Using a geometric series, it is found that he swims 1897 yards in the first week.
In a geometric series, the quotient between consecutive terms is always the same, and it is called common ratio q.
The general equation of a geometric series is given by:
![a_n = a_1q^{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%20a_1q%5E%7Bn-1%7D)
In which
is the first term.
The sum of the first n terms is given by:
![S_{n} = \frac{a_1(1 - q^n)}{1 - q}](https://tex.z-dn.net/?f=S_%7Bn%7D%20%3D%20%5Cfrac%7Ba_1%281%20-%20q%5En%29%7D%7B1%20-%20q%7D)
In this problem:
- 200 yards on the first day, thus
. - Each day, the distance increases by 10%, since 100% + 10% = 110% = 1.1,
. - First week is first 7 days, thus
![n = 7](https://tex.z-dn.net/?f=n%20%3D%207)
Then:
![S_{n} = \frac{a_1(1 - q^n)}{1 - q}](https://tex.z-dn.net/?f=S_%7Bn%7D%20%3D%20%5Cfrac%7Ba_1%281%20-%20q%5En%29%7D%7B1%20-%20q%7D)
![S_{7} = \frac{200(1 - 1.1^7)}{1 - 1.1}](https://tex.z-dn.net/?f=S_%7B7%7D%20%3D%20%5Cfrac%7B200%281%20-%201.1%5E7%29%7D%7B1%20-%201.1%7D)
![S_{7} = 1897](https://tex.z-dn.net/?f=S_%7B7%7D%20%3D%201897)
He swims 1897 yards in the first week.
A similar problem is given at brainly.com/question/23711475
Rectangles are similar figures, thus if scaled copies of each other then the ratios of corresponding sides must be equal
compare ratios of lengths and widths
rectangles A and B
k =
=
← ratio of lengths
k =
=
← ratio of widths
scale factors are equivalent, hence rectangle A is a scaled copy of B
rectangles C and B
k =
=
← ratio of lengths
k =
=
← ratio of width
scale factors (k ) are not equal, hence C is not a scaled copy of B
rectangles A and C
k =
=
← ratio of lengths
k =
← ratio of widths
the scale factors are not equal hence A is not a scaled copy of C
Answer:
No
Step-by-step explanation:
No it is not a perfect square because you can not factor it.