Find an equation of the circle that has center (6.-3) and passes through (1, 1).
1 answer:
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Answer:
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
∴ = 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
∴ = 1 × 2 = 2 miles
∴ = 2 × 2 = 4 miles
∴ = 4 × 2 = 8 miles
∴ = 8 × 2 = 16 miles
∴ = 16 × 2 = 32 miles
∴ = 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
∴ = 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
∴ = 10 + 3 = 13 miles
∴ = 13 + 3 = 16 miles
∴ = 16 + 3 = 19 miles
∴ = 19 + 3 = 22 miles
∴ = 22 + 3 = 25 miles
∴ = 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
∵ = 1 , r = 2 and n = 7
∴
∴ = 127
∴ Juan will run 127 miles in the final week
The rule of the sum of nth term in the arithmetic sequence is
∵ n = 7, = 10 and
= 28
∴
∴ = 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
If a line is parallel to another it has the same slope. Since the equation y = 1/3x +8 is parallel to the line we are trying to find, our second line will have the slope of 1/3x as well
This is the equation of a line:
y = mx + b
m = slope = 1/3x
b = y intercept = unknown
We have to find b to make this equation complete. How do we do this?
First plug what you know into the equation: y = 1/3x + b
Second we must solve for b. To do this plug a point that passes through the line (in this case they said (6, -2) passes through the line) into the x and y of the equation:
-2 = 1/3(6) + b
Now solve for b!
-2 = 6/3 + b
-2 = 2 + b
- 2 - 2 = b
-4 = b
The equation parallel to y=1/3x + 8 and passes through point (6, -2) is y = 1/3x - 4
The image below is the two line one a coordinate plane. As you can see, they are parallel to each other
Hope this helped!
