Answer:
y = 1/6 x^2 + 8/3 x + 49/6
Step-by-step explanation:
This is a parabola which opens upwards.
The distance of a point (x, y) from the focus is
√[(x - -8)^2 + (y - -1)^2] and
the distance of the point from the line y = -4
= y - -4
These distances are equal for a parabola so:
√[(x - -8)^2 + (y - -1)^2] = y + 4
Squaring both sides:
(x + 8)^2 + (y + 1)^2 = (y + 4)^2
x^2 + 16x + 64 + y^2 + 2y + 1 = y^2 + 8y + 16
x^2 + 16x + 64 + 1 - 16 = 8y - 2y
6y = x^2 + 16x + 49
y = 1/6 x^2 + 8/3 x + 49/6 is the equation of the parabola.
Answer:
$5564.87
Step-by-step explanation:
We are to determine the difference between the future values of each investment
The formula for calculating future value:
FV = P (1 + r)^mn
FV = Future value
P = Present value
R = interest rate
N = number of years
m = number of compounding
Madeline
P = Present value = 51,000
R = interest rate = 0.06125 / 365 = 0.000168
N = number of years = 13
m = number of compounding = 365
51,000 x (1.000168)^4745 = 113,070.20
Harper
51,000 x (1.004792)^156 = 107,505.33
Difference = 113,070.20 - 107,505.33 = $5,564.87
Answer:
33.75 miles in 45 minutes,
45 miles in an hour
Step-by-step explanation:
45 minutes: 2 1/3= 7/3 ---> 7/3*3=7,
1 3/4= 7/4 ---> 7/4*3=5.25
car travels 5.25 miles for every 7 minutes,
45/7*5.25= 33.75 miles
1 hour (60 minutes):
using that the car travels 5.25 miles for every 7 minutes,
60/7*5.25= 45 miles
Hope that makes sense!
0 = 0
The input is an identity: it is true for all values
