Answer:
12 meters
Step-by-step explanation:
Draw a picture of the two pathways 30° apart. Add a circle representing the illumination of the light on one of the pathways. Draw a line from the center of the circle to the last point where it intersects the pathway without lights.
This forms a triangle. One leg is x, the length of the pathway without lights. Another leg is 5n, where n is an integer. This represents how far the light is from where the pathways meet. The third and final leg is 6, the radius of the illumination.
Use law of cosine to solve:
6² = x² + (5n)² − 2x(5n) cos 30°
36 = x² + 25n² − 5√3 xn
0 = x² − 5√3 xn + 25n² − 36
In order to have a solution, the discriminant must be greater than or equal to 0.
b² − 4ac ≥ 0
(-5√3 n)² − 4(1)(25n² − 36) ≥ 0
75n² − 100n² + 144 ≥ 0
144 − 25n² ≥ 0
144 ≥ 25n²
144/25 ≥ n²
12/5 ≥ n
So n must be an integer less than 12/5, or 2.4. Therefore, the largest value of n is 2. Substituting:
0 = x² − 5√3 x(2) + 25(2)² − 36
0 = x² − 10√3 x + 64
Solve with quadratic formula:
x = [ 10√3 ± √(300 − 4(1)(64)) ] / 2(1)
x = (10√3 ± √44) / 2
x = 5√3 ± √11
x ≈ 5.34 or 11.98
We want the larger value of x. So approximately 12 meters of the pathway without lights is illuminated.
Answer:
The formula for this arithmetic sequence:
Step-by-step explanation:
As
- weighing about a ton on their 14th birthday, weighing about a ton on their 14th birthday, the average T-Rex grew 4.6 pounds per day from the age 14 to 18 years.
Let the general term of the arithmetic sequence represent the weight in tons of the T-Rex where is the number of days.
Therefore, the formula for this arithmetic sequence:
Keywords: arithmetic sequence
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Answer:
The test statistic value 't' = 3.074
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given sample size 'n' = 15
mean of the Population 'μ' = $39
mean of the sample x⁻ = $42
standard deviation of the sample 's' = $3.78
Degrees of freedom ν = n-1 = 15-1 =14
Null hypothesis : There is no significance difference between the means
H₀ : x⁻ = 'μ'
Alternative hypothesis : There is significance difference between the means
H₀ : x⁻ ≠ 'μ'
<u><em>Test statistic </em></u>
<em>t = 3.074</em>
The test value of t-statistic <em>t = 3.074</em>
<em>The calculated value </em> <em>t = 3.074 > 1.769 at 0.05 level of significance</em>
<em>null hypothesis is rejected</em>
<em>Alternative hypothesis is accepted</em>
<u><em>Final answer</em></u><em>:-</em>
There is significance difference between the means
<em></em>
Answer:a. (5 * 9) * (10^3 * 10^7)
45 * 10^3+7
45 * 10^10 = 4.5 * 10^11
b. 7 * 10^5/2 * 10^2
7 * 10^3/2
7 * 1000/2
7 * 500 = 3500 or 3.5 * 10^3
Step-by-step explanation: