Answer: 15x + 6
5x + 2x+3 = 7x+3
6x+4 + 7x+3 = 13x + 7
13x+7 + 2x-1 = 15x+ 6
Answer:
What is the change in y-values from
Point A to Point B?
50
What is the change in x-values from
Point A to Point B?
1
What is the rate of change of the linear function?
50
feet per second
Step-by-step explanation:
Before you try to undersand the formula for how to rewrite<span> a </span>logarithm<span> equation as exponential equation, you should be comfortable solving exponential</span>
Upward motion
Hope that helps
Answer:
a) This integral can be evaluated using the basic integration rules. ![\int 11x^{4}dx = \frac{11}{5} x^{5}+C](https://tex.z-dn.net/?f=%5Cint%2011x%5E%7B4%7Ddx%20%3D%20%5Cfrac%7B11%7D%7B5%7D%20x%5E%7B5%7D%2BC)
b) This integral can be evaluated using the basic integration rules. ![\int 8x^{1}x^{4}dx=\frac{4}{3}x^{6}+C](https://tex.z-dn.net/?f=%5Cint%208x%5E%7B1%7Dx%5E%7B4%7Ddx%3D%5Cfrac%7B4%7D%7B3%7Dx%5E%7B6%7D%2BC)
c) This integral can be evaluated using the basic integration rules. ![\int 3x^{31}x^{4}dx=\frac{x^{36}}{12}+C](https://tex.z-dn.net/?f=%5Cint%203x%5E%7B31%7Dx%5E%7B4%7Ddx%3D%5Cfrac%7Bx%5E%7B36%7D%7D%7B12%7D%2BC)
Step-by-step explanation:
a) ![\int 11x^{4}dx](https://tex.z-dn.net/?f=%5Cint%2011x%5E%7B4%7Ddx)
In order to solve this problem, we can directly make use of the power rule of integration, which looks like this:
![\int kx^{n}=k\frac{x^{n+1}}{n+1}+C](https://tex.z-dn.net/?f=%5Cint%20kx%5E%7Bn%7D%3Dk%5Cfrac%7Bx%5E%7Bn%2B1%7D%7D%7Bn%2B1%7D%2BC)
so in this case we would get:
![\int 11x^{4}dx=11 \frac{x^{4+1}}{4+1}+C](https://tex.z-dn.net/?f=%5Cint%2011x%5E%7B4%7Ddx%3D11%20%5Cfrac%7Bx%5E%7B4%2B1%7D%7D%7B4%2B1%7D%2BC)
![\int 11x^{4}dx=11 \frac{x^{5}}{5}+C](https://tex.z-dn.net/?f=%5Cint%2011x%5E%7B4%7Ddx%3D11%20%5Cfrac%7Bx%5E%7B5%7D%7D%7B5%7D%2BC)
b) ![\int 8x^{1}x^{4}dx](https://tex.z-dn.net/?f=%5Cint%208x%5E%7B1%7Dx%5E%7B4%7Ddx)
In order to solve this problem we just need to use some algebra to simplify it. By using power rules, we get that:
![\int 8x^{1}x^{4}dx=\int 8x^{1+4}dx=\int 8x^{5}dx](https://tex.z-dn.net/?f=%5Cint%208x%5E%7B1%7Dx%5E%7B4%7Ddx%3D%5Cint%208x%5E%7B1%2B4%7Ddx%3D%5Cint%208x%5E%7B5%7Ddx)
So we can now use the power rule of integration:
![\int 8x^{5}dx=\frac{8}{5+1}x^{5+1}+C](https://tex.z-dn.net/?f=%5Cint%208x%5E%7B5%7Ddx%3D%5Cfrac%7B8%7D%7B5%2B1%7Dx%5E%7B5%2B1%7D%2BC)
![\int 8x^{5}dx=\frac{8}{6}x^{6}+C](https://tex.z-dn.net/?f=%5Cint%208x%5E%7B5%7Ddx%3D%5Cfrac%7B8%7D%7B6%7Dx%5E%7B6%7D%2BC)
![\int 8x^{5}dx=\frac{4}{3}x^{6}+C](https://tex.z-dn.net/?f=%5Cint%208x%5E%7B5%7Ddx%3D%5Cfrac%7B4%7D%7B3%7Dx%5E%7B6%7D%2BC)
c) The same applies to this problem:
![\int 3x^{31}x^{4}dx=\int 3x^{31+4}dx=\int 3x^{35}dx](https://tex.z-dn.net/?f=%5Cint%203x%5E%7B31%7Dx%5E%7B4%7Ddx%3D%5Cint%203x%5E%7B31%2B4%7Ddx%3D%5Cint%203x%5E%7B35%7Ddx)
and now we can use the power rule of integration:
![\int 3x^{35}dx=\frac{3x^{35+1}}{35+1}+C](https://tex.z-dn.net/?f=%5Cint%203x%5E%7B35%7Ddx%3D%5Cfrac%7B3x%5E%7B35%2B1%7D%7D%7B35%2B1%7D%2BC)
![\int 3x^{35}dx=\frac{3x^{36}}{36}+C](https://tex.z-dn.net/?f=%5Cint%203x%5E%7B35%7Ddx%3D%5Cfrac%7B3x%5E%7B36%7D%7D%7B36%7D%2BC)
![\int 3x^{35}dx=\frac{x^{36}}{12}+C](https://tex.z-dn.net/?f=%5Cint%203x%5E%7B35%7Ddx%3D%5Cfrac%7Bx%5E%7B36%7D%7D%7B12%7D%2BC)