Answer:
a.
Step-by-step explanation:
Since f(x) is the function for the populational density at a certain sidewalk for a 5 mile stretch, a definite integral of that function will yield the total number of people within the integration intervals. If we are interested in the number of people in the whole 5 mile stretch, we must integrate f(x) from x = 0 miles to x = 5 miles:
Therefore, the answer is alternative a.
Answer:
24 units
Step-by-step explanation:
Start by plotting on the rectangular coordinate system the four points given: (6,-3), (3,-6), (-1,-2) , and (2, 1)
Please see attached image for guidance with the answer.
These four points are represented with green dots in the image.
Notice that such rectangle can be viewed as inscribed in a larger square that is 7 units by 7 units, and on which these four points (the vertices of the rectangle) touch the square's perimeter.
So to make the calculation simple, we can find the area of the larger square (very simple to calculate since it is 7 times 7 = 49) and subtract from it the area of the four triangles that are depicted in yellow and in light green. Such result will give us the area of the rectangle (white background).
Out of the four triangles whose areas we need to extract, we notice that they are all right angle triangles with simple formulas to calculate their areas: base times height divided by 2.
The triangles in green have base 3 and height 3 so their areas are: (3 * 3) /2 = 4.5. since they are two of these the total area of the green triangles is 4.5*2 = 9
We do something similar with the yellow triangles, noticing that their base and heights are 4 and 4 respectively which gives an area of (4*4)/2 = 8
Again, since there are two of them, we multiply this by 2: 8 * 2 = 16
Now to calculate the area of the white rectangle we do:
Area of big square minus area of green triangles minus area of yellow triangles: 49 - 9 - 16 = 24
