Answer:
a. Present value of a lump sum =
PV = FV / ( 1 + i )ⁿ
b. Present value of an annuity =
P = PMT x ((1 – (1 / (1 + r)⁻ⁿ )) / r)
Step-by-step explanation:
a. Present Value of a Lump sum =
PV = FV / ( 1 + i )ⁿ
Where variables in the formula are explained as follows
PV = Present Value of the given amount today
FV = Future Value of the given amount
i = Discount rate
n = Number of periods
b. Present value of an annuity is given as:
P = PMT x ((1 – (1 / (1 + r)⁻ⁿ)) / r)
The variables in the equation are explained as the follows:
P = the present value of annuity
PMT = Payment per period or the amount in each annuity payment
r = the interest or discount rate
n = total number of periods or the number of payments left to receive
FIRST PARTWe need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative
Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached
Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13
cos α = side adjacent to the angle / hypotenuse
cos α = -5/13
Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

SECOND PARTSolve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β



Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β



Find tan (α - β)


Simplify the denominator


Simplify the numerator


Simplify the fraction

Answer:
396010000
Step-by-step explanation: You multiply 19,900 * 19900 because there are 2 pools and you will get your answer
Answer:
It's in the screenshot hope it helpsss
Step-by-step explanation: