Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36
miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.
3w + 6r ≥ 36
3w + 6r ≤ 90
Which combination of hours can Keitaro walk and run in a month to reach his goal?
2 hours walking; 12 hours running
4 hours walking; 3 hours running
9 hours walking; 12 hours running
12 hours walking; 10 hours running
3w + 6r ≥ 36
3w + 6r ≤ 90
Which combination of hours can Keitaro walk and run in a month to reach his goal?
2 hours walking; 12 hours running
4 hours walking; 3 hours running
9 hours walking; 12 hours running
12 hours walking; 10 hours running
2 answers:
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Answer:
a). r =
b). At least 5 terms should be added.
Step-by-step explanation:
Formula representing sum of infinite geometric sequence is,
Where a = first term of the sequence
r = common ratio
a). If the sum is seven times the value of its first term.
7(1 - r) = 1
7 - 7r = 1
7r = 7 - 1
7r = 6
r =
b). Since sum of n terms of the geometric sequence is given by,
If the sum of n terms of this sequence is more than half the value of the infinite sum.
>
n[log(0.85714)] < log(0.5)
-n(0.06695) < -0.30102
n >
n > 4.496
n > 4.5
Therefore, at least 5 terms of the sequence should be added.