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The sum of the squares of two consecutive positive odd integers is 74. What is the value of the smaller integer?
Let x = the lesser odd integer and let x + 2 = the greater odd integer. The translation of the sentence, "The sum of the squares of two consecutive odd integers is 74," is the equation x2 + (x + 2)2 = 74. Multiply (x + 2)2 out as (x + 2)(x + 2) by using the distributive property: x2 + (x2 + 2x + 2x + 4) = 74. Combine such as terms on the left side of the equation: 2x2 + 4x + 4 = 74. Put the equation in standard form through subtracting 74 from both sides, and set it equal to zero: 2x2 + 4x - 70 = 0; factor the trinomial completely: 2(x2 + 2x - 35) = 0; 2(x - 5)(x + 7) = 0. Set each factor equal to zero and solve: 2 ≠ 0 or x - 5 = 0 or x + 7 = 0; x = 5 or x = -7. Because you are seems for a positive integer, reject the solution of x = -7. Thus, the smaller positive integer is 5.
Area with Parametric Equations In this section we will find out a formula for ascertaining the area under a parametric curve specified by the parametric equations, x = f (t)
Solve discrete harmonic mapping of a given surface patch (suppose the surface is genus-0 and with one boundary) 1. Map the boundary loop onto a unit rectangle using chord-length
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the sides of a right angle triangle are a,a+d,a+2d with a and d both positive.the ratio of a to d a)1:2 b)1:3 c)3:1 d)5:2 answer is (c) i.e. 3:1 Solution: Applying
help solve these type equations.-4.1x=-4x+4.5
which of these is between 5,945,089 and 5,956,108
Explain with the help of number line (-6)+(+5)
Concrete to Abstract : Mathematics, like all human knowledge, grows out of our concrete experiences. Let us take the example of three-dimensional shapes. Think about how you came
5.6:4=x:140
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