let me write this.

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This is 25 times 6.

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And this number right here, what is this?

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This is 25 times-- let's see, 12 times 4 is 48.

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And you're going to have one more.

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25 times 49, if I'm doing my math right.

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Let me double check that.

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49 times 25.

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9 times 5 is 45.

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4 times 5 is 20, plus 4 is 24.

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Get rid of that, put a 0 here.

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2 times 9 is 18.

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2 times 4 is 8, plus 1 is 9.

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We get a 5.

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Get a 12.

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Yep, it's 1,225.

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So this is 25 times 49.

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This is 25 times 6.

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Let me cancel this.

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Cross that out.

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This 25 cancels with that 25.

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And so, does it look-- you know, 49 is 7 times 7.

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So that looks about as simple as we can get it.

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So this is equal to-- we could write it as 6,000 over 49 is

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equal to the square root of a.

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So if we want to solve for a, we can square both sides of

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this equation.

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So let's do that.

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Let me rewrite this.

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So you have the square root of a is equal to 6,000 over 49.

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We want to square both sides of this equation.

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So we square both sides of this equation and we will get

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a, the altitude, that how far above the ground Jerome is, is

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going to be equal to-- well, 6,000 squared over 49 squared.

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Or you could view it as 6,000 divided by 49 squared.

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So let's figure out what that number is just to

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get a sense of things.

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And let me get a calculator out for this one.

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I'll just get a calculator out.

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Let me clear it out.

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All right, so we want to do 6,000 squared divided by 49

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squared, which is equal to 1,400-- or, we'll round up,

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14,994 feet.

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This is equal to 14,993 feet.

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I'm assuming that this equation is taking our feet,

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our altitude in feet.

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They didn't mention it here, but I'm assuming that in feet,

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because that makes sense.

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If you can see for about 150 miles, it makes sense that

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you're about 15,000 feet in the air.

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