Question

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.

Answer 1

somebody?
@terenzreignz ?

Answer 2

Any good at word problems?

Answer 3

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

Answer 4

I may as well be reading greek myself

Answer 5

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

Answer 6

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

Answer 7

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...

Answer 8

Allrgihty :)

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

Yes, exactly, and just solve for v.

Answer 13

Thanks :D

Answer 14

How is your smart score NOT a hundred?

Answer 15

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)

Answer 16

so v=25 or -25 right?

Answer 17

No...

Answer 18

opppsss let me try that again

Answer 19

Help me here

Answer 20

That sounded pushy sorry

Answer 21

\[\Large\ 2.5=0.004v^{2}\]

What to do?
Well, divide both sides by 0.004.

Answer 22

Ack should have thought of that

Answer 23

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

Answer 24

Then what do I do?

Answer 25

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

Answer 26

So that would be 25 right?

Answer 27

Yes.

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

well -25^2= -625

Answer 32

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

Answer 33

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

Answer 34

Wait...You lost me!

Answer 35

/sigh/
WHAT is a negative times a negative?

Answer 36

OHHH! Sorry positive :P

Answer 37

all those parenthesis and multiplication caught me off guard sorry

Answer 38

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

Answer 39

625!

Answer 40

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.

Answer 41

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

Answer 42

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

Answer 43

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

Answer 44

Thanks TJ :) Slow learner over here :P

Answer 45

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

Answer 46

Ha all I can do is try :)

Answer 47

and practice!

Answer 48

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:
\[\Large 72 = 2\color{red}x^2\]
\[\Large 78 = 3\color{blue}y^2+3\]

Answer 49

Allrighty :) One second

Answer 50

...and how old are you again?

Answer 51

algebra 1

Answer 52

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

Answer 53

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

Answer 54

That's good. Now the second.

Answer 55

working on it one second

Answer 56

y=5 or -5

Answer 57

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

Answer 58

Great :D

Answer 59

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

Answer 60

OK

Answer 61

x=7 or -7

Answer 62

Nope.

Answer 63

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

Answer 64

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

Answer 65

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

Answer 66

That's the truth
OK I need help

Answer 67

Okay.
Pay attention:

Answer 68

ok

Answer 69

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

Answer 70

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

Answer 71

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

Answer 72

If we multiply them:
\[\Large \color{blue}{-7}\color{red}{v^2} =343\]

Their product should be negative!
\[\Large \color{blue}{-7v^2} =343\]

Answer 73

Everything understood?

Answer 74

Yup :) I think

Answer 75

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

Answer 76

so -7*v^2 =-343

Answer 77

Okay?

Answer 78

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

Answer 79

Ok

Answer 80

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

Answer 81

right

Answer 82

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

Answer 83

Right

Answer 84

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

Answer 85

how did we get a positive?

Answer 86

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

Answer 87

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

Answer 88

Then there are NO SOLUTIONS.

Answer 89

TRICK QUESTION

Answer 90

Wait right?

Answer 91

Any questions?

Answer 92

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

Answer 93

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

Answer 94

That would be-64

Answer 95

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

Answer 96

-16

Answer 97

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

Answer 98

what mistake?