Sailors need to consider the speed of the wind when adjusting the sails on their boat. The force F (in pounds per square foot) on a sail when the wind is blowing perpendicular to the sail can be modeled by the function F = 0.004v2 where v is the wind speed (in knots).
Find the wind speed that will produce a force of 2.5 pounds per square foot on a sail.

- anonymous

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- schrodinger

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- anonymous

somebody?
@terenzreignz ?

- anonymous

Any good at word problems?

- terenzreignz

Well, let's have a real good think...

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## More answers

- anonymous

I may as well be reading greek myself

- anonymous

speaking of which thanks for the help on the exponents! i finally grasp them!

- anonymous

ack my interenet is coming in and out! if i disapear then that's why

- terenzreignz

Glad to hear it. I trust you'll excuse me for not being able to drill you on word problems, though, for two reasons...
ONE, All word problems are different, there is no single unbreakable method to do them, you have to give them real thought...
TWO, making up word problems takes time, not like those things I make you simplify...
Having said that, let's work on this one...

- anonymous

Allrgihty :)

- terenzreignz

If you're given models (fancy word for equations), use them.
They're probably key.
We have...
\[\Large F=0.004v^2\]

- terenzreignz

Where F is the force, and v is the speed, aye?

- anonymous

OK So that means
\(\Large\ 2.5=0.004v^{2}\)

- terenzreignz

Yes, exactly, and just solve for v.

- anonymous

Thanks :D

- anonymous

How is your smart score NOT a hundred?

- terenzreignz

Well...
http://openstudy.com/users/satellite73
There's no way anybody's catching up to those stats anytime soon
(btw, there can only be one user with a 100 ss)

- anonymous

so v=25 or -25 right?

- terenzreignz

No...

- anonymous

opppsss let me try that again

- anonymous

Help me here

- anonymous

That sounded pushy sorry

- terenzreignz

\[\Large\ 2.5=0.004v^{2}\]
What to do?
Well, divide both sides by 0.004.

- anonymous

Ack should have thought of that

- anonymous

OK so \(\LARGE\ 625=v^{2}\)

- anonymous

Then what do I do?

- terenzreignz

You have \[\Large v^2 = 625\]
So, it's the square of v, so to get v, what do you do?

- anonymous

So that would be 25 right?

- terenzreignz

Yes.

- anonymous

\(\LARGE\ 25^{2}\) is 625

- anonymous

On these questions do I have to have two answers?
Becusae I know on some questions similer to this it's like
x= # or #

- terenzreignz

Well, what else other than 25 would yield 625 when squared?

- anonymous

well -25^2= -625

- anonymous

But I don't think that would be a vaild answer?

- terenzreignz

True that \[\Large -25^2 = -625\]
But...
\[\large (-25)^2= (-25)(-25) = (-1)(25)(-1)(25)=(-1)(-1)(25)(25)\\\large =(25)(25)= 625\]

- anonymous

Wait...You lost me!

- terenzreignz

/sigh/
WHAT is a negative times a negative?

- anonymous

OHHH! Sorry positive :P

- anonymous

all those parenthesis and multiplication caught me off guard sorry

- terenzreignz

Riiight.
And WHAT is
\[\Large (-25)^2 = (-25)(-25) = \color{red}?\]

- anonymous

625!

- terenzreignz

We can't have this... when you're in elementary algebra, I (and I'm pretty sure your instructor, too) \(\large \color{red}{expect}\) you to have firm grasp of your pre-algebra... particularly dealing with negatives.

- terenzreignz

And yes, the 'other' answer is -25
SINCE
-25 times -25 is POSITIVE 625.

- anonymous

My mistake!
I promise not to make it more then once errr atleast twice :)

- terenzreignz

You mean... you promise you won't do it AGAIN.
EVER.
okay? ^_^

- anonymous

Thanks TJ :) Slow learner over here :P

- terenzreignz

Can I trust you to not make that mistake again? ^_^

- anonymous

Ha all I can do is try :)

- anonymous

and practice!

- terenzreignz

LOL
The correct answer is no. You WILL make that mistake again... (because you're human)
So the best we can do is try to prevent them.
That's why you will do these for me...
Now.
Solve for the unknown:
\[\Large 72 = 2\color{red}x^2\]
\[\Large 78 = 3\color{blue}y^2+3\]

- anonymous

Allrighty :) One second

- terenzreignz

...and how old are you again?

- anonymous

algebra 1

- terenzreignz

That's not an age I know of... -.-

- anonymous

OK the first equation would be x=6 or -6

- terenzreignz

That's good. Now the second.

- anonymous

working on it one second

- anonymous

y=5 or -5

- terenzreignz

Okay... I accept your apology. ^_^

- anonymous

Great :D

- terenzreignz

Let me just make sure you know what you're doing... Try this one:
\[\Large -7v^2 =343\]

- anonymous

OK

- anonymous

x=7 or -7

- terenzreignz

Nope.

- terenzreignz

Let's try v=7, shall we?
\[\Large -7(\color{red}7)^2\]\[\Large = -7(49)\]\[\Large = -343\]\[\Large \color{red}\ne 343\]

- anonymous

Oh OK the negative threw me off let me try once more

- terenzreignz

Just remember to be more careful... there is no 'try once more' when exams come.

- anonymous

That's the truth
OK I need help

- terenzreignz

Okay.
Pay attention:

- anonymous

ok

- terenzreignz

\[\Large -7v^2 =343\]

- terenzreignz

\[\Large \color{blue}{-7}v^2 =343\]
THIS is negative.

- terenzreignz

\[\Large -7\color{red}{v^2} =343\]THIS is positive.

- terenzreignz

If we multiply them:
\[\Large \color{blue}{-7}\color{red}{v^2} =343\]
Their product should be negative!
\[\Large \color{blue}{-7v^2} =343\]

- terenzreignz

Everything understood?

- anonymous

Yup :) I think

- terenzreignz

Remember that a square is always positive, okay (unless it's the square of zero)

- anonymous

so -7*v^2 =-343

- terenzreignz

Okay?

- terenzreignz

NO! Listen first... and just answer when I ask you.

- anonymous

Ok

- terenzreignz

Okay, so you understand why \[\Large -7\color{red}{v^2} =343\]this part is always positive, right?

- anonymous

right

- terenzreignz

So, since -7 is negative and v^2 is positive, their product -7v^2 should be negative, right?

- anonymous

Right

- terenzreignz

So we know that this part \[\Large \color{blue}{-7v^2} =343\] is negative, so ask yourself...

- anonymous

how did we get a positive?

- terenzreignz

exactly.
Why is something we're sure is negative... equal to a positive?

- terenzreignz

We know that -7v^2 is negative, and yet it's made to be equal to 343, a positive.

- terenzreignz

Then there are NO SOLUTIONS.

- anonymous

TRICK QUESTION

- anonymous

Wait right?

- terenzreignz

Any questions?

- terenzreignz

Okay, quick drill... what is
\[\Large -8^2 = \color{red}?\]

- anonymous

no...sorry there was no answer to that question! I keep forgetting a question can have no soultions
http://barfblog.com/wp-content/uploads/2013/06/homer-doh.jpg

- anonymous

That would be-64

- terenzreignz

Good. What about \(\Large (-4)^2 = \color{red}? \)

- anonymous

-16

- terenzreignz

And, as predicted, you made that mistake... again...

- anonymous

what mistake?

- anonymous

ekkk 16

- anonymous

SIXTEEN!

- terenzreignz

Look, if you see the parentheses encompassing the minus sign, then, the minus sign itself is also squared. Got it?

- anonymous

NO NEGATIVE!

- terenzreignz

Don't interrupt. Obviously, if I already said no to -16, it would be 16. -.-

- anonymous

sorry trying to redeem myself

- terenzreignz

Well, you don't exactly redeem yourself on true-false questions, now do you? :P
You tell me 'false', and I say it's wrong, and then you tell me 'true', does that redeem it?
I don't think so :P
We need more drills...

- anonymous

No it doesn't redeem it :P OK thanks for not throwing your hands up in frustration and closing openstudy! (well you could have done that....

- terenzreignz

I could...but, I risk some peace of mind. Now, evaluate these, as quickly as you can:
4²
-10²
(-3)²
-7²
(-9)²
Go.

- anonymous

OK 16
100
9
49
81

- terenzreignz

Okay, now evaluate these...
(-2)²
-2²
-(-4)²
(-5)²
10²
Go.

- anonymous

OK
4
4
-16
25
100

- anonymous

I wasn't for sure on the
-(-4)^2

- terenzreignz

I won't accept it if it isn't final. Make up your mind.

- anonymous

Ok 16

- terenzreignz

You scored.... 60%.

- terenzreignz

Not good enough.

- anonymous

ouch

- terenzreignz

^_^
Here's the proper way to do things
\[\Large \left[\begin{matrix}TJ's \ Scale & \\ 0\%-80\% &pathetic\\80\% - 95\%&lacking\\95\%-99\% & passable\\100\%&good \ enough\end{matrix}\right]\]

- terenzreignz

Now, let's work on your common errors...

- anonymous

(-2)²=4
-2²=4
-(-4)²=-16
(-5)²=25
10²=100

- terenzreignz

Forget those, they're history.
What YOU need to understand is the difference between
(-2)²
and
-2²

- anonymous

OK

- terenzreignz

All right?
What (-2)² means is that you're INCLUDING the minus-sign in what you're squaring.
So, what (-2)² REALLY means is
(-2)(-2).
Now, what is this equal to?

- anonymous

4

- terenzreignz

Now, what THIS means:
-2²
is you square the 2 (alone!) *first*
-(2)(2)
and then put the negative sign AFTER.
The gist of it? the minus-sign is NOT squared to produce a plus sign.
So...
-2² = -(2)(2)
is equal to?

- anonymous

-4

- terenzreignz

Baby steps? ^_^
Now, do these:
(-1)²
-4²
-(-8)²
9²
5²-4²

- terenzreignz

And for goodness' sake, make it ... *good enough*

- anonymous

OK So that would be
1
-16
-64
81
9

- terenzreignz

See? Good enough ^_^

- anonymous

yayy!

- terenzreignz

Now, do this:
A word problem. Let's see what you're capable of.
When you have a right triangle, the longest side is called the hypotenuse.
The other two sides are called legs.
They are related by what's called the Pythagorean Theorem.
It states that
a² + b² = c²
Where c is the length of the hypotenuse, and a and b are the two legs.
If c = 13, and b = 5, find a.

- anonymous

OK
a^2+5^2=13^2
a^2+25=169
a^2=144
a=12 or -12

- terenzreignz

Okay... I say good enough :)
But with word problems, you have to also consider context.

- terenzreignz

We are talking about lengths here...there are no *negative* lengths...

- anonymous

Opps

- terenzreignz

So, 12 is the only answer.

- anonymous

OK! Got it!

- terenzreignz

Don't worry about it, each word problem always has its own twists...

- anonymous

Thanks TJ! I got to go! Thanks for all your help :)

- anonymous

You probally cringe everytime you see me online :P

- terenzreignz

I don't, in fact, it feels great when you understand.
I need to go too
Practice.
Signing off.
---------------------------------------
Terence out.

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