Answer:
Step-by-step explanation:z=180
Interior angle =180
To get the solution, we are looking for, we need to point out what we know.
1. We assume, that the number 45.5 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 45.5 is 100%, so we can write it down as 45.5=100%.
4. We know, that x is 6.81% of the output value, so we can write it down as x=6.81%.
5. Now we have two simple equations:
1) 45.5=100%
2) x=6.81%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
45.5/x=100%/6.81%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 6.81% of 45.5
45.5/x=100/6.81
(45.5/x)*x=(100/6.81)*x - we multiply both sides of the equation by x
45.5=14.684287812041*x - we divide both sides of the equation by (14.684287812041) to get x
45.5/14.684287812041=x
3.09855=x
x=3.09855
now we have:
6.81% of 45.5=3.09855
Hope this helps!
<span>150 degrees.
Let's assume the center camera is pointed to at an angle of 0 degrees. Since it has a coverage of 60 degrees, then it will cover the angles from -30 to +30 degrees. Now we'll continue to use the +/- 30 degree coverage for the other two cameras. The second camera is aimed at 45 degrees, so it's range of coverage is 15 degrees to 75 degrees (45 +/- 30). Notice that the range from 15 degrees to 30 degrees is covered by 2 cameras. Now the 3rd camera is pointed at -45 degrees, so its coverage is from -15 degrees to -75 degrees. It also has an overlap with the 1st camera from -15 to -30 degrees.
The total coverage of all three cameras ranges from -75 degrees to 75 degrees. That means that an arc of 150 degrees in total is covered by all three cameras.</span>
Answer:
A = {3,5,6}
B = {1,3}
<u><em>A x B</em></u> = {(3,1),(3,3),(5,1),(5,3),(6,1),(6,3)}
Domain of A x B = (The x figures in ascending order)
=> {3,5,6} (Figures repeating more than once must be written only 1 time)
Range of A x B = (The y figures in ascending order)
=> {1,3}
<u><em>B x A </em></u>= {(1,3),(3,3),(1,5),(3,5),(1,6),(3,6)}
Domain of B x A = {1,3}
Range of A x B = {3,5,6}
Answer:
A), B) and D) are true
Step-by-step explanation:
A) We can prove it as follows:
B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that 
. Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then 
.
C) Consider 
. This set is orthogonal because 
, but S is not orthonormal because the norm of (0,2) is 2≠1.
D) Let A be an orthogonal matrix in 
. Then the columns of A form an orthonormal set. We have that 
. To see this, note than the component 
of the product 
is the dot product of the i-th row of 
and the jth row of 
. But the i-th row of is equal to the i-th column of . If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then 
E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.
In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set 
and suppose that there are coefficients a_i such that 
. For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then 
then 
.
