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Andrei [34K]
3 years ago
7

Z = the sales tax percentage for a randomly selected amazon purchase, where n = the total number of possible sales tax percentag

es for online purchases Describe the set of possible values for the variable.
Mathematics
1 answer:
nikitadnepr [17]3 years ago
7 0

Answer:

[0,Z_n]

Step-by-step explanation:

Z = the sales tax percentage for a randomly selected amazon purchase, where n = the total number of possible sales tax percentages for online purchases

Since Amazon is an online purchase, The set of possible values for the variable is a positive real number. It is a positive real number that must be within Z_n. It cannot exceed the tax percentage for online purchases that can be found in Amazon. Z_n is a set of online purchases that can be found on Amazon, therefore the set of possible values for the variable is [0,Z_n]

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For what values of θ is sinθ < cosθ when 0 ≤ θ < π ?
zysi [14]
<h3>Answer:  0 \le \theta < \frac{\pi}{4}</h3>

=========================================================

How to get this answer:

Use the unit circle to note that \sin\theta = \cos\theta = \frac{\sqrt{2}}{2} when \theta = \frac{\pi}{4} (aka 45 degrees)

Beyond this point, cosine is smaller than sine. This means that anything from 0 to pi/4 will have sine be smaller than cosine. It might help to graph y = sin(x) and y = cos(x) on the interval from x = 0 to x = pi.

The two curves y = sin(x) and y = cos(x) intersect at the point \left(\frac{\pi}{4}, \frac{\sqrt{2}}{2}\right)

-------------------------------

Here's a more detailed picture of whats going on.

\sin \theta < \cos \theta\\\\\sin \theta < \sqrt{1-\sin^2\theta}\\\\\sin^2 \theta < 1-\sin^2\theta \\\\2\sin^2 \theta < 1\\\\\sin^2 \theta < \frac{1}{2}\\\\\sin \theta < \sqrt{\frac{1}{2}}\\\\\sin \theta < \frac{1}{\sqrt{2}}\\\\\sin \theta < \frac{\sqrt{2}}{2}\\\\\theta < \arcsin\left(\frac{\sqrt{2}}{2}\right)\\\\\theta < \frac{\pi}{4}\\\\

Intersect the intervals 0 \le \theta < \pi and \theta < \frac{\pi}{4} and you'll end up with the final answer 0 \le \theta < \frac{\pi}{4}

4 0
2 years ago
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