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One integer is two more than another. The sum of the lesser integer and double the greater is 7. What is the greater integer?
Let x = the greater integer and y = the lesser integer. From the ?rst sentence within the question we get the equation x = y + 2. From the second sentence in the question we get y + 2x = 7. Substitute x = y + 2 within the second equation: y + 2(y + 2) = 7; use the distributive property to simplify to: y + 2y + 4 = 7. Combine like terms to obtain: 3y + 4 = 7; subtract 4 from both sides of the equation: 3y + 4 - 4 = 7 - 4. Simplify to 3y = 3.Divide both sides of the equation through 3: 3y/3 =3/3; thus y = 1. Since the greater is two more than the lesser, the greater is 1 + 2 = 3.
Functional and variations.Block III, Consider the functional S[y]=?_1^2 v(x^2+y'')dx , y(1)=0,y(2)=B Show that if ?=S[y+eg]-S[y], then to second order in e, ?=1/2 e?_1^2¦?g^'
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