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.
Answer:
The 9th term will be -24
Step-by-step explanation:
The 9th term will be equal to
= - 8 - 2(n - 1)
= - 8 - 2(9 - 1)
= - 8 - 18 + 2
= - 24
Answer:
7,040 yards
Step-by-step explanation:
there are 1,760 yards in a mile, so 1,760 multiplied by 4 is 7,040
Answer:
$0.06 per square inch
Step-by-step explanation:
The question should be:
<em>"If tile costs $8.50 per square foot, how much does it cost per square inch?"</em>
<em />
To solve this, we basically need a conversion from feet to inches. BUT 2 times, since we are talking about "square feet" and "square inches".
We know 1 feet = 12 inches
Also, since we are going from square feet to square inches [big to small], we have to divide TWICE.
Thus, we will have:
We are dividing 8.5 (the cost) by 12, 2 times since we want square feet in square inches. The answer is:
So, tile costs $0.06 per square inch
N2+40-28=
Combine like terms
n2+40-28=n2+12
Factor out 2
n•2+12=2(n+6)
Therefore the answer is 2(n+6)
