anonymous
  • anonymous
3x^2-7x-3=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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amistre64
  • amistre64
3times3 is 9 which doesnt factor into 7.... so quadratic it :)
anonymous
  • anonymous
after using the quadratic formula, how do you complete the problem?
amistre64
  • amistre64
that is the completed problem. you could try doing the "complete the square" method; but all that method does is prove that the quad formula works.

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anonymous
  • anonymous
my textbook says to find the nearest degree.. x = sin of theta
amistre64
  • amistre64
then find what x equals and take the sine inverse of it. the inverse trig funtions take numbers for inputs and spit back angles. Does that make sense?
anonymous
  • anonymous
not really :/
amistre64
  • amistre64
lets walk you thru it then :) first get the values for x with the quad formula. 7/6 (+-) sqrt(49-(4)(-3)(3))/ 6 7/6 (+-) sqrt(49+36)/6 7/6 (+-) sqrt(85)/6 you with me so far?
anonymous
  • anonymous
ok, let me see.
anonymous
  • anonymous
where do you get 49?
amistre64
  • amistre64
the quad form reads: -middle (+-) sqrt(middle^2 -4(first)(last)) all over 2(first). or more formally: -b (+-) sqrt(b^2-4(a)(c)) --------------------- 2(a) right? -7 times -7 = 49
anonymous
  • anonymous
oh. it's b^2? no wonder i never got any solution out of that. thank you very much! +5
amistre64
  • amistre64
we got numbers for our x now; (7/6 (+-) sqrt(85)/6) if I did it correctly right?
anonymous
  • anonymous
umm.. i'm still solving it. i got the b^2 correct
anonymous
  • anonymous
my calculator says -49 instead of 49. so weird´Ż×
amistre64
  • amistre64
lol.... maybe user error? To find out what sin(t) is when x equals some number we write it like this: sin(t) = x To find out what "t" is we need to get rid of the (sin) part. And we do that by using what is called the sine inverse function.
anonymous
  • anonymous
i think it was supposed to be 7 not -7
amistre64
  • amistre64
all it changes in the end is the sign of (7/6) to (-7/6) which may or may not be an issue
anonymous
  • anonymous
got it. \[x=7\pm \sqrt{49+36} \div 6\]
amistre64
  • amistre64
if your equation you gave was correct, then it was supposed to be (-7)^2 = 49. But (7)^2 = 49 just the same
amistre64
  • amistre64
good :) you ready to learn about sin inverse? its symbol is (sin^-1)
anonymous
  • anonymous
i know sin^-1 but i'm stuck in where should i go next.
amistre64
  • amistre64
lets walk it thru. It asks us to find sin(t) = x right?
anonymous
  • anonymous
sin \[\theta\]
amistre64
  • amistre64
theta is simply a name, I will make it simpler and just name it "t" do you think I can do that?
anonymous
  • anonymous
yea, sure. :)
amistre64
  • amistre64
lol...good, mathmaticians like to rename things all the time, makes them feel important :)
anonymous
  • anonymous
XD
amistre64
  • amistre64
we have: sin(t) = x we need to get rid of the "sin" part. So lets apply sin^-1 to each side to get: t = sin^-1(x) Now plug the numbers into your scientific calculator to get an angle for t, formally known as theta
anonymous
  • anonymous
wait. i'm confused here. do i continue with the quad. formula?
amistre64
  • amistre64
the quad formula simply gave us the values for x....its job is done and it can go take a well deserved break...
anonymous
  • anonymous
so i continue with this:\[3\sin^2\theta-7\sin \theta-3=0\]
amistre64
  • amistre64
aha!!! you were holding back vital information...hmmm
anonymous
  • anonymous
opps.. am i in trouble?
amistre64
  • amistre64
nah....just makes the problem more understandable now :)
anonymous
  • anonymous
XD. so how do i continue?
amistre64
  • amistre64
just the same as before :) sin(t) = x and solve for t But I gotta tell wonder, do you have the problem written correctly becuase I get some wierd stuff when I plug it into the calculator..
anonymous
  • anonymous
the textbook says to use the quadratic formula to find,to the nearest degree, all values of theta in the interval 0 degrees [less than or equal to] theta [less than] 360 degrees that satisfy each equation.
amistre64
  • amistre64
338.29 degrees is what I get, which is in Quad4 but it is also hiding in Quad3 under the disguise of 201.71 degrees.
amistre64
  • amistre64
[7+sqrt(85)] /6 is greater then 1 so it spits out an error. x = 2.7 and that aint between -1 and 1 so it is a false reading.
amistre64
  • amistre64
[7-sqrt(85)]/6 = -0.3699 which IS between -1 and 1 so it is a good value of x.
amistre64
  • amistre64
is there anyway to verify the answer?
anonymous
  • anonymous
i got the same answer as you. -0.3699240762
amistre64
  • amistre64
either were both geniuses or were both idiots...take your pick :)
anonymous
  • anonymous
GENIUS! :D
amistre64
  • amistre64
yay!!!
amistre64
  • amistre64
the thing about sin^-1 is that it only gives an angle that is on the right hand side of a circle. So you have to remember to look over to the other sid eto see where it matches up at.
amistre64
  • amistre64
does any of that make sense to you?
anonymous
  • anonymous
somewhat, let me think over~
anonymous
  • anonymous
i think i got it, thanks for helping me though(:

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