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anonymous
 one year ago
Find the number a such that the line x = a divides the region bounded by the curves x = y2 − 1 and the yaxis into 2 regions with equal area. Give your answer correct to 3 decimal places.
anonymous
 one year ago
Find the number a such that the line x = a divides the region bounded by the curves x = y2 − 1 and the yaxis into 2 regions with equal area. Give your answer correct to 3 decimal places.

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1At first the full are that we are talking about: The boundaries are: \(\large\color{black}{ \displaystyle x=y^21 }\) \(\large\color{black}{ \displaystyle x=0 }\)  dw:1437950043784:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So far we can tell that 1<a<0.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1rearrangement \(x=y^21\) \(y=\sqrt{x+1}\) \(\large\color{slate}{\displaystyle\int\limits_{1}^{0}\left(\sqrt{x+1}\right)~dx}\) is the area of the full region. Now, we are splitting it into two regions that stop and start (respectively) at x=a. \(\large\color{slate}{\displaystyle\int\limits_{1}^{a}\left(\sqrt{x+1}\right)~dx=\int\limits_{a}^{0}\left(\sqrt{x+1}\right)~dx}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(and initially, want to say that I mean that a is between x=1 and x=0) any questions/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got this far but cant seem to get a good answer I got an answer of .023

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \displaystyle \int\limits_{1}^{a}\left(\sqrt{x+1}\right)~dx=\int\limits_{a}^{0}\left(\sqrt{x+1}\right)~dx\) \(\large \displaystyle \left.(x+1)^{3/2}~~\right^{a}_{1}=\left.(x+1)^{3/2}~\right^{0}_{a}\) \(\large \displaystyle (a+1)^{3/2}0^{3/2}=(1)^{3/2} (a+1)^{3/2}\) \(\large \displaystyle (a+1)^{3/2}=1 (a+1)^{3/2}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \displaystyle2 (a+1)^{3/2}=1\) \(\large \displaystyle(a+1)^{3/2}=1/2\) \(\large \displaystyle a+1=(1/2)^{2/3}\) \(\large \displaystyle a=1/\sqrt[3]{4}1\) \(a\approx 0.37\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1this is what i got

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1we can do a taylor polynomial approximation for \(\sqrt[3]{4}\) if you like:)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you very much!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1questions about the problem?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no your explanation answers all questions thank you very much
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