Answer:
In second place came Juliet Simms, long thought to be the one to beat — and, technically, Jermaine did just that.
Explanation:
Answer:
'Do not try to substitute work with prayer' means a person should not be lazy and shirk his duties laying the burden of the work on God. ... It is only when a person uses the abilities endowed to him by God that he can achieve something in life. Nothing can be achieved without making an effort.
Would love a brainliest if you don't mind!
The indefinite integral expressed as an infinite series is;
![= (\Sigma^{\infty} _{n = 0} (-1)^{n} \frac{1 }{2n + 1} * \frac{(x)^{4n + 3}}{4n + 3}) + C](https://tex.z-dn.net/?f=%3D%20%20%28%5CSigma%5E%7B%5Cinfty%7D%20_%7Bn%20%3D%200%7D%20%28-1%29%5E%7Bn%7D%20%5Cfrac%7B1%20%7D%7B2n%20%2B%201%7D%20%2A%20%5Cfrac%7B%28x%29%5E%7B4n%20%2B%203%7D%7D%7B4n%20%2B%203%7D%29%20%2B%20C)
<h3>How to find indefinite integral?</h3>
We will first have to look for the Maclaurin series of arctan(x).
We'll recall that from online tables of integral, this Maclaurin series of arctan(x) will have the general formula;
![arctan(x) = \Sigma^{\infty} _{n = 0} (-1)^{n} \frac{x^{2n + 1} }{2n + 1}](https://tex.z-dn.net/?f=arctan%28x%29%20%3D%20%20%5CSigma%5E%7B%5Cinfty%7D%20_%7Bn%20%3D%200%7D%20%28-1%29%5E%7Bn%7D%20%5Cfrac%7Bx%5E%7B2n%20%2B%201%7D%20%7D%7B2n%20%2B%201%7D)
When we apply that general Maclaurin series of arctan(x) to our question of arctan(x²), we have the expression as;
![arctan(x^{2} ) = \Sigma^{\infty} _{n = 0} (-1)^{n} \frac{(x^2)^{2n + 1} }{2n + 1}](https://tex.z-dn.net/?f=arctan%28x%5E%7B2%7D%20%29%20%3D%20%20%5CSigma%5E%7B%5Cinfty%7D%20_%7Bn%20%3D%200%7D%20%28-1%29%5E%7Bn%7D%20%5Cfrac%7B%28x%5E2%29%5E%7B2n%20%2B%201%7D%20%7D%7B2n%20%2B%201%7D)
⇒ ![= \Sigma^{\infty} _{n = 0} (-1)^{n} \frac{(x)^{4n + 2} }{2n + 1}](https://tex.z-dn.net/?f=%3D%20%20%5CSigma%5E%7B%5Cinfty%7D%20_%7Bn%20%3D%200%7D%20%28-1%29%5E%7Bn%7D%20%5Cfrac%7B%28x%29%5E%7B4n%20%2B%202%7D%20%7D%7B2n%20%2B%201%7D)
We now integrate the expression that we got above in the following manner to get;
![\int\limitsarctan(x^{2} ) = \int\Sigma^{\infty} _{n = 0} (-1)^{n} \frac{(x)^{4n + 2} }{2n + 1} dx](https://tex.z-dn.net/?f=%5Cint%5Climitsarctan%28x%5E%7B2%7D%20%29%20%3D%20%20%5Cint%5CSigma%5E%7B%5Cinfty%7D%20_%7Bn%20%3D%200%7D%20%28-1%29%5E%7Bn%7D%20%5Cfrac%7B%28x%29%5E%7B4n%20%2B%202%7D%20%7D%7B2n%20%2B%201%7D%20dx)
⇒ ![= (\Sigma^{\infty} _{n = 0} (-1)^{n} \frac{1 }{2n + 1} * \frac{(x)^{4n + 3}}{4n + 3}) + C](https://tex.z-dn.net/?f=%3D%20%20%28%5CSigma%5E%7B%5Cinfty%7D%20_%7Bn%20%3D%200%7D%20%28-1%29%5E%7Bn%7D%20%5Cfrac%7B1%20%7D%7B2n%20%2B%201%7D%20%2A%20%5Cfrac%7B%28x%29%5E%7B4n%20%2B%203%7D%7D%7B4n%20%2B%203%7D%29%20%2B%20C)
Thus, that expression gives us the indefinite integral of arctan(x²) as an infinite series.
Read more about the indefinite integral at; brainly.com/question/12231722
The distance between the campsite and the rest area is 9 miles.
The given parameters:
- <em>Initial speed of the campers, u = 4.5 mph</em>
- <em>Final speed of the campers, v = 4 mph</em>
<em />
Let the time of motion from the campsite to rest area = t (hours)
Time for return trip = t hours + 15 mins
= (t + 0.25) hours
Let the distance between the campsite and rest area = d
d = 4.5t
d = 4(t + 0.25)
4.5t = 4(t + 0.25)
4.5t = 4t + 1
4.5t - 4t = 1
0.5t = 1
t = 2 hours
The distance between the campsite and the rest area is calculated as follows;
d = 4.5t
d = 4.5 x 2
d = 9 miles
Thus, the distance between the campsite and the rest area is 9 miles.
Learn more about distance and speed here: brainly.com/question/2854969
Because they need the money for other necessities such as paying rent, insurance, living expenses, transportation, and even paying for college and books for college. and it’s likely they are making minimum wage if they have a job so it is hard to keep up and pay that much per month