1² + 3² + 4² + 4(n - 1)² = ¹/₃n(2n - 1)(2n + 1)
1² + 3² + 4² + (2n - 2)² = ¹/₃n(2n - 1)(2n + 1)
1 + 9 + 16 + (2n - 2)(2n - 2) = ¹/₃n(2n(2n + 1) - 1(2n + 1))
10 + 16 + (2n(2n - 2) - 2(2n - 2)) = ¹/₃n(2n(2n) + 2n(1) - 1(2n) - 1(1) 16 + (2n(2n) - 2n(2) - 2(2n) + 2(2)) = ¹/₃n(4n² + 2n - 2n - 1)
26 + (4n² - 4n - 4n + 4) = ¹/₃n(4n² - 1)
26 + (4n² - 8n + 4) = ¹/₃n(4n² - 1)
26 + 4n² - 8n + 4 = ¹/₃n(4n²) - ¹/₃n(1)
4n² - 8n + 4 + 26 = 1¹/₃n³ - ¹/₃n
4n² - 8n + 30 = 1¹/₃n³ - ¹/₃n
+ ¹/₃n + ¹/₃n
4n² - 7²/₃n + 30 = 1¹/₃n³
-1¹/₃n³ + 4n² - 7²/₃n + 30 = 0
-3(-1¹/₃n³ + 4n² - 7²/₃n + 30) = -3(0)
-3(-1¹/₃n³) - 3(4n²) - 3(-7²/₃n) - 3(30) = 0
4n³ - 12n² + 23n - 90 = 0
Answer:
Step-by-step explanation:
Given,
Leaning Tower of Pisa is shifted, P = 13.5 ft
Height of Leaning Tower of Pisa, B = 186 ft
Now, degree of tilt of the tower from vertical
Hence, angle of tilt is equal to
Answer:
5
Step-by-step explanation:
The equation of a line is y=mx+b. b is the y-intercept when the line is graphed. The y-intercept is when the line intersects the y-axis. m is the slope of the line. In the given equation, m is equal 5, thus the slope is 5.
Answer:
11.3 feet
Step-by-step explanation:
let x= answer
x²+4²=12²
x²=128
x=11.3137085
which rounds to
11.3
Answer:
a) when x = Raw Score: 42
Standard deviation = σ = -10.3
b) Raw Score: 81
Standard deviation = σ = 2.67
Step-by-step explanation:
Find the standard deviation if the mean of a sample is 72, a z-score of 3
Z score formula is given :
z = (x-μ)/σ,
where
x is the raw score
μ is the population mean = 73
σ is the population standard deviation
z = 3
a) when x = Raw Score: 42
z = (x-μ)/σ
3 = 42 - 73/σ
Cross Multiply
3σ = 42 - 73
3σ = -31
σ = -31/3
σ = -10.3
b) Raw Score: 81
z = (x-μ)/σ
3 = 81 - 73/σ
Cross Multiply
3σ = 81 - 73
3σ = 8
σ = 8/3
σ = 2.67
