Answer: Choice A. 1/64
Work Shown:
f(x) = 4^x
f(-3) = 4^(-3)
f(-3) = 1/(4^3) ... see note below
f(-3) = 1/64
Note: I'm using the rule that a^(-b) = 1/(a^b)
Answer:
1. 3
2. 1
3. 2
4. 4
5. 5
Step-by-step explanation:
Assume 0 < <em>x</em>/2 < <em>π</em>/2. Then
tan²(<em>x</em>/2) + 1 = sec²(<em>x</em>/2) ===> sec(<em>x</em>/2) = √(1 - tan²(<em>x</em>/2))
===> cos(<em>x</em>/2) = 1/√(1 - tan²(<em>x</em>/2))
===> cos(<em>x</em>/2) = 1/√(1 - <em>t</em> ²)
We also know that
sin²(<em>x</em>/2) + cos²(<em>x</em>/2) = 1 ===> sin(<em>x</em>/2) = √(1 - cos²(<em>x</em>/2))
Recall the double angle identities:
cos(<em>x</em>) = 2 cos²(<em>x</em>/2) - 1
sin(<em>x</em>) = 2 sin(<em>x</em>/2) cos(<em>x</em>/2)
Then
cos(<em>x</em>) = 2/(1 - <em>t</em> ²) - 1 = (1 + <em>t</em> ²)/(1 - <em>t</em> ²)
sin(<em>x</em>) = 2 √(1 - 1/(1 - <em>t</em> ²)) / √(1 - <em>t</em> ²) = 2<em>t</em>/(1 - <em>t</em> ²)
a) Aiden's taxable income is $50,450.
The taxable income is equal to the gross income minus the standard deduction.
= $50,450 ($63,000 - $12,550).
b) Aiden's marginal tax rate = 22% (for taxable income falling under the income bracket of $40,526 to $86,375 for the tax 2021 year. It is assumed that Aiden is single.
c) Aiden's effective tax rate = 13.72%. The effective tax rate = total taxes due divided by Aiden's taxable income.
= 13.72% ($6,922/$50,450 x 100)
Related links on taxable income at brainly.com/question/1160723
