I'll do problem 13 to get you started.
The expression is the same as
Then we can do a bit of algebra like so to change that n into n-1
This is so we can get the expression in a(r)^(n-1) form
- a = 8/7 is the first term of the geometric sequence
- r = 2/7 is the common ratio
Note that -1 < 2/7 < 1, which satisfies the condition that -1 < r < 1. This means the infinite sum converges to some single finite value (rather than diverge to positive or negative infinity).
We'll plug those a and r values into the infinite geometric sum formula below
S = a/(1-r)
S = (8/7)/(1 - 2/7)
S = (8/7)/(5/7)
S = (8/7)*(7/5)
S = 8/5
S = 1.6
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Answer in fraction form = 8/5
Answer in decimal form = 1.6
The answer is B, D, A, C.
Let's all of them have the same exponent so we can compare them. Let 23 be the common exponent since it is the smallest one:
Planet A: 5.97 * 10²⁴ = 5.97 * 10¹⁺²³ = 5.97 * 10 * 10²³ = 59.7 * 10²³<span>
Planet B: 3.30 * 10</span>²³<span>
Planet C: 1.89 * 10</span>²⁷ = 1.89 * 10⁴⁺²³ = 1.89 * 10⁴ * 10²³ = 1.89 * 10,000 * 10²³ = 18,900 * 10²³<span>
Planet D: 4.87*10</span>²⁴ = 4.87 * 10¹⁺²³ = 4.87 * 10 * 10²³ = 48.7 * 10²³
Since 3.30 * 10²³ < 48.7 * 10²³ < 59.7 * 10²³ < 18,900 * 10²³, then <span> the order of these planets from least to greatest is B < D < A < C</span>
Answer:
1,436.03
Step-by-step explanation:
Answer: more grandparents prefer using a hard copy than a digital copy
Step-by-step explanation: