Answer:
x = -10 ° + π/6 + (2 π n_1)/3 for n_1 element Z
or x = 30 ° + π/2 + 2 π n_2 for n_2 element Z
Step-by-step explanation:
Solve for x:
sin(2 x) = cos(x + 30 °)
Rewrite the right hand side using cos(θ) = sin(θ + π/2):
sin(2 x) = sin(30 ° + π/2 + x)
Take the inverse sine of both sides:
2 x = -30 ° + π/2 - x + 2 π n_1 for n_1 element Z
or 2 x = 30 ° + π/2 + x + 2 π n_2 for n_2 element Z
Add x to both sides:
3 x = -30 ° + π/2 + 2 π n_1 for n_1 element Z
or 2 x = 30 ° + π/2 + x + 2 π n_2 for n_2 element Z
Divide both sides by 3:
x = -10 ° + π/6 + (2 π n_1)/3 for n_1 element Z
or 2 x = 30 ° + π/2 + x + 2 π n_2 for n_2 element Z
Subtract x from both sides:
Answer: x = -10 ° + π/6 + (2 π n_1)/3 for n_1 element Z
or x = 30 ° + π/2 + 2 π n_2 for n_2 element Z
The amount of money in the account if compounded quarterly at 6% after 9 years is $22,217
<h3>Compound interest</h3>
- Principal, P = $13,000
- Time, t = 9 years
- Interest rate, r = 6% = 0.06
- Number of periods, n = 4
A = P(1 + r/n)^nt
= 13,000(1 + 0.06/4)^4×9
= 13,000(1 + 0.015)^36
= 13,000(1.015)^36
= 13000(1.709)
= $22,217
Learn more about compound interest:
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Answer:
$9,220,000(0.888)^t
Step-by-step explanation:
Model this using the following formula:
Value = (Present Value)*(1 - rate of decay)^(number of years)
Here, Value after t years = $9,220,000(1 -0.112)^t
Value after t years = $9,220,000(0.888)^t
Answer:
-6 and -6
Step-by-step explanation:
-6+(-6)=-12
-6x-6=36
