Taking the observation point as a vertex. The line to the observed window is the hypotenuse of a right triangle formed with the horizontal distance between the two buildings and the opposite leg to the angle of elevation.
The tangent of this angle is the ratio between the opposite leg and the adjacent leg. And the opposite leg is also the height from the height of the observation window to the observed window.
If h is the height from ground level to the second window, we will call h - 40 to the opposite leg and d to the adjacent leg that is also the horizontal distance between the buildings.
tangent(43º) = 0,93251509 = (h - 40)/d
h = tangent(43º)*d + 40 feet = 0,93251509*110 feet + 40 feet = 142.58 feet
Answer = C.) = 140 feet above the ground level is the second window.
Answer:
x = 3 or x = -1/4
Step-by-step explanation:
from (x-3)(4x+1) = 0
We can see that a * b = 0
so a = 0 or b = 0
thus
x - 3 = 0 or 4x + 1 = 0
we solve x = 3 or x = -1/4
It has been given that exactly 0.1 of the radioactive nuclei in a sample decay each hour. Thus, after n hours, the fraction of nuclei is given by the model expression: .
Now, to find the value of n equal to one half-life, all that we need to do is to equate the above expression to half or 0.500 (to the indicated places of decimal) and solve for n.
Thus, we will get:
Taking the log to the base 10 on both sides, we get: (Please note that we can take the log to any base)
Dividing both sides by log(0.900), we get:
hours
Therefore the value of n equal to one half-life is 6.579 hours.