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sophbell
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MHB Calculating Total Area Under a Trapezoidal Curve for Water Tank Fill Time
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The area represented under the curve is a triangle (up to t = 2 hours) plus a rectangle. How do you find the sum of that area?sophbell said:
-Dan
- #3
HOI
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Draw a horizontal line at "100" all the way across. Draw a vertical line at "2" all the way up and down. That divides the area into a right triangle with one leg of length 2 and the other of length 200, a rectangle with width 2 and height 100, and another rectangle with height 300 and unknown width. What is the area of the triangle and the first rectangle?
If that is less than 1000, subtract if from 1000. How wide must the second rectangle be so that its area is that difference?
If that is less than 1000, subtract if from 1000. How wide must the second rectangle be so that its area is that difference?
- #4
Prove It
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MHB
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topsquark said:
Surely it's a trapezium and a rectangle...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles.
In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra
Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/
by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation
$$
a^n+b^n=c^n
$$
has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy
"Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I posted this in the Lame Math thread, but it's got me thinking.
Is there any validity to this? Or is it really just a mathematical trick?
Naively, I see that i2 + plus 12 does equal zero2.
But does this have a meaning?
I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero?
Ibix offered a rendering of the diagram using what I assume is matrix* notation...
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