Given Vallias' value for int_{0}^{sqrt{a}} x^{2}dx, calculate his value for int_{0}^{a} sqrt{x}dx, using graph.

ediculeN 2020-11-12 Answered
Given Vallias' value for 0ax2dx,
calculate his value for 0axdx, using graph.
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oppturf
Answered 2020-11-13 Author has 94 answers

Step 1
Let's look at this picture and look at the regions
image
Step 2
From the above figure, it is observed that length and breadth of the rectangle are a and square root of a. the area of rectangle can be given as follows.
Area of the =0ax2dx+0axdx
length×breadth=0ax2dx+0axdx
a×a=0ax2dx+0axdx
0axdx=aa0ax2dx
Thus, for given Wallis's value for 0ax2dx, it be obtained that
0axdx=aa0ax2dx

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The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Total:
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
a) What percent are Black?
b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P (A and B)=P(A)P(B)P(A and B)=P(A)P(B).
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
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h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
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