T=number of years since start of the study.
y=city´s population.
first year:
y=390,000+0.073(390,000)=390,000(1+0.073) (=418470)
Second year:
y=(390,000(1+0.073) + 0.073(390,000(1+0.073) =
=390,000(1+0.073) (1+0.073)
=390,000(1+0.073)²
(≈449,018.31)
Third year: if you calculate it you would have:
y=390,000(1+0.073)³
Fourth year: if you compute it you would have:
y=390,000 (1+0.073)⁴
t th year:
y=390,000(1+0.073)^t
Answer: y=390,000(1+0.073)^t
Answer:
Recursive formula for this geometric sequence, -125, -25, -5, -1 will be:
where ![a_1=-125](https://tex.z-dn.net/?f=a_1%3D-125)
Step-by-step explanation:
As we know that when we define a sequence by describing the relationship between its successive terms, it means we are defining the sequence recursively.
Given that,
-125, -25, -5, -1
![\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}](https://tex.z-dn.net/?f=%5Cmathrm%7BCompute%5C%3Athe%5C%3Aratios%5C%3Aof%5C%3Aall%5C%3Athe%5C%3Aadjacent%5C%3Aterms%7D%3A%5Cquad%20%5C%3Ar%3D%5Cfrac%7Ba_%7Bn%2B1%7D%7D%7Ba_n%7D)
![\frac{-25}{-125}=\frac{1}{5},\:\quad \frac{-5}{-25}=\frac{1}{5},\:\quad \frac{-1}{-5}=\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B-25%7D%7B-125%7D%3D%5Cfrac%7B1%7D%7B5%7D%2C%5C%3A%5Cquad%20%5Cfrac%7B-5%7D%7B-25%7D%3D%5Cfrac%7B1%7D%7B5%7D%2C%5C%3A%5Cquad%20%5Cfrac%7B-1%7D%7B-5%7D%3D%5Cfrac%7B1%7D%7B5%7D)
![\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}](https://tex.z-dn.net/?f=%5Cmathrm%7BThe%5C%3Aratio%5C%3Aof%5C%3Aall%5C%3Athe%5C%3Aadjacent%5C%3Aterms%5C%3Ais%5C%3Athe%5C%3Asame%5C%3Aand%5C%3Aequal%5C%3Ato%7D)
![r=\frac{1}{5}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B1%7D%7B5%7D)
![\mathrm{The\:first\:element\:of\:the\:sequence\:is}](https://tex.z-dn.net/?f=%5Cmathrm%7BThe%5C%3Afirst%5C%3Aelement%5C%3Aof%5C%3Athe%5C%3Asequence%5C%3Ais%7D)
![a_1=-125](https://tex.z-dn.net/?f=a_1%3D-125)
![a_n=a_1\cdot r^{n-1}](https://tex.z-dn.net/?f=a_n%3Da_1%5Ccdot%20r%5E%7Bn-1%7D)
![\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:](https://tex.z-dn.net/?f=%5Cmathrm%7BTherefore%2C%5C%3Athe%5C%3A%7Dn%5Cmathrm%7Bth%5C%3Aterm%5C%3Ais%5C%3Acomputed%5C%3Aby%7D%5C%3A)
![a_n=-125\left(\frac{1}{5}\right)^{n-1}](https://tex.z-dn.net/?f=a_n%3D-125%5Cleft%28%5Cfrac%7B1%7D%7B5%7D%5Cright%29%5E%7Bn-1%7D)
As the recursive formula makes us able to find the next term in the sequence from the proceeding term by multiplying the preceding term by r.
Therefore,
Recursive formula for this geometric sequence, -125, -25, -5, -1 will be:
where ![a_1=-125](https://tex.z-dn.net/?f=a_1%3D-125)
Answer:
![\sqrt{149\\ \\](https://tex.z-dn.net/?f=%5Csqrt%7B149%5C%5C%20%5C%5C)
However, that's the length of "c" and you're looking to drag it in. So,o you drag in 10^2+7^2=a^2.
Then, as shown by the first picture attatched, you can drag in the one with "c" and "a" with the five shown.
Step-by-step explanation:
To find "c" the diagonal, as explained, you need to use the theorem twice. You can first use it by finding "a", as you already have "b". To find a, you do 10^2+7^2=a^2, the hypotenuse.
100+49=149.
So, a is root 149.
a^2+b^2=c^2 so
149+25=174
Answer:
28.71 x 0.066 = 1.89486
Step-by-step explanation:
Answer: C) 15
Step-by-step explanation:
Use the Pythagorean theorem
=
+ ![9^{2}](https://tex.z-dn.net/?f=9%5E%7B2%7D)
= ![225](https://tex.z-dn.net/?f=225)
![x = \sqrt{225}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%7B225%7D)
![x = 15](https://tex.z-dn.net/?f=x%20%3D%2015)