Sherrell mowed 1/15 more than Trace because when you convert the fractions to equivalent fractions with the same denominator, you get 6/15 and 5/15.
<span>The function can only change from increasing to decreasing, and visa-versa at those points where the slope of the function is 0. And the slope of the function is determined by the first derivative of the function. So let's calculate the first derivative.
f(t) = (t^3 + 3t^2)^3
f'(t) = d/dt[ (t^3 + 3t^2)^3 ]
f'(t) = 3(t^3 + 3t^2)^2 * d/dt[ t^3 + 3t^2 ]
f'(t) = 3(d/dt[ t^3 ] + 3 * d/dt[ t^2 ])(t^3 + 3t^2)^2
f'(t) = 3(3t^2 + 3 * 2t)(t^3 + 3t^2)^2
f'(t) = 3(3t^2 + 6t)(t^3 + 3t^2)^2
Simplify
f'(t) = 3(3t^2 + 6t)(t^3 + 3t^2)^2
f'(t) = 3 * 3t(t + 2)(t^3 + 3t^2)^2
f'(t) = 9t(t + 2)(t^2(t + 3))^2
f'(t) = 9t(t + 2)t^4(t + 3)^2
f'(t) = 9t^5(t + 2)(t + 3)^2
And looking at the function, it becomes obvious that the roots (or inflection points) are at t = 0, t = -2, and t = -3.
Now the only places where f(t) can switch directions is at those 3 inflection points. And at exactly those inflection points the curve is neither increasing, nor decreasing.
If the slope of the function is positive, then its value is increasing, and if the slope is negative, then the function is decreasing. So all we need to do is calculate the value of the first derivative for any value between each inflection point plus one value smaller than the smallest inflection point and another value higher than the highest inflection point.
Range from [-infinity, -3)
f'(-4) = 18432
Since the value is positive, the function is increasing from [-infinity, -3)
Range from (-3, -2)
f'(-2.5) = 30.51758
Since the value is positive, the function is increasing from (-3, -2)
Range from (-2, 0)
f(-1) = -36
Since the value is negative, the function is decreasing from (-2, 0)
Range from (0, infinity)
f(1) = 64
Since the value is positive, the function is increasing from (0, +infinity)
To summarize:
increasing from [-infinity, -3)
increasing from (-3,-2)
decreasing from (-2,0)
increasing from (0,infinity]</span>
Answer:
a. z-score for the number of sags for this transformer is ≈ 1.57 . The number of sags found in this transformer is within the highest 6% of the number of sags found in the transformers.
b. z-score for the number of swells for this transformer is ≈ -3.36. The number of swells found in the transformer is extremely low and within the lowest 1%
Step-by-step explanation:
z score of sags and swells of a randomly selected transformer can be calculated using the equation
z= where
- X is the number of sags/swells found
- M is the mean number of sags/swells
- s is the standard deviation
z-score for the number of sags for this transformer is:
z= ≈ 1.57
the number of sags found in the transformer is within the highest 6% of the number of sags found in the transformers.
z-score for the number of swells for this transformer is:
z= ≈ -3.36
the number of swells found in the transformer is extremely low and within the lowest 1%
Answer: 4
there are six sides on a cube. all sides/edges are equal so 6 sides times 4 units = 24.