Algebra Pre-Algebra and Basic Algebra Math Forum

June 17th, 2017, 12:32 AM   #1
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 June 17th, 2017, 03:01 AM #2 Global Moderator   Joined: Dec 2006 Posts: 18,166 Thanks: 1424 A clearer version . . . Bridge.PNG 26. The cross-section of a platform is shown above. All measurements are in metres. (a) Find the height of the platform. (b) Find the cross-sectional area of the platform. (c) Find the volume of the concrete required to $\ \ \ \,\,$ build this platform if it is 20 metres long. Answers: (a) The height of the platform is (1 - (-2)) metres = 3 metres. (b) Cross-sectional area = $\displaystyle 3e^{-2} + \int_{e^{-2}}^e (1 - \ln(x))dx = 3e^{-2} + {\large[}2x - x*\ln(x){\large]}_{e^{-2}}^e$ metres² = $\displaystyle \left(e - e^{-2}\right)$ metres². (c) Required volume = $\displaystyle 20\left(e - e^{-2}\right)$ metres³. Thanks from topsquark
 June 17th, 2017, 04:40 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,829 Thanks: 753 But this is definitely not an "algebra", not even an "AlgeBRAAAAA" problem!
 June 21st, 2017, 06:18 PM #4 Newbie   Joined: Jun 2017 From: New York Posts: 1 Thanks: 0 Where you should start. Calculus was invented as a tool for solving problems. Prior to the development of calculus, there were a variety of different problems that could not be addressed using the mathematics that was available. For example, scientists did not know how to measure the speed of an object when that speed was changing over time. Also, a more effective method was desired for finding the area of a region that did not have straight edges. Geometry, algebra, and trigonometry, which were well understood, did not provide the necessary tools to adequately address these problems. Last edited by skipjack; August 7th, 2017 at 08:44 PM.
 June 21st, 2017, 06:39 PM #5 Senior Member     Joined: Sep 2015 From: Southern California, USA Posts: 1,607 Thanks: 819 thanks for cutting and pasting that Quora article (without tribute) on the history of calculus. I'm sure that it helped the OP no end. Thanks from topsquark
June 21st, 2017, 06:41 PM   #6
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Quote:
 Originally Posted by John Farman Calculus was invented as a tool for solving problems.
I thought it was a plot to make students miserable.

Skipjack, where did $e^{-2}$ come from? That's not on OP's diagram, and of course without some clue we don't know what the negative $y$-value is for the bottom of the shape.

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