Answer:
D) arccsc (x) = arcsin (1/x)
Step-by-step explanation:
Here's how you can prove it: Consider a right triangle with hypotenuse 1 and a side length 1/x. If θ is the angle opposite of 1/x, then:
sin θ = 1/x
and
csc θ = x
Solving for θ:
θ = arcsin (1/x)
θ = arccsc (x)
Therefore:
arccsc (x) = arcsin (1/x)
Add all of the sides together. Make sure to use a common denominator because you are adding fractions. Don't forget your unit label (feet)
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B
The end behavior of a positive cubic function states that as x approaches infinity, y approaches infinity.
Similarly, as x approaches negative infinity, y approaches negative infinity.
This means that when written in interval notation, the range is (-inf, +inf).
(4/7)-(1/3)
(12/31)-(7/21)
(5/21) is left
Or
In decimal form
(4/7)=0.571
(1/3)= 0.333
0.571-0.333
=0.238
