anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
somebody? @terenzreignz ?
anonymous
  • anonymous
Any good at word problems?
terenzreignz
  • terenzreignz
Well, let's have a real good think...

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More answers

anonymous
  • anonymous
I may as well be reading greek myself
anonymous
  • anonymous
speaking of which thanks for the help on the exponents! i finally grasp them!
anonymous
  • anonymous
ack my interenet is coming in and out! if i disapear then that's why
terenzreignz
  • 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
  • anonymous
Allrgihty :)
terenzreignz
  • terenzreignz
If you're given models (fancy word for equations), use them. They're probably key. We have... \[\Large F=0.004v^2\]
terenzreignz
  • terenzreignz
Where F is the force, and v is the speed, aye?
anonymous
  • anonymous
OK So that means \(\Large\ 2.5=0.004v^{2}\)
terenzreignz
  • terenzreignz
Yes, exactly, and just solve for v.
anonymous
  • anonymous
Thanks :D
anonymous
  • anonymous
How is your smart score NOT a hundred?
terenzreignz
  • 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
  • anonymous
so v=25 or -25 right?
terenzreignz
  • terenzreignz
No...
anonymous
  • anonymous
opppsss let me try that again
anonymous
  • anonymous
Help me here
anonymous
  • anonymous
That sounded pushy sorry
terenzreignz
  • terenzreignz
\[\Large\ 2.5=0.004v^{2}\] What to do? Well, divide both sides by 0.004.
anonymous
  • anonymous
Ack should have thought of that
anonymous
  • anonymous
OK so \(\LARGE\ 625=v^{2}\)
anonymous
  • anonymous
Then what do I do?
terenzreignz
  • terenzreignz
You have \[\Large v^2 = 625\] So, it's the square of v, so to get v, what do you do?
anonymous
  • anonymous
So that would be 25 right?
terenzreignz
  • terenzreignz
Yes.
anonymous
  • anonymous
\(\LARGE\ 25^{2}\) is 625
anonymous
  • 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
  • terenzreignz
Well, what else other than 25 would yield 625 when squared?
anonymous
  • anonymous
well -25^2= -625
anonymous
  • anonymous
But I don't think that would be a vaild answer?
terenzreignz
  • 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
  • anonymous
Wait...You lost me!
terenzreignz
  • terenzreignz
/sigh/ WHAT is a negative times a negative?
anonymous
  • anonymous
OHHH! Sorry positive :P
anonymous
  • anonymous
all those parenthesis and multiplication caught me off guard sorry
terenzreignz
  • terenzreignz
Riiight. And WHAT is \[\Large (-25)^2 = (-25)(-25) = \color{red}?\]
anonymous
  • anonymous
625!
terenzreignz
  • 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
  • terenzreignz
And yes, the 'other' answer is -25 SINCE -25 times -25 is POSITIVE 625.
anonymous
  • anonymous
My mistake! I promise not to make it more then once errr atleast twice :)
terenzreignz
  • terenzreignz
You mean... you promise you won't do it AGAIN. EVER. okay? ^_^
anonymous
  • anonymous
Thanks TJ :) Slow learner over here :P
terenzreignz
  • terenzreignz
Can I trust you to not make that mistake again? ^_^
anonymous
  • anonymous
Ha all I can do is try :)
anonymous
  • anonymous
and practice!
terenzreignz
  • 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
  • anonymous
Allrighty :) One second
terenzreignz
  • terenzreignz
...and how old are you again?
anonymous
  • anonymous
algebra 1
terenzreignz
  • terenzreignz
That's not an age I know of... -.-
anonymous
  • anonymous
OK the first equation would be x=6 or -6
terenzreignz
  • terenzreignz
That's good. Now the second.
anonymous
  • anonymous
working on it one second
anonymous
  • anonymous
y=5 or -5
terenzreignz
  • terenzreignz
Okay... I accept your apology. ^_^
anonymous
  • anonymous
Great :D
terenzreignz
  • terenzreignz
Let me just make sure you know what you're doing... Try this one: \[\Large -7v^2 =343\]
anonymous
  • anonymous
OK
anonymous
  • anonymous
x=7 or -7
terenzreignz
  • terenzreignz
Nope.
terenzreignz
  • 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
  • anonymous
Oh OK the negative threw me off let me try once more
terenzreignz
  • terenzreignz
Just remember to be more careful... there is no 'try once more' when exams come.
anonymous
  • anonymous
That's the truth OK I need help
terenzreignz
  • terenzreignz
Okay. Pay attention:
anonymous
  • anonymous
ok
terenzreignz
  • terenzreignz
\[\Large -7v^2 =343\]
terenzreignz
  • terenzreignz
\[\Large \color{blue}{-7}v^2 =343\] THIS is negative.
terenzreignz
  • terenzreignz
\[\Large -7\color{red}{v^2} =343\]THIS is positive.
terenzreignz
  • 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
  • terenzreignz
Everything understood?
anonymous
  • anonymous
Yup :) I think
terenzreignz
  • terenzreignz
Remember that a square is always positive, okay (unless it's the square of zero)
anonymous
  • anonymous
so -7*v^2 =-343
terenzreignz
  • terenzreignz
Okay?
terenzreignz
  • terenzreignz
NO! Listen first... and just answer when I ask you.
anonymous
  • anonymous
Ok
terenzreignz
  • terenzreignz
Okay, so you understand why \[\Large -7\color{red}{v^2} =343\]this part is always positive, right?
anonymous
  • anonymous
right
terenzreignz
  • terenzreignz
So, since -7 is negative and v^2 is positive, their product -7v^2 should be negative, right?
anonymous
  • anonymous
Right
terenzreignz
  • terenzreignz
So we know that this part \[\Large \color{blue}{-7v^2} =343\] is negative, so ask yourself...
anonymous
  • anonymous
how did we get a positive?
terenzreignz
  • terenzreignz
exactly. Why is something we're sure is negative... equal to a positive?
terenzreignz
  • terenzreignz
We know that -7v^2 is negative, and yet it's made to be equal to 343, a positive.
terenzreignz
  • terenzreignz
Then there are NO SOLUTIONS.
anonymous
  • anonymous
TRICK QUESTION
anonymous
  • anonymous
Wait right?
terenzreignz
  • terenzreignz
Any questions?
terenzreignz
  • terenzreignz
Okay, quick drill... what is \[\Large -8^2 = \color{red}?\]
anonymous
  • 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
  • anonymous
That would be-64
terenzreignz
  • terenzreignz
Good. What about \(\Large (-4)^2 = \color{red}? \)
anonymous
  • anonymous
-16
terenzreignz
  • terenzreignz
And, as predicted, you made that mistake... again...
anonymous
  • anonymous
what mistake?
anonymous
  • anonymous
ekkk 16
anonymous
  • anonymous
SIXTEEN!
terenzreignz
  • terenzreignz
Look, if you see the parentheses encompassing the minus sign, then, the minus sign itself is also squared. Got it?
anonymous
  • anonymous
NO NEGATIVE!
terenzreignz
  • terenzreignz
Don't interrupt. Obviously, if I already said no to -16, it would be 16. -.-
anonymous
  • anonymous
sorry trying to redeem myself
terenzreignz
  • 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
  • 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
  • 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
  • anonymous
OK 16 100 9 49 81
terenzreignz
  • terenzreignz
Okay, now evaluate these... (-2)² -2² -(-4)² (-5)² 10² Go.
anonymous
  • anonymous
OK 4 4 -16 25 100
anonymous
  • anonymous
I wasn't for sure on the -(-4)^2
terenzreignz
  • terenzreignz
I won't accept it if it isn't final. Make up your mind.
anonymous
  • anonymous
Ok 16
terenzreignz
  • terenzreignz
You scored.... 60%.
terenzreignz
  • terenzreignz
Not good enough.
anonymous
  • anonymous
ouch
terenzreignz
  • 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
  • terenzreignz
Now, let's work on your common errors...
anonymous
  • anonymous
(-2)²=4 -2²=4 -(-4)²=-16 (-5)²=25 10²=100
terenzreignz
  • terenzreignz
Forget those, they're history. What YOU need to understand is the difference between (-2)² and -2²
anonymous
  • anonymous
OK
terenzreignz
  • 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
  • anonymous
4
terenzreignz
  • 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
  • anonymous
-4
terenzreignz
  • terenzreignz
Baby steps? ^_^ Now, do these: (-1)² -4² -(-8)² 9² 5²-4²
terenzreignz
  • terenzreignz
And for goodness' sake, make it ... *good enough*
anonymous
  • anonymous
OK So that would be 1 -16 -64 81 9
terenzreignz
  • terenzreignz
See? Good enough ^_^
anonymous
  • anonymous
yayy!
terenzreignz
  • 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
  • anonymous
OK a^2+5^2=13^2 a^2+25=169 a^2=144 a=12 or -12
terenzreignz
  • terenzreignz
Okay... I say good enough :) But with word problems, you have to also consider context.
terenzreignz
  • terenzreignz
We are talking about lengths here...there are no *negative* lengths...
anonymous
  • anonymous
Opps
terenzreignz
  • terenzreignz
So, 12 is the only answer.
anonymous
  • anonymous
OK! Got it!
terenzreignz
  • terenzreignz
Don't worry about it, each word problem always has its own twists...
anonymous
  • anonymous
Thanks TJ! I got to go! Thanks for all your help :)
anonymous
  • anonymous
You probally cringe everytime you see me online :P
terenzreignz
  • 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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