Answer:
x ∈ {0.063170, 0.722228, 1.633966, 2.293024}
Step-by-step explanation:
It is probably convenient to replace csc(4x) with its equivalent, 1/sin(4x). Then add 4 and multiply by sin(4x)/4.
1/sin(4x) -4 = 0
1/sin(4x) = 4
1/4 = sin(4x)
Using the inverse sine function, we find ...
4x = arcsin(1/4) +2kπ . . . . in radians
and the supplementary solution, ...
4x = π -arcsin(1/4) +2kπ
Dividing these by 4 gives the possible values of x.
x = arcsin(1/4)/4 +kπ/2
x = π/4 -arcsin(1/4) +kπ/2
The four smallest positive solutions will be found where k = 0 or 1.
x ∈ {0.063170, 0.722228, 1.633966, 2.293024}
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I like a graphing calculator for solving these quickly and easily.
Answer:
Step-by-step explanation:
Given:
∠1 and ∠2 are supplementary.
To prove:
l║m
Proof:
∠2 is a supplement of a. ∠1 (Given)
∠3 is a supplement of b. ∠1 [Linear pair of angles are supplementary]
Since supplements of the same angle are congruent,
c. ∠1 ≅ d. ∠2
Since ∠2 and ∠3 are also corresponding angles, l║m by the converse of same side interior angles postulate.
Answer:
c = -18
Step-by-step explanation:
We need to distribute the -3 to each term within the parentheses. This essentially means finding the sum of the product of -3 with each of those inner terms:
-3 * c + (-3) * 14 + 3 = 15
-3c - 42 + 3 = 15
-3c = 15 + 42 - 3 = 54
c = 54/(-3) = -18
c = -18
Answer:
an equivalent fraction for 1/2 is 5/10 an equivalent fraction for 1/3 is 3/9 hope this helps
Step-by-step explanation:
Step-by-step explanation:
I do not know sorry sorry
