Radical equations
Applying Radical Equations 1 Applying Radical Equations 1
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- The distance a person can see on a clear day is estimated by
- the formula v is equal to 1,225 times the square root of
- a, all of that over 1,000, where v is visibility.
- So that right there is visibility in miles, and a is
- equal to altitude.
- Fair enough.
- Now, they say if Jerome can see for 150 miles-- so that's
- how far he could see; so that is the visibility, that is v--
- about how far above the ground is he?
- So they want to know what the altitude is.
- About how far off the ground is he?
- This is a.
- And this is what we don't know.
- We know that his visibility is 150 miles.
- We want to know what a is.
- So we could look at this formula for visibility as a
- function of altitude here.
- We know what the visibility is.
- It is 150 miles.
- v is 150 miles.
- So we can say that v, or 150 miles, is equal to 1,225 times
- the square root of a-- a is how far above the ground he
- is-- times the square root of a, all of that over 1,000.
- Now we can multiply both sides of this equation.
- We want to isolate this radical here, so that we can
- solve for it.
- What we can do is we can multiply both sides of this
- equation times 1,000 over 1,225.
- Let me scroll to the left a little bit.
- 1,000 over 1,225.
- And the whole point of that is so that we can isolate the
- square root of a.
- This 1,000 cancels with that 1,000.
- That 1,225 cancels with that 1,225.
- And we get-- and I always like to have the variable I'm
- solving for on the left-hand side, so let's put it there.
- So let me just switch sides as well.
- So we get the square root of a is equal to all of this
- business over here, is equal to 1,000 times this 150, all
- of that over 1,225.
- And it looks like there's some simplification
- that we can do here.
- Both of these numbers seem divisible by 25.
- This number up here, 150, that's 25 times 6.
- So let me write this.
- This is 25 times 6.
- And this number right here, what is this?
- This is 25 times-- let's see, 12 times 4 is 48.
- And you're going to have one more.
- 25 times 49, if I'm doing my math right.
- Let me double check that.
- 49 times 25.
- 9 times 5 is 45.
- 4 times 5 is 20, plus 4 is 24.
- Get rid of that, put a 0 here.
- 2 times 9 is 18.
- 2 times 4 is 8, plus 1 is 9.
- We get a 5.
- Get a 12.
- Yep, it's 1,225.
- So this is 25 times 49.
- This is 25 times 6.
- Let me cancel this.
- Cross that out.
- This 25 cancels with that 25.
- And so, does it look-- you know, 49 is 7 times 7.
- So that looks about as simple as we can get it.
- So this is equal to-- we could write it as 6,000 over 49 is
- equal to the square root of a.
- So if we want to solve for a, we can square both sides of
- this equation.
- So let's do that.
- Let me rewrite this.
- So you have the square root of a is equal to 6,000 over 49.
- We want to square both sides of this equation.
- So we square both sides of this equation and we will get
- a, the altitude, that how far above the ground Jerome is, is
- going to be equal to-- well, 6,000 squared over 49 squared.
- Or you could view it as 6,000 divided by 49 squared.
- So let's figure out what that number is just to
- get a sense of things.
- And let me get a calculator out for this one.
- I'll just get a calculator out.
- Let me clear it out.
- All right, so we want to do 6,000 squared divided by 49
- squared, which is equal to 1,400-- or, we'll round up,
- 14,994 feet.
- This is equal to 14,993 feet.
- I'm assuming that this equation is taking our feet,
- our altitude in feet.
- They didn't mention it here, but I'm assuming that in feet,
- because that makes sense.
- If you can see for about 150 miles, it makes sense that
- you're about 15,000 feet in the air.
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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