Answer:
Equation of parabola: 8*(y - 2) = (x - 3)^2
or
y = (1/8)*(x - 3)^2 + 2
Step-by-step explanation:
focus at (3,4) and its directrix y = 0.
Focus equation: (h, k + c) = (3, 4)
Directrix equation y = k - c = 0
so h = 3, k + c = 4, k - c = 0
Solve the system : k + c = 4 and k - c = 0
add the equations together: k + c + k - c = 4 + 0
2k = 4
k = 2
so k + c = 4, 2 + c = 4, c = 2
4c (y - k) = (x - h)^2
4*2 *(y - 2) = (x - 3)^2
8*(y - 2) = (x - 3)^2
Answer:
Part 1) 
Part 2) 
Step-by-step explanation:
Part 1) we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
Apply log both sides
![log(2)=log[(1.01)^{6t}]](https://tex.z-dn.net/?f=log%282%29%3Dlog%5B%281.01%29%5E%7B6t%7D%5D)
solve for t

Part 2) we know that
The formula to calculate continuously compounded interest is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
substitute in the formula above
Apply ln both sides
![ln(2)=ln[(e)^{0.06t}]](https://tex.z-dn.net/?f=ln%282%29%3Dln%5B%28e%29%5E%7B0.06t%7D%5D)


You have to multiply each pair of sides and then add all the numbers together which would give you your answer
Answer: The water level drops each hour by 0.1472 inches/hour.
Step-by-step explanation:
We are given that Between 9 AM and 6:10 AM the water level in a swimming pool decreased by 5/12 inches assuming that the water level decreased at a constant rate.
Firstly, we will find the number of hours between 6:10 AM and 9 AM, that is;
Number of hours = From 6:10 AM and 9 AM, there are 2 hours and 50 minutes
So, Number of hours = = 2.833 hours
Also, the water level in a swimming pool decreased by = = 0.417 inches
Now, to find how much did the water level drop each hour, we will divide the amount of water level in a swimming pool decreased by the time interval given, that is;
=
= 0.1472 inches/hour.
This means that the water level drops each hour by 0.1472 inches/hour.
0.1472 as a fraction is 92/625
Answer:
$30,920
Step-by-step explanation:
Divide $61,840 by 2