Find all solutions to the equation:
1 answer:
Let z = sin(x). This means z^2 = (sin(x))^2 = sin^2(x). This allows us to go from the equation you're given to this equation: 7z^2 - 14z + 2 = -5
That turns into 7z^2 - 14z + 7 = 0 after adding 5 to both sides. Use the quadratic formula to solve for z. The only solution is z = 1 (see attached image). Since we made z = sin(x), this means sin(x) = 1. All solutions to this equation will be in the form x = (pi/2) + 2pi*n, which is the radian form of the solution set. If you need the degree form, then it would be x = 90 + 360*n
The 2pi*n (or 360*n) part ensures we get every angle coterminal to pi/2 radians (90 degrees), which captures the entire solution set.
Note: The variable n can be any integer.
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Answer:
602 tourists visited only the LEGOLAND.
Step-by-step explanation:
To solve this problem, we must build the Venn's Diagram of this set.
I am going to say that:
-The set A represents the tourists that visited LEGOLAND
-The set B represents the tourists that visited Universal Studios
-The set C represents the tourists that visited Magic Kingdown.
-The value d is the number of tourists that did not visit any of these parks, so:
We have that:
In which a is the number of tourists that only visited LEGOLAND, is the number of tourists that visited both LEGOLAND and Universal Studies,
is the number of tourists that visited both LEGOLAND and the Magic Kingdom. and
is the number of students that visited all these parks.
By the same logic, we have:
This diagram has the following subsets:
There were 1,107 tourists suveyed. This means that:
We start finding the values from the intersection of three sets.
The problem states that:
36 tourists had visited all three theme parks. So:
72 tourists had visited both LEGOLAND and Universal Studios. So:
79 tourists had visited both the Magic Kingdom and Universal Studios
68 tourists had visited both the Magic Kingdom and LEGOLAND
258 tourists had visited Universal Studios:
268 tourists had visited the Magic Kingdom:
How many tourists only visited the LEGOLAND (of these three)?
We have to find the value of a, and we can do this by the following equation:
602 tourists visited only the LEGOLAND.
1. 2sin²(-2490) + tan(1410)
2(0.25) - 0.6
0.5 + 0.6
1.1
2.
2(0.25) - 0.6
0.5 + 0.6
1.1
2.