two pathways meet at 30 degrees to eachother. one pathway has lighting and the other does not. the distance between successive l
ights on the lighted pathway is 5 meters. each light has a range of effective illumination of 6 meters. what length of the pathway without lights is illuminated by the pathway with lights?
1 answer:
Answer:
length of path illuminated = 17.615 m
Step-by-step explanation:
To solve the problem graphically,
1. draw two lines at 30 degrees to each other.
2. place lights at 0, 5, 10 from the intersection (assuming there is a light at the intersection.
3. draw circles of 6m at each light.
4. The furthest intersection of the circles with the other path is the end of the illuminated path.
5. See diagram attached, which is (6.658,5.766) from the illuminated path.
6. The distance of the un-illuminated path is obtained by Pythagoras theorem,
distance, d = sqrt(6.658^2+5.766^2) = 8.808m
Since the path is illuminated on each side of the intersection, the total length of illuminated path = 2d = 17.615m
d
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Answer:
We conclude that 50.
Step-by-step explanation:
We are given that x bar = 60, s = 12, n = 30, and alpha = 0.10
Also, Null Hypothesis, :
= 50
Alternate Hypothesis, :
50
The test statistics we will use here is;
T.S. = ~
where, X bar = sample mean = 60
s = sample standard deviation = 12
n = sample size = 30
So, Test statistics = ~
= 4.564
At 10% significance level, t table gives critical value of 1.311 at 29 degree of freedom. Since our test statistics is more than the critical value as 4.564 > 1.311 so we have sufficient evidence to reject null hypothesis as our test statistics will fall in the rejection region.
P-value is given by, P( > 4.564) = less than 0.05% {using t table}
Here also, P-value is less than the significance level as 0.05% < 10% , so we will reject null hypothesis.
Therefore, we conclude that 50.
Answer:
see attached
Step-by-step explanation:
The domain is the horizontal extent of the graph. The graph extends to infinity in both directions horizontally (that's what the arrows mean). There are no "holes" because the open circle at x=-1 is matched by a filled circle at the same location.
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The range is the vertical extent of the graph. The minimum is -3, which is included in the range. The maximum is infinity (as indicated by the up-pointing arrow).
