Answer: This is a statement. This is not a question.
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Answer:
(√7)/3
Step-by-step explanation:
The relationship between tangent and cosine is ...
tan(α) = √(1/cos(α)² -1)
The cosine of the angle is given as 3/4, so the tangent is ...
tan(arccos(3/4)) = √(1/(3/4)² -1) = √(16/9 -1) = √(7/9)
tan(arccos(3/4)) = (√7)/3
Answer:
The two numbers following 1,-2,3,-4,5... are -6 and 7.
Step-by-step explanation:
index: 1 2 3 4 5 ....
value: 1 -2 3 -4 5
Let the index be n. Then the first term is a(1), the secon is a(2), and so on.
a(2) = 2*(-1)^(2-1) = 2*(-1) = -2 (correct)
a(3) = 3*(-1)^(3-1) = 3*(-1)^2 = 3 (correct)
a(4) = 4*(-1)^(4-1) = 4*(-1)^3 = -4 (correct)
So the general formula for a(n) is: a(n)=n(-1)^(n-1)
Thus,
a(5) = 5(-1)^4 = 5
a(6) = 6(-1)^5 = -6
a(7) = 7(-1)^6 = 7
The "next two numbers in the pattern" are -6 and 7. The first 7 numbers are
1,-2,3,-4,5, -6, 7
Answer:
there is an economic principle that states that 1 dollar today is worth more than 1 dollar in the future, since an invested dollar could earn interests and gain value.
For example, we can assume a 6% interest rate (0.5% monthly interest rate), and using the present value formula we can determine the present value of $100:
- given to us in 30 days = $100 / (1 + 0.5%)¹ = $99.50
- given to us in 150 days = $100 / (1 + 0.5%)⁵ = $97.54
- given to us in 300 days = $100 / (1 + 0.5%)¹⁰ = $95.13
In order to calculate the value of $100 given to us tomorrow, we would need to determine a daily interest rate = 6% / 360 = 0.00017
- $100 given to us tomorrow = $100 / (1 + 0.00017)¹ = $99.98
since the amount of money is not that large and the interest rate is rather low, the difference in value is not that large. But imagine if you used a 24% interest rate instead of 6% (monthly interest rate = 2%)
- $100 given to us in 30 days = $100 / (1 + 2%)¹ = $98.04
- $100 given to us in 150 days = $100 / (1 + 2%)⁵ = $90.57
- $100 given to us in 300 days = $100 / (1 + 2%)¹⁰ = $82.03
as the interest rate increases, the present value decreases.
