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How many syllables are in foggy?
The word foggy has 2 syllables.(Fog - gy).
How many syllables are in the word shaggy?
The word shaggy has two syllables. Shag-gy.
How many syllables in the word mete orology?
There are six syllables in meteorology. Me/te/or/ol/o/gy
How do you write 4308 in expanded form?
4,308 = (4 x 1000) + (3 x 100) + (0 x 10) + (8 x 1)
Show that the rectangle of maximum area for given perimeter P is always a square?
Suppose there exists some rectangle whose center is the point (x,y) = (0,0) with a given perimeter P and that we'd like to find the dimensions which maximize its area. The method we will use is called Lagrange Multipliers. Then f(x,y) = P = 4x + 4y and g(x,y) A = xy. (fx, fy) = L(gx, gy) (for some constant L which exists on the set of real numbers) (4, 4) = L(y,x) (4, 4) = (Ly, Lx) But then Lx = 4 = Ly which yields Lx = Ly and x = y. Therefore when the area is maximized, the x component equals the y component. Furthermore, a rectangle centered at (0,0) whose corner falls on some point (x,y) at which x = y is a square.
