Answer:
~1.8 mile
Step-by-step explanation:
Michael lives at the closest point to the school (the origin) on Maple Street, which can be represented by the line y = 2x – 4.
This means Michael's house will be the intersection point of line y1 (y = 2x - 4) and line y2 that is perpendicular to y1 and passes the origin.
Denote equation of y2 is y = ax + b,
with a is equal to negative reciprocal of 2 => a = -1/2
y2 pass the origin (0, 0) => b = 0
=> Equation of y2:
y = (-1/2)x
To find location of Michael's house, we get y1 = y2 or:
2x - 4 = (-1/2)x
<=> 4x - 8 = -x
<=> 5x = 8
<=> x = 8/5
=> y = (-1/2)x = (-1/2)(8/5) = -4/5
=> Location of Michael' house: (x, y) = (8/5, -4/5)
Distance from Michael's house to school is:
D = sqrt(x^2 + y^2) = sqrt[(8/5)^2 + (-4/5)^2) = ~1.8 (mile)
F(11) means to replace x in the equation with 11
12(11) + 5
12 x 11 = 132
Now you have 132 + 5 = 137
F(11) = 137
9514 1404 393
Answer:
$110.52
Step-by-step explanation:
The formula for the amount resulting from continuous compounding is ...
A = P·e^(rt) . . . . . principal P compounded continuously at annual rate r for t years
Using your values, we have ...
A = 100·e^(0.05·2) = 100e^0.1 = 110.52
The resulting amount is $110.52.
Answer:
300
Step-by-step explanation:
V=4/3 * pi* r^3
If you sub in 100 for V, do some manipulation you get r cubed to equal 23.78.
Now put the value of 23.78 in for r cubed and V comes out to be 300
