Your answer is either A or D
Amanda purchased a 30 year $10,000 bond at par value with a 4% coupon.
We find the coupon amount each year
Coupon amount = actual amount of bond * 4%
= 10,000 * 0.04 = 400
Coupon amount for every year = 400
Total value of coupons for 30 years = 400 * 30 = 12000
$12,000 is the total value of the coupons
13pi/12 lies between pi and 2pi, which means sin(13pi/12) < 0
Recall the double angle identity,
sin^2(x) = (1 - cos(2x))/2
If we let x = 13pi/12, then
sin(13pi/12) = - sqrt[(1 - cos(13pi/6))/2]
where we took the negative square root because we expect a negative value.
Now, because cosine has a period of 2pi, we have
cos(13pi/6) = cos(2pi + pi/6) = cos(pi/6) = sqrt[3]/2
Then
sin(13pi/12) = - sqrt[(1 - sqrt[3]/2)/2]
sin(13pi/12) = - sqrt[2 - sqrt[3]]/2
You can verify this by plugging the numbers into the Pythagorean theorem,
, where c is the hypotenuse (the longest side, in this case 53).
So it would be:
The equation is true.
2809 = 2809
9514 1404 393
Answer:
5/6
Step-by-step explanation:
If q is the quantity of cereal in the box before Heba ate some, the problem tells us ...
q - 1/12 = 3/4
q = 3/4 + 1/12 = 9/12 + 1/12 = 10/12
q = 5/6
There was 5/6 of a box before Heba ate.
