What is the 7th term in the sequence of square numbers?
2 answers:
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Answer:
4x +3y = 10
Step-by-step explanation:
The radius CD has slope Δy/Δx = (1-(-2))/(8-4) = 3/4.
The equation for the perpendicular line through point C(4, -2) can be written as ...
Δx(x -4) +Δy(y -(-2)) = 0
4(x -4) +3(y +2) = 0
4x +3y -10 = 0 . . . . . . general form equation for the line
4x +3y = 10 . . . . . . . . .standard form equation for the line
Answer:
Since a/2⁽ⁿ ⁺ ¹⁾b < a/2ⁿb, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.
Step-by-step explanation:
Let a/b be the rational number in its simplest form. If we divide a/b by 2, we get another rational number a/2b. a/2b < a/b. If we divide a/2b we have a/2b ÷ 2 = a/4b = a/2²b. So, for a given rational number a/b divided by 2, n times, we have our new number c = a/2ⁿb where n ≥ 1
Since = a/(2^∞)b = a/b × 1/∞ = a/b × 0 = 0, the sequence converges.
Now for each successive division by 2, a/2⁽ⁿ ⁺ ¹⁾b < a/2ⁿb and
a/2⁽ⁿ ⁺ ¹⁾b/a/2ⁿb = 1/2, so the next number is always half the previous number.
So, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.