Given z=4+3i evaluate z
1 answer:
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Answer:
A
Step-by-step explanation:
Given 2 sides and the included angle use the Cosine rule to solve for x
x² = 1.6² + 1.1² - (2 × 1.6 × 1.1 × cos78° )
= 2.56 + 1.21 - ( 3.52 × cos78° )
= 3.77 - 0.7318
= 3.0382
Take the square root of both sides
x = = 1.7 → A
Answer:
Step-by-step explanation:
we know that
In a parallelogram opposite sides are congruent
In this problem
we have that
AB and DC are opposite sides
AD and BC are opposite sides
so
AB=DC
AD=BC
step 1
Find the value of x
AB=DC
substitute the given values
solve for x
step 2
Find the length of AD
we have that
substitute the value of x
step 3
Find the length of BC
Remember that
AD=BC ----> by opposite sides
therefore
Answer:
(a)
(b) 10
(c)
(d) 0
(e) 1024
Step-by-step explanation:
(a)
A = {x ∈ Z | 0 < x, x² ≤ 100}
We need to find all the elements of given set.
The given conditions are
... (1)
Taking square root on both sides.
.... (2)
Using (1) and (2) we get
Since x ∈ Z,
(b)
We need to find the value of | {x ∈ Z | 0 < x, x² ≤ 100}| or |A|. It means have to find the number of elements in set A.
| {x ∈ Z | 0 < x, x² ≤ 100}| = 10
(c)
B = {x ∈ Z | x > 10, x² ≤ 100}
We need to find all the elements of given set.
The given conditions are
... (3)
It means
.... (4)
Inequality (3) and (4) have no common solution, so B is null set or empty set.
(d)
We need to find the value of |{x ∈ Z | x > 10, x² ≤ 100}| or |B|. It means have to find the number of elements in set B.
|{x ∈ Z | x > 10, x² ≤ 100}| = 0
(e)
We need to find the value of | P(A) |. P(A) is the power set of set A.
Number of elements of a power set is
where, n is the number of elements of set A.
We know that the number of elements of set is 10. So the value of |P(A)| is
Therefore |P(A)|=1024.