Vector A has a magnitude of 6.00 units and is directed at 60° to the positive x-axis. Vector B has a magnitude of 6.00 units and
is directed at 120° to the positive x-axis. Find the magnitude and direction of vector C such that A+B+C=0. Place the three vectors so that one begins where the previous ends.What do you observe?
1 answer:
Answer:
C has a magnitud of 10.4 units and is directed 270° from the positive x-axis
Step-by-step explanation:
As it shows on the attached picture, the xA and xB have equal magnitudes but opposite directions, therefore they cancel eachother out in the x-axis.
However, the yA and yB are equal in magnitud, but have the same direction. So, the create a total vector the is completely on the y-axis and it's magnitude is 2*(sin(60°)*6)=10.4 units.
In order for C to cancel this vector, it's magnitude also needs to be 10.4 units, but pointing the other way. Therefore, the angle needs to be 270° from the positive x-axis.
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Answer:
34175 people will live in Pattersonville 8 years from now
Step-by-step explanation:
Initial population of Pattersonville =40,500
We are given that The census indicated that the population of the town has been decreasing by 2.1% per year .
Now we are supposed to find If this trend continues , approximately how many people will live in Pattersonville 8 years from now
Formula :
Where N(t)= Population after t years
= Initial population
r = rate of decrease = 2.1 %=0.021
t = 8 years
Substitute the values in the formula :
So,
N(8)=34175.63223
So, 34175 people will live in Pattersonville 8 years from now
Answer:
p(on schedule) ≈ 0.7755
Step-by-step explanation:
A suitable probability calculator can show you this answer.
_____
The z-values corresponding to the build time limits are ...
z = (37.5 -45)/6.75 ≈ -1.1111
z = (54 -45)/6.75 ≈ 1.3333
You can look these up in a suitable CDF table and find the difference between the values you find. That will be about ...
0.90879 -0.13326 = 0.77553
The probability assembly will stay on schedule is about 78%.
