Answer:
8(3j-2)
Step-by-step explanation:
Answer:
(a) even function
(b) odd function
Step-by-step explanation:
From the given information;
Any function x(t) can be said to be the sum of even and odd functions.
i.e.
where;
x(t) is a real function.
For a real and even function, the Fourier transform is also real and even.
Also, the Fourier Transform of a real and odd function is imaginary and odd.
The behavior of X(f) largely depends on the behavior of x(t).
If x(t) is real and even, then x(f) is real and even valued function
Thus, the real part of X(f) is an even function.
If x(t) is real and odd, then x(f) is imaginary and odd valued function
Thus, the imaginary part of X(f) is an odd function.
Probability can never be greater than 1. Therefore 11.05 is not a possible value for a probability.
If points A, E and C are colinear, then they lie on the same line. The same statement you can say about points B, F and D.
1. Consider triangles AOC and BOD. In these triangles:
- AO≅OB (given);
- CO≅OD (given);
- ∠AOC≅∠BOD (as vertical angles).
Thus, ΔAOC≅ΔBOD by SAS Postulate (If any two corresponding sides and their included angle are the same in both triangles, then the triangles are congruent). Corresponding parts of congruent triangles are congruent, then
- AC≅BD;
- ∠ACO≅∠BDO;
- ∠CAO≅∠DBO.
Since angles ACO and BDO are alternate interior angles between lines AE and BF with transversal CD and these angles are congruent, then lines AE and BF are parallel.
This gives you that
2. Consider triangles ECO and FDO. In these triangles
- ∠CEO≅∠OFD (previous proof);
- CO≅OD (given);
- ∠ECO≅∠ODF (previous proof).
Therefore, ΔECO≅ΔFDO by AAS Postulate (if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent). Then CE≅FD.
3. Note that
Since AC≅BD and CE≅DF, then AE=AC+CE=BD+DF=BF.
