9514 1404 393
Answer:
(c) 1.649
Step-by-step explanation:
For a lot of these summation problems it is worthwhile to learn to use a calculator or spreadsheet to do the arithmetic. Here, the ends of the intervals are 1 unit apart, so we only need to evaluate the function for integer values of x.
Almost any of these numerical integration methods involve some sort of weighted sum. For <em>trapezoidal</em> integration, the weights of all of the middle function values are 1. The weights of the first and last function values are 1/2. The weighted sum is multiplied by the interval width, which is 1 for this problem.
The area by trapezoidal integration is about 1.649 square units.
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In the attached, we have shown the calculation both by computing the area of each trapezoid (f1 does that), and by creating the weighted sum of function values.
Answer:
Step-by-step explanation:
Use distribution
This problem here would be a little tricky. Let us take into account first the variables presented which are the following: a collection of triangular and square tiles, 25 tiles, and 84 edges. Triangles and squares are 2D in shape so they give us a variable of 3 and 4 to work on those edges. Let us say that we represent square tiles with x and triangular tiles with y. There would be two equations which look like these:
x + y = 25 and 4x + 3y = 84
The first one would refer to the number of tiles and the second one to number of edges.
We will be using the first equation to the second equation and solve for one. So if we will be looking for y for instance, then x in the second equation would be substituted with x = 25 - y which would look like this:
4 (25 - y) + 3y = 84
Solve.
100 - 4y + 3y = 84
-4y +3y = 84 - 100
-y = -16
-y/-1 = -16/-1
y = 16
Then:
x = 25 -y
x = 25 - 16
x = 9
So the answer is that there are 9 square tiles and 16 triangular tiles.
Answer:
Depends on how much it costs...
Step-by-step explanation:
Exact value of x will be 8 x sin(60)
Exact value of sin 60 = √3/2
So √3/2 x 8= 8 √3/2
Can be simplified to 4 √3
