The answer is 16 pi or about 50.27
Answer:
Distance between cars rounded to the nearest foot is : 1903 ft
Step-by-step explanation:
Notice that two right triangles can be used to represent the diagram of this situation. One between the car whose angle of depression is 
, and the other with the car with angle of depression 
(see attached image)
Each triangle in the attached image is depicted with a different color. and as one can see, the distance between both cars is the addition of the side "x" in one triangle, to the side "y" in the other.
Notice as well that the information known for both right-angle triangles is one acute angle, and the side opposite to it. And what one needs to find is the side adjacent to this acute angle. Then, the function to use in both triangles, is the tangent:
a) For the [orange] triangle :
b) For the [green] triangle:
Therefore the total distance between cars is:
1081.42 ft + 821.19 ft = 1902.61 ft
which to the nearest foot can be rounded as: 1903 ft
Answer:
18 minutes
Step-by-step explanation:
A = A₀ (½)^(t / T)
where A is the final amount,
A₀ is the initial amount,
t is the time,
and T is the half life.
A = 140 when t = 10. Solve for the half life:
140 = 700 (½)^(10 / T)
0.2 = ½^(10 / T)
log 0.2 = (10 / T) log 0.5
10 / T = 2.32
T = 4.31
When A = 40, t is:
40 = 700 (½)^(t / 4.31)
0.057 = ½^(t / 4.31)
log 0.057 = (t / 4.31) log 0.5
t / 4.31 = 4.13
t = 17.8
Rounded to the nearest whole number, it takes 18 minutes.
Answer:
The equation is: y = 1/2x + 7
Step-by-step explanation:
The slope of j is -2. The slope of a line perpendicular to line j has a negative inverse: 1/2. The point is (-8, 3).
Use the point slope form of the equation:
y - y1 = m(x - x1)
Substitute:
y - 3 = 1/2(x - (-8))
y - 3 = 1/2x + 4
y = 1/2x + 4 + 3
y = 1/2x + 7
Proof:
Solve for f(x) when x = -8.
f(x) = 1/2x + 7
f(-8) = 1/2(-8) + 7
= -8/2 + 7
= -4 + 7
= 3, giving the point (-8, 3)
