Help with math

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PhoKingGuy

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Nov 15, 2007
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Do you like Phil Collins? I've been a big Genesis fan ever since the release of their 1980 album, Duke. Before that, I really didn't understand any of their work. Too artsy, too intellectual. It was on Duke where Phil Collins' presence became more apparent. I think Invisible Touch was the group's undisputed masterpiece. It's an epic meditation on intangibility. At the same time, it deepens and enriches the meaning of the preceding three albums. Christy, take off your robe. Listen to the brilliant ensemble playing of Banks, Collins and Rutherford. You can practically hear every nuance of every instrument. Sabrina, remove your dress. In terms of lyrical craftsmanship, the sheer songwriting, this album hits a new peak of professionalism. Sabrina, why don't you, uh, dance a little. Take the lyrics to Land of Confusion. In this song, Phil Collins addresses the problems of abusive political authority. In Too Deep is the most moving pop song of the 1980s, about monogamy and commitment. The song is extremely uplifting. Their lyrics are as positive and affirmative as anything I've heard in rock. Christy, get down on your knees so Sabrina can see your asshole. Phil Collins' solo career seems to be more commercial and therefore more satisfying, in a narrower way. Especially songs like In the Air Tonight and Against All Odds. Sabrina, don't just stare at it, eat it. But I also think Phil Collins works best within the confines of the group, than as a solo artist, and I stress the word artist. This is Sussudio, a great, great song, a personal favorite.
 

slayer202

Lifer
Nov 27, 2005
13,682
119
106
Do you like Phil Collins? I've been a big Genesis fan ever since the release of their 1980 album, Duke. Before that, I really didn't understand any of their work. Too artsy, too intellectual. It was on Duke where Phil Collins' presence became more apparent. I think Invisible Touch was the group's undisputed masterpiece. It's an epic meditation on intangibility. At the same time, it deepens and enriches the meaning of the preceding three albums. Christy, take off your robe. Listen to the brilliant ensemble playing of Banks, Collins and Rutherford. You can practically hear every nuance of every instrument. Sabrina, remove your dress. In terms of lyrical craftsmanship, the sheer songwriting, this album hits a new peak of professionalism. Sabrina, why don't you, uh, dance a little. Take the lyrics to Land of Confusion. In this song, Phil Collins addresses the problems of abusive political authority. In Too Deep is the most moving pop song of the 1980s, about monogamy and commitment. The song is extremely uplifting. Their lyrics are as positive and affirmative as anything I've heard in rock. Christy, get down on your knees so Sabrina can see your asshole. Phil Collins' solo career seems to be more commercial and therefore more satisfying, in a narrower way. Especially songs like In the Air Tonight and Against All Odds. Sabrina, don't just stare at it, eat it. But I also think Phil Collins works best within the confines of the group, than as a solo artist, and I stress the word artist. This is Sussudio, a great, great song, a personal favorite.

haha nice
 

DrPizza

Administrator Elite Member Goat Whisperer
Mar 5, 2001
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The integral is relatively simple to do using a trig substitution. Just because it's on the end tables, doesn't mean it's difficult - after all, even the integral of sinu du is there.
 

DrPizza

Administrator Elite Member Goat Whisperer
Mar 5, 2001
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Umm, just at first glance, it appears you have some addition signs when they should be subtraction (in your square roots)

After that, it's pretty trivial to do what you want. Rewrite the x (x²-a&#178^-(1/2) in the numerator as a fraction. i.e. you'll have a fraction within your fraction. To rid yourself of this problem, multiply the numerator and denominator by sqrt(x²-a&#178. Don't distribute in the denominator. Notice that the numerator can now cancel out most of the denominator, leaving you with what you were seeking.
 
Last edited:

chuckywang

Lifer
Jan 12, 2004
20,139
1
0
Multiply top and bottom by sqrt(x^2 - a^2)

The top becomes: sqrt(x^2-a^2) + x, which cancels with the original bottom.
 
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