Answer:
The height of the lighthouse is approximately 166.6 feet.
Step-by-step explanation:
Let the height of the lighthouse be represented by s, then;
Tan 48° = (opposite) ÷ (adjacent)
Tan 48° = s ÷ 150
⇒ s = 150 × Tan 48°
= 150 × 1.1106
= 166.59
s ≅ 166.6 feet
Therefore, the height of the lighthouse is approximately 166.6 feet.
Using the expression 5x + 23, the answers are as follows:
1. 5 is the coefficient.
2. 2 is the base
3. 3 is the exponent.
4. X is the variable.
The first step to determining the answer to this item is to calculate for the effective interest using the equation,
ieff = (1 + i/m)^m - 1
where ieff is the effective interest, i is the given interest and m is the number of compounding period.
Part A: m in this item is equal to 12.
Substituting,
ieff = (1 + 0.10/12)^12 - 1 = 0.1047
The amount of money after n years is calculated through the equation,
An = A(1 + ieff)^n
If An/A = 2 then,
2 = (1 + 0.1047)^n
The value of n is 6.96 years
Part B: For the continuously compounding,
An = Ae^(rt)
An/A = 2 = e^(0.10t)
The value of t is equal to 6.93 years.
Hence, the answers:
<em>Part A: 6.96 years</em>
<em>Part B: 6.93 years</em>
