Mathematics, 03.04.2020 17:13 mirellaenriquez5529

Juan and Lizzy are in the final week of their training for a marathon. Juan's goal is to run one mile on the first day of the week and double the amount he runs each day for the next six days. Lizzy's goal is to run 10 miles on the first day of the week and increase the amount she runs by 3 miles each day for the next six days. 1: Juan's marathon training schedule is an example of a(n) : arithmetic or geometric 2: Lizzy's marathon training schedule is an example of a(n) : arithmetic or geometric 3: Who will be better prepared for the marathon: Juan or Lizzy

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Answer from: drainy0uandthefish

1. Juan's marathon training schedule is an example of a geometric sequence

2. Lizzy's marathon training schedule is an example of an arithmetic sequence

3. Lizzy will be better prepared for the marathon

Step-by-step explanation:

In the arithmetic sequence there is a common difference between each two consecutive terms

In the geometric sequence there is a common ratio between each two consecutive terms

Juan's Schedule

∵ Juan's will run one mile on the first day of the week

∴ $a_{1}$ = 1

∵ He will double the amount he runs each day for the next

6 days

- That means he multiplies each day by 2 to find how many miles

he will run next day

∴ $a_{2}$ = 1 × 2 = 2 miles

∴ $a_{3}$ = 2 × 2 = 4 miles

∴ $a_{4}$ = 4 × 2 = 8 miles

∴ $a_{5}$ = 8 × 2 = 16 miles

∴ $a_{6}$ = 16 × 2 = 32 miles

∴ $a_{7}$ = 32 × 2 = 64 miles

That means there is a common ratio 2 between each two consecutive days

1. Juan's marathon training schedule is an example of a geometric sequence

Lizzy's Schedule

∵ Lizzy's will run 10 miles on the first day of the week

∴ $a_{1}$ = 10

∵ She will increase the amount she runs by 3 miles each day for

the next six days

- That means she adds each day by 3 to find how many miles

she will run next day

∴ $a_{2}$ = 10 + 3 = 13 miles

∴ $a_{3}$ = 13 + 3 = 16 miles

∴ $a_{4}$ = 16 + 3 = 19 miles

∴ $a_{5}$ = 19 + 3 = 22 miles

∴ $a_{6}$ = 22 + 3 = 25 miles

∴ $a_{7}$ = 25 × 3 = 28 miles

That means there is a common difference 3 between each two consecutive days

2. Lizzy's marathon training schedule is an example of an arithmetic sequence

The rule of the sum of nth term in the geometric sequence is $S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

∵ $a_{1}$ = 1 , r = 2 and n = 7

∴ $S_{7}=\frac{1(1-2^{7})}{1-2}$

∴ $S_{7}$ = 127

∴ Juan will run 127 miles in the final week

The rule of the sum of nth term in the arithmetic sequence is $S_{n}=\frac{n}{2}[a_{1}+a_{n}]$

∵ n = 7, $a_{1}$ = 10 and $a_{7}$ = 28

∴ $S_{7}=\frac{7}{2}(10+28)$

∴ $S_{7}$ = 133

∴ Lizzy will run 133 miles in the final week

∵ 133 miles > 127 miles

∴ Lizzy will run more miles than Juan

3. Lizzy will be better prepared for the marathon

Answer from: Quest

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph

there is a hike in both the graphs so the graphs are increasing on their domain.x-intercept of log x and log 6x are differentthere is a vertical asymptote of both the graphs so there is no y-interceptas both the graphs are increasing so there is no horizontal asymptote

Answer from: Quest

hence, the required result is $b-a=\left[\begin{array}{ccc}1& 1& -2\\1& 1& -2\\1& 1& -2\end{array}\right]$