Answer:
A). 101 inches
B). 110 years
Step-by-step explanation:
Years since planting Circumference Difference
1 3 -
2 5 (5 - 3) = 2
3 7 (7 - 5) = 2
4 9 (9 - 7) = 2
5 11 (11 - 9) = 2
6 13 (13 - 11) = 2
There is a difference of 2 in every successive term of the circumference.
Therefore, the given sequence is an arithmetic sequence.
Explicit formula of an arithmetic sequence is given by,
![A_n=a+(n-1)d](https://tex.z-dn.net/?f=A_n%3Da%2B%28n-1%29d)
Here a = first term
n = number of terms
d = common difference
From the given table,
![A_n=3+(n-1)2](https://tex.z-dn.net/?f=A_n%3D3%2B%28n-1%292)
![A_n=2n+1](https://tex.z-dn.net/?f=A_n%3D2n%2B1)
Here
= circumference after 'n' years
n = Age of the plant
By this formula,
Circumference of a tree after 50 years,
![A_{50}=2(50)+1](https://tex.z-dn.net/?f=A_%7B50%7D%3D2%2850%29%2B1)
= 101 inches
Age of tree with the circumference = 221 inches,
221 = 2n + 1
2n = 220
n = 110 years
Answer:
![\{\frac{4}{9} \}](https://tex.z-dn.net/?f=%5C%7B%5Cfrac%7B4%7D%7B9%7D%20%5C%7D)
Step-by-step explanation:
First off, we are given a parabola by definition:
![f(x) = 9x^2 + 4x + k \\ a = 9, b = 4, c = k;](https://tex.z-dn.net/?f=f%28x%29%20%3D%209x%5E2%20%2B%204x%20%2B%20k%20%5C%5C%20a%20%3D%209%2C%20b%20%3D%204%2C%20c%20%3D%20k%3B)
Since
, our parabola has an upward opening.
Should we think about it graphically, it will be no wonder that we should pay our attention to the points of the parabola intersecting the abscissa axis. In other words, we need our vertex to intersect the x axis only once per se.
The vertex:
![V_{x} = \frac{-b}{2a} = \frac{-4}{2 * 9} = - \frac{2}{9} \\ V_{y} = 9V_{x}^2 + 4V_{x} + k = 9(- \frac{2}{9})^2 + 4(- \frac{2}{9}) + k = 9 * \frac{4}{9^2} - \frac{8}{9} + k = \frac{4}{9} - \frac{8}{9} + k = - \frac{4}{9} + k](https://tex.z-dn.net/?f=V_%7Bx%7D%20%3D%20%5Cfrac%7B-b%7D%7B2a%7D%20%3D%20%5Cfrac%7B-4%7D%7B2%20%2A%209%7D%20%3D%20-%20%5Cfrac%7B2%7D%7B9%7D%20%5C%5C%20V_%7By%7D%20%3D%209V_%7Bx%7D%5E2%20%2B%204V_%7Bx%7D%20%2B%20k%20%3D%209%28-%20%5Cfrac%7B2%7D%7B9%7D%29%5E2%20%2B%204%28-%20%5Cfrac%7B2%7D%7B9%7D%29%20%2B%20k%20%3D%209%20%2A%20%5Cfrac%7B4%7D%7B9%5E2%7D%20-%20%5Cfrac%7B8%7D%7B9%7D%20%2B%20k%20%3D%20%5Cfrac%7B4%7D%7B9%7D%20-%20%5Cfrac%7B8%7D%7B9%7D%20%2B%20k%20%3D%20-%20%5Cfrac%7B4%7D%7B9%7D%20%2B%20k)
As a result, our
is parametric.
suits us because
. If
, we do not have any roots at all. We have two roots if
.
Answer:
solve what
Step-by-step explanation:
there's no question
Answer:
4892
because its to the zero power
Step-by-step explanation: