Answer:
around 3
Step-by-step explanation:
A solution to an equation is a number that can be plugged in for the variable to make a true number statement. Example 1: Substituting 2 for x in. 3x+5=11. gives.
You can figure this out if you just look at (x+a)^2 = x^2 + 2ax + a^2. See, the constant term, a^2, is the coefficient of x (2a), divided by 2 (2a/2=a), and then squared (a^2)
<span>So you equation has 8x. 8/2 = 4, and 4^2 = 16. So the answer is A.</span>
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)
Answer:
21.98 to the nearest hundredth.
Step-by-step explanation:
Geometric mean of x and y is √(xy)
= √(21*23)
= 21.98.