F+G:
![F+G=\begin{bmatrix}{-1.8} & {-8.6} & {} \\ {2.85} & {-1.4} & {} \\ {-1.8} & {5.1} & {}\end{bmatrix}+\begin{bmatrix}{1.32} & {-1.9} & {} \\ {2.25} & {0.0} & {} \\ {-6.2} & {1.4} & {}\end{bmatrix}](https://tex.z-dn.net/?f=F%2BG%3D%5Cbegin%7Bbmatrix%7D%7B-1.8%7D%20%26%20%7B-8.6%7D%20%26%20%7B%7D%20%5C%5C%20%7B2.85%7D%20%26%20%7B-1.4%7D%20%26%20%7B%7D%20%5C%5C%20%7B-1.8%7D%20%26%20%7B5.1%7D%20%26%20%7B%7D%5Cend%7Bbmatrix%7D%2B%5Cbegin%7Bbmatrix%7D%7B1.32%7D%20%26%20%7B-1.9%7D%20%26%20%7B%7D%20%5C%5C%20%7B2.25%7D%20%26%20%7B0.0%7D%20%26%20%7B%7D%20%5C%5C%20%7B-6.2%7D%20%26%20%7B1.4%7D%20%26%20%7B%7D%5Cend%7Bbmatrix%7D)
Then, add the elements that occupy the same position:
![H=\begin{bmatrix}{-1.8+1.32} & {-8.6+(-1.9)} & {} \\ {2.85+2.25} & {-1.4+0.0} & {} \\ {-1.8+(-6.2)} & {5.1+1.4} & {}\end{bmatrix}](https://tex.z-dn.net/?f=H%3D%5Cbegin%7Bbmatrix%7D%7B-1.8%2B1.32%7D%20%26%20%7B-8.6%2B%28-1.9%29%7D%20%26%20%7B%7D%20%5C%5C%20%7B2.85%2B2.25%7D%20%26%20%7B-1.4%2B0.0%7D%20%26%20%7B%7D%20%5C%5C%20%7B-1.8%2B%28-6.2%29%7D%20%26%20%7B5.1%2B1.4%7D%20%26%20%7B%7D%5Cend%7Bbmatrix%7D)
Solve
![H=\begin{bmatrix}{-0.48} & {-10.5} & {} \\ {5.1} & {-1.4} & {} \\ {-8} & {6.5} & {}\end{bmatrix}](https://tex.z-dn.net/?f=H%3D%5Cbegin%7Bbmatrix%7D%7B-0.48%7D%20%26%20%7B-10.5%7D%20%26%20%7B%7D%20%5C%5C%20%7B5.1%7D%20%26%20%7B-1.4%7D%20%26%20%7B%7D%20%5C%5C%20%7B-8%7D%20%26%20%7B6.5%7D%20%26%20%7B%7D%5Cend%7Bbmatrix%7D)
So, we find the element at address h31:
![H=\begin{bmatrix}{h11} & {h12} & {} \\ {h21} & {h22} & {} \\ {h31} & {h32} & {}\end{bmatrix}](https://tex.z-dn.net/?f=H%3D%5Cbegin%7Bbmatrix%7D%7Bh11%7D%20%26%20%7Bh12%7D%20%26%20%7B%7D%20%5C%5C%20%7Bh21%7D%20%26%20%7Bh22%7D%20%26%20%7B%7D%20%5C%5C%20%7Bh31%7D%20%26%20%7Bh32%7D%20%26%20%7B%7D%5Cend%7Bbmatrix%7D)
In this case, position h31 is - 8.0
Answer:
Set
−
3
+
3
√
3
i
equal to
0
.
−
3
+
3
√
3
i
=
0
Since
−
3
+
3
√
3
i
≠
0
, there are no solutions.
Step-by-step explanation:
Answer:
x=90 y=45
Step-by-step explanation:
Answer is C
y and 45 are vertical angles
x=90 (right angle)
We write an inequality:
![f(x) > g(x)](https://tex.z-dn.net/?f=f%28x%29%20%3E%20g%28x%29)
![3^x + 3 > 3x + 10](https://tex.z-dn.net/?f=3%5Ex%20%2B%203%20%3E%203x%20%2B%2010)
![3^x > 3x + 7](https://tex.z-dn.net/?f=3%5Ex%20%3E%203x%20%2B%207)
This equation cannot be solved using trivial methods found in high-school classes, so we resort to graphical examination.
![3x+7](https://tex.z-dn.net/?f=3x%2B7)
is a linear function while
![3^x](https://tex.z-dn.net/?f=3%5Ex)
is an exponential one (with limit zero as
![x](https://tex.z-dn.net/?f=x)
approaches
![- \infty](https://tex.z-dn.net/?f=-%20%5Cinfty)
). We see that
![3^x = 3x+7](https://tex.z-dn.net/?f=3%5Ex%20%3D%203x%2B7)
at approximately
![x=2.4](https://tex.z-dn.net/?f=x%3D2.4)
and
![x=-2.3](https://tex.z-dn.net/?f=x%3D-2.3)
.
Indeed, using a computer algebra system such as the ones on modern TI calculators and on many internet sites gives equality at
![x=2.42, -2.31](https://tex.z-dn.net/?f=x%3D2.42%2C%20-2.31)
. By observing our graph, we see that
![f(x) > g(x)](https://tex.z-dn.net/?f=f%28x%29%20%3E%20g%28x%29)
when
![x > 2.42](https://tex.z-dn.net/?f=x%20%3E%202.42)
or
![x < -2.31](https://tex.z-dn.net/?f=x%20%3C%20-2.31)
.