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anonymous
 5 years ago
The polynominal .0012x^3.09x^2+1.5x+13 models natural gas consumption in trillions cubic feet, where x=0 corresponds to 1960, x=1 to 1961 and so on. Between 1970 and 1990 gas was about 10.8 trillion cubic feet.
Natural gas consumption was 10.8 trillion cubic feet in year?
anonymous
 5 years ago
The polynominal .0012x^3.09x^2+1.5x+13 models natural gas consumption in trillions cubic feet, where x=0 corresponds to 1960, x=1 to 1961 and so on. Between 1970 and 1990 gas was about 10.8 trillion cubic feet. Natural gas consumption was 10.8 trillion cubic feet in year?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You have to find x such that\[10.8 \times 10^{12}=0.0012x^30.09x^2+1.5x+13\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Have you learnt techniques for estimation?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Actually, it should be\[10.8=0.0012x^30.09x^2+1.5x+13\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay, if you go to this site, I've plugged in the equation and you should see a plot, along with estimated solutions: http://www.wolframalpha.com/input/?i=10.8%3D0.0012x^3%E2%88%920.09x^2%2B1.5x%2B13

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lokisan Hero, its me chai. can i ask you some help to solve this problem Find the equation of the perpendicular bisector of the line joining the points A and B in the following exercises 2. The points A(2,3), B(6,5), and C(8,5) are vertices of a triangle. Find the equation of the median.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hang on, chai. I'll finish this first.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You'll see that this polynomial spits out 10.8 if x=1.35, x=27.98, x=48.38.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now, we're not going backward in time, so x=1.35 can be discarded.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0We have two other solutions, though. \[x \approx 28\]and\[x \approx 48\]These would correspond to the years\[1960+28 = 1988\]and\[1960+48 = 2008\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It seems as if the question wants you to find when consumption was 10.8 trillion between the years 1970 and 1990...well, if this is the case, the answer is 1988.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0AH I see where I was messing up I didnt take out the 1.35

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, and if this question was one that was created before 2008, the 2008 solution wouldn't even be looked at either.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, well thank you .. wow its so easy to forget things that need to be eliminated

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah. If you need to estimate solutions manually, you should look into the NewtonRaphson method, or bisection method...you can probably find clips on these on YouTube.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I really appreciate that you explain the problems to me, it helps me to understand so the next one I have with different figures I will be able to do correctly  Ok I will look into those :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no probs...good luck :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You have to find the equation of the line that is 1) perpendicular to the line that joins A and B, and 2) cuts the middle of A and B.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now, a line that is perpendicular to AB will have a slope, m, such that\[m_1m_{AB}=1 \rightarrow m_{AB}=\frac{1}{m_1}\] where m_{AB} is the slope of AB. The slope of AB is found by\[m_{AB}=\frac{53}{6(2)}=\frac{8}{8}=1\]so the slope of the line perpendicular to AB must be\[m_1=\frac{1}{1}=1\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now, in order to find the line, we need one more thing  a point. We're told we want the line to cut through the middle of AB, so we have to find the midpoint of AB. This is found by taking the average of the x and y coordinates of A and B as such:\[M_{AB}=\left( \frac{2+6}{2},\frac{3+(5)}{2} \right)=\left( 2,1 \right)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The equation of the line can then be found using the pointgradient formula:\[yy_1=m_{AB}(xx_1)\]that is,\[y(1)=(1)(x2) \rightarrow y+1=x2\]so \[y=x3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and ,m here too! =) sorry for being a nag but i still have some questions for the solution you stated .

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This is the equation of your line, chai :)
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