The final velocity is
The distance traveled by the ball at time t is
The maximum distance traveled by the object is
The given parameters;
initial velocity of the ball, u = 20 m/s
acceleration due to gravity, g = 9.8 m/s²
The final velocity can be calculate as;
The distance traveled by the ball at time t;
The maximum distance traveled by the object is calculated as;
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Answer:
The capacitance is 1.75 nF
Explanation:
From the question we are given that
The inner radius is
The outer radius is
Length of the capacitor is
The dielectric constant is
The dielectric constant is
Generally the capacitance of a capacitor can be mathematically represented as
(a) standard deviation = σ = 4.9996
(b) variance = σ² = 24.996
<h2>Explanation:</h2><h2 /><em>Given frequency table (find attached as Table 1);</em>
<u></u>
(a) To find the sample standard deviation and sample variance, follow these steps;
<em>i. Calculate the mid-point c for each group by using the mid-point formula;</em>
c = (lower bound + upper bound) / 2
=> c = (6.51 + 8.50) / 2 = 7.505
=> c = (8.51 + 10.50) / 2 = 9.505
=> c = (10.51 + 12.50) / 2 = 11.505
=> c = (12.51 + 14.50) / 2 = 13.505
=> c = (14.51 + 16.50) / 2 = 15.505
<em>So the new table becomes (find attached as Table 2);</em>
<em>ii. Calculate the total number of samples (n) which is the sum of all the frequencies.</em>
n = 50+18+42+20+46
n = 176
<em>iii. Calculate the mean (M)</em>
This is done by first multiplying the midpoints by the corresponding frequencies and then dividing the result by the total number of samples (n).
M = [(7.505 x 50) + (9.505 x 18) + (11.505 x 42) + (13.505 x 20) + (15.505 x 46)] / 176
M = [375.25 + 171.09 + 483.21 + 270.1 + 713.23] / 176
M = [2012.88] / 176
M = 11.44
<em>iv. Find the variance (σ²);</em>
The variance is calculated using the following formula
σ² = [Σ(f x c²) - (n x M²)] / (n - 1) ------------(i)
Where;
f = frequency of each boundary data point
<em>=> Let's first calculate </em>Σ(f x c²).
This is done by finding the sum of the product of the frequency (f) of each boundary point and the square of their corresponding mid-points(c)
Σ(f x c²) = [(50 x 7.505²) + (18 x 9.505²) + (42 x 11.505²) + (20 x 13.505²) + (46 x 15.505²)]
Σ(f x c²) = [(2816.25125) + (1626.21045) + (5559.33105) + (3647.7005) + (11058.63115)]
Σ(f x c²) = 24708.1244
<em>=> Now calculate (n x M²)</em>
n x M² = 176 x 11.44²
n x M² = 23033.7536
<em>=> Now substitute these values into equation (i) to calculate the variance</em>
σ² = [Σ(f x c²) - (n x M²)] / (n - 1)
σ² = [24708.1244 - 23033.7536] / (176 - 1)
σ² = [4374.3708] / (175)
σ² = 24.996
Therefore, the variance is 24.996
<em>v. Find the standard deviation (σ)</em>
The standard deviation is the square root of the variance. i.e
σ = √σ²
σ = √24.996
σ = 4.9996
Therefore, the standard deviation is 4.9996
