Answer:
Option C. ![\$23,134.61](https://tex.z-dn.net/?f=%5C%2423%2C134.61)
Step-by-step explanation:
we know that
![A=\frac{P[(1+r)^{n} -1]}{r(1+r)^{n}}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7BP%5B%281%2Br%29%5E%7Bn%7D%20-1%5D%7D%7Br%281%2Br%29%5E%7Bn%7D%7D)
we have
![P=\$400](https://tex.z-dn.net/?f=P%3D%5C%24400)
![r=0.075/12=0.00625](https://tex.z-dn.net/?f=r%3D0.075%2F12%3D0.00625)
![n=6*12=72\ months](https://tex.z-dn.net/?f=n%3D6%2A12%3D72%5C%20months)
substitute in the formula
![A=\frac{400[(1+0.00625)^{72} -1]}{0.00625(1+0.00625)^{72}}\\ \\A=\frac{226.446972}{0.009788}\\ \\A=\$23,134.61](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B400%5B%281%2B0.00625%29%5E%7B72%7D%20-1%5D%7D%7B0.00625%281%2B0.00625%29%5E%7B72%7D%7D%5C%5C%20%5C%5CA%3D%5Cfrac%7B226.446972%7D%7B0.009788%7D%5C%5C%20%5C%5CA%3D%5C%2423%2C134.61)
Answer:
The answer is B. f(x) = (x − 1)(x − 2)(x + 1)(x + 2)
Step-by-step explanation:
Answer:
The scale factor will be 0.25 and the length of the side will be 8.75 cm. Hope it helps :)
Step-by-step explanation:
Answer:
yes they are good job
Step-by-step explanation:
Answer:
![\int\limits {5^x} \, dx = \frac{5^x}{ln\ x} + c](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B5%5Ex%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7B5%5Ex%7D%7Bln%5C%20x%7D%20%2B%20c)
Step-by-step explanation:
Note that the integral of
is not ![\frac{1}{6}x^6 + c](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7Dx%5E6%20%2B%20c)
The solution is as follows:
Given
![5^x](https://tex.z-dn.net/?f=5%5Ex)
Required
Integrate
Represent the given expression using integral notation
![\int\limits {5^x} \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B5%5Ex%7D%20%5C%2C%20dx)
This question can't be solved directly;
We'll make use of exponential rules which states;
![\int\limits {a^x} \, dx = \frac{a^x}{ln\ x} + c](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Ba%5Ex%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Ba%5Ex%7D%7Bln%5C%20x%7D%20%2B%20c)
By comparing
with
;
we can substitute 5 for a;
Hence, the expression
becomes
![\int\limits {5^x} \, dx = \frac{5^x}{ln\ x} + c](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B5%5Ex%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7B5%5Ex%7D%7Bln%5C%20x%7D%20%2B%20c)
-------------------------------------------------------------------------------------
However, the integral of
is ![\frac{1}{6}x^6 + c](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7Dx%5E6%20%2B%20c)
This is shown below:
Given that ![x^5](https://tex.z-dn.net/?f=x%5E5)
Applying power rule;
Power rule states that
![\int\limits{x^n}\ dx = \frac{x^{n+1}}{n+1} + c](https://tex.z-dn.net/?f=%5Cint%5Climits%7Bx%5En%7D%5C%20dx%20%3D%20%5Cfrac%7Bx%5E%7Bn%2B1%7D%7D%7Bn%2B1%7D%20%2B%20c)
In this case (
), n = 5;
So,
becomes
![\int\limits{x^5}\ dx = \frac{x^{5+1}}{5+1} + c](https://tex.z-dn.net/?f=%5Cint%5Climits%7Bx%5E5%7D%5C%20dx%20%3D%20%5Cfrac%7Bx%5E%7B5%2B1%7D%7D%7B5%2B1%7D%20%2B%20c)
![\int\limits{x^5}\ dx = \frac{x^{6}}{6} + c](https://tex.z-dn.net/?f=%5Cint%5Climits%7Bx%5E5%7D%5C%20dx%20%3D%20%5Cfrac%7Bx%5E%7B6%7D%7D%7B6%7D%20%2B%20c)
![\int\limits{x^5}\ dx= \frac{x^{6}}{6} + c](https://tex.z-dn.net/?f=%5Cint%5Climits%7Bx%5E5%7D%5C%20dx%3D%20%5Cfrac%7Bx%5E%7B6%7D%7D%7B6%7D%20%2B%20c)