ta123
need help on the attachment
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ta123
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LagrangeSon678
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come on no has helped you with this yet?
ta123
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no
LagrangeSon678
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should i solve this or go to sleep.....
ta123
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solve before going, please
ta123
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Oops! forgot to sleep after going
LagrangeSon678
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okay, first things first, lets find the first derivaitve of the function your where given
LagrangeSon678
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can you find it?
ta123
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9sec^(2)x
LagrangeSon678
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okay good
LagrangeSon678
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now can you please evaluate:
f(pi/4)=9sec^2(pi/4)
ta123
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square root of 2
ta123
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is it right?
LagrangeSon678
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basically to make it more accesible we can write this as:
f(pi/4)=9[sec(pi/4)]^2
LagrangeSon678
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further more we can write it as: f(pi/4)=9[1/cos(pi/4)]^2
LagrangeSon678
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then evalutaing we get:
f(pi/4)=9[1/sqrt(2)/(2)]^2
ta123
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what square root 2/2???
LagrangeSon678
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further: f(pi/4)=9[sqrt(2)]^2
which the gives us: f(pi/4)=9(2), which is 18
Thus f(pi/4)=18
LagrangeSon678
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yes, look at the unit circle, at pi/4 or 45 degrees, cos is sqr(2)/2, now if we rationalize the numerator we get just sqrt(2)
ta123
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oh, thought your doing sec
LagrangeSon678
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i rewrote secx as 1/cosx
ta123
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how come?
LagrangeSon678
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just to make is easier for me, but if realise that sec(pi/4) is sqrt(2) then more power to you
LagrangeSon678
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Now we have found the slope (m) of our line, it is 18
ta123
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y-y=m(x-x)
LagrangeSon678
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yes, but we will use this form, y=mx+b
LagrangeSon678
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i am getting sleepy lets finish this problem
ta123
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ok
ta123
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what would be the b in the slope formula
LagrangeSon678
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Now remeber we said, that we have the x coordinate in the beining of pi/4, lets evaluate the orginal function at this point, this will give us the y in our line.
f(pi/4)=9tan(pi/4)
=9(1)
=9
now we have our x which is pi/4, we have our slope which is 18, lets plug this info into our line:
9=18(pi/4)+b
this means that b is = to 9-18pi/4
LagrangeSon678
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now lets substitute everyting in:
y=18x-(36-18pi)/(4)
LagrangeSon678
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are we good?
ta123
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36??
LagrangeSon678
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i combined 9 and 18pi/4
LagrangeSon678
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yes?
ta123
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still don't see how you can 36??
LagrangeSon678
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|dw:1316152625201:dw|
ta123
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you could've just simplify it to 9pi/2
LagrangeSon678
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okay, then smarty pants do it your way, regardless we came to a correct answer
ta123
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sorry, so the finally would look like this 18x+9(1-pi/2)
LagrangeSon678
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sure
ta123
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I just look the answer choices and so which one was the closest, but how come they have it 18x+9(1-pi/2) instead of just 18x+9pi/2
LagrangeSon678
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distribute the negative sign, first
ta123
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huh?
ta123
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what negative sign?
LagrangeSon678
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|dw:1316153351852:dw|
LagrangeSon678
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got it ?
ta123
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but was there a 9-18pi/4 at the beginning
LagrangeSon678
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yes there was
LagrangeSon678
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can you not see it:
|dw:1316153548845:dw|
ta123
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I meant why was 9-18pi/4 at the begginig
LagrangeSon678
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above i accidentally wrote:y=18x-(36-18pi)/(4), but is was really suppose to be :
y=18x+(36-18pi)/(4), sorry about the typo
LagrangeSon678
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okay, so can we lay this problem to rest?
ta123
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I guess, but still don't get why they have 9-18pi/4 plug into b instead of just 18pi/4 by itself
LagrangeSon678
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Now remeber we said, that we have the x coordinate in the beining of pi/4, lets evaluate the orginal function at this point, this will give us the y in our line.
f(pi/4)=9tan(pi/4)
=9(1)
=9
now we have our x which is pi/4, we have our slope which is 18, lets plug this info into our line:
9=18(pi/4)+b
this means that b is = to 9-18pi/4
LagrangeSon678
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|dw:1316153804630:dw|
ta123
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oh, ok now we can lay this problem to rest, thanks so much for being patience
LagrangeSon678
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its good you ask questions, i know i can confusing sometimes :)
ta123
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Thanks for giving me a metal
ta123
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yeah I just want to understand the problem instead of just getting the answer
ta123
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because I might see it on the test, but thanks again
LagrangeSon678
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anytime