The range of the provided inverse sine function in terms of <em>x</em>, and <em>y </em>y = sin-1x is [-π/2, π/2].
<h3>What is the range of the function?</h3>
Range of a function is the set of all the possible output values which are valid for that function.
The trigonometry function given in the problem is,
The above function can be written as,
The above function is the arc of sine function. The domain of arc of sine ranges from -1 to 1.
This is the domain of the inverse of sine function. In the attached image below, the graph of inverse sine function is plotted. The range of this function is,
Thus, the range of the provided inverse sine function in terms of <em>x</em>, and <em>y </em>y = sin-1x is [-π/2, π/2].
Learn more about the range of the function here;
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Answer:
The radius of the cylinder is 7 in
Step-by-step explanation:
To calculate the radius of a cylinder we have to use the following formula:
v = volume = 980π in³
h = height = 20in
π = pi
r = radius
v = (π * r²) * h
we replace with the known values
980π in³ = (π * (r)²) * 20in
980π in³ / 20in = π * (r)²
49 in² = (r)²
√(49 in²) = r
7 in = r
The radius of the cylinder is 7 in
2/ 3 - (3 - 1) * 3 - 1 = -4
Simplify
= 2/-4
which is
= -2/4
Then simplify again
= -1/2
Remember Rise/Run
So in this one you would start at -7 on the y-intercept, and then go down one, and over to the right two.
Answer:
The number of times it would take more than 27 minutes to manufacture a pair of running shoes is 2.275 times or approximately 2 times per every 100 shoes
Step-by-step explanation:
The average time it takes to manufacture a pair of shoes = 21 minutes;
The standard deviation = 3 minutes
To find how often it takes more than 27 minutes to manufacture a pair of running shoes, we have;
Standard score, given as follows;
Where;
x = The raw score = 27 minutes
μ = The average score = 21 minutes
σ = The standard deviation = 3 minutes
From which we have;
Therefore, it is borderline unusual with a p value of P(z>2) = 1 - 0.97725 = 0.02275
Therefore, the number of times out of 100 that it would take more than 27 minutes to manufacture a pair of running shoes = 100 × 0.02275 = 2.275 times which is approximately 2 times in every 100 shoes.
