Solve the following problem.
2 answers:
Answer: C
Step-by-step explanation:
Pythagorean's Theorem can only be used for right triangles. For the triangle above, the Law of Cosines must be used. The Law of Cosines can be used when you're given two sides and an angle. The general formula is below:
For the triangle above:
a = 23
b = 20
∅ = 47°
Therefore:
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Answer:
We conclude that:
Please also check the attached graph.
Step-by-step explanation:
Given
Given the function
To determine
What is the domain of the function y=-720t + 3600
We know that the domain of the function is the set of input argument values for which the function is real and defined.
Given the function
From the given function, it is clear that the function has no undefined points nor domain constraints.
Therefore, the domain of the function is
Thus, we conclude that:
Please also check the attached graph.
<h3>Answer: -7 < x < 17</h3>
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Explanation:
Plug in the lower bound of the domain, which is x = -3
f(x) = 3x+2
f(-3) = 3(-3)+2
f(-3) = -9+2
f(-3) = -7
If x = -3, then the output is y = -7. Since f(x) is an increasing function (due to the positive slope), we know that y = -7 is the lower bound of the range.
If you plugged in x = 5, you should find that f(5) = 17 making this the upper bound of the range.
The range of f(x) is -7 < y < 17
Recall that the domain and range swap places when going from the original function f(x) to the inverse
This swap happens because how x and y change places when determining the inverse itself. In other words, you go from y = 3x+2 to x = 3y+2. Solving for y gets us y = (x-2)/3 which is the inverse.
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In short, we found the range of f(x) is -7 < y < 17.
That means the domain of the inverse is -7 < x < 17 since the domain and range swap roles when going from original to inverse.