Answer:
Explanation:
Given
Mass of car A
Mass of car B
velocity of cart A=3 m/s
velocity of cart B=-7 m/s
Conserving momentum
A girl performed 50 J of work lifting a heavy box. It took her 5 seconds to lift
1 answer:
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Answer:
D = -4/7 = - 0.57
C = 17/7 = 2.43
Explanation:
We have the following two equations:
First, we isolate C from equation (2):
using this value of C from equation (3) in equation (1):
<u>D = - 0.57</u>
Put this value in equation (3), we get:
<u>C = 2.43</u>
<h2>Answer:</h2>
(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
By looking at the acceleration of the object.
In fact, Netwon's second law states that the resultant of the forces acting on an object is equal to the product between the mass m of the object and its acceleration:
So, when static friction is acting on the object, if the object is still not moving we know that all the forces are balanced: in fact, since the object is stationary, its acceleration is zero, and so the resultant of the forces (left term in the formula) must be zero as well (i.e. the forces are balanced).
In fact, Netwon's second law states that the resultant of the forces acting on an object is equal to the product between the mass m of the object and its acceleration:
So, when static friction is acting on the object, if the object is still not moving we know that all the forces are balanced: in fact, since the object is stationary, its acceleration is zero, and so the resultant of the forces (left term in the formula) must be zero as well (i.e. the forces are balanced).