Answer:
- short base: 6 yards
- long base: 8 yards
Step-by-step explanation:
Our understanding of your figure is shown below.
The question says the "shortest side" and the "width" have the same dimension. If the "width" is a reference to "height 6 yards", then it seems the "shortest side" is 6 yards. Since the slant sides are longer than the height, the "shortest side" is also the "short base."
The short base is 6 yards.
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The long base overhangs the short base by 1 yard on either end, so it is a total of 2 yards longer than the short base. It it 6+2 = 8 yards long.
The long base is 8 yards.
The maxima of f(x) occur at its critical points, where f '(x) is zero or undefined. We're given f '(x) is continuous, so we only care about the first case. Looking at the plot, we see that f '(x) = 0 when x = -4, x = 0, and x = 5.
Notice that f '(x) ≥ 0 for all x in the interval [0, 5]. This means f(x) is strictly increasing, and so the absolute maximum of f(x) over [0, 5] occurs at x = 5.
By the fundamental theorem of calculus,
The definite integral corresponds to the area of a trapezoid with height 2 and "bases" of length 5 and 2, so
Given the dataset
We start by computing the average:
We compute the difference bewteen each element and the average:
We square those differences:
And take the average of those squared differences: we sum them
And we divide by the number of elements:
Finally, we take the square root of this quantity and we have the standard deviation:
Answer: x = -7/3
Step-by-step explanation:
https://www.symbolab.com/solver/step-by-step/%5Cleft(3x%20%2B%207%5Cright)2%20%3D%20-6x%20-%2014
there are the steps
