write an equation of the line with the same slope as the line given by 5x+2y=8 and as the same y-intercept as 3x-7y=10
2 answers:
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Answer:
Step-by-step explanation:
Given:
Two fair number cubes i.e. two dice consisting the numbers 1, 2, 3, 4, 5, 6 on their faces and have equal probability of each number.
The dice are rolled.
To find:
Probability of getting the sum of two numbers as 4.
Solution:
First of all, let us have a look at the total possibilities when two dice are rolled:
([1][1], [1][2], [1][3], [1][4], [1][5], [1][6],
[2][1], [2][2], [2][3], [2][4], [2][5], [2][6],
[3][1], [3][2], [3][3], [3][4], [3][5], [3][6],
[4][1], [4][2], [4][3], [4][4], [4][5], [4][6],
[5][1], [5][2], [5][3], [5][4], [5][5], [5][6],
[6][1], [6][2], [6][3], [6][4], [6][5], [6][6])
These are total 36 possible outcomes.
For getting a sum as 4:
Possible number of favorable cases are 3 (as highlighted in BOLD in above)
Formula for probability of an event E can be observed as:
Required probability is:
The two parabolas intersect for
and so the base of each solid is the set
The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, . But since -2 ≤ x ≤ 2, this reduces to
.
a. Square cross sections will contribute a volume of
where ∆x is the thickness of the section. Then the volume would be
where we take advantage of symmetry in the first line.
b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of
We end up with the same integral as before except for the leading constant:
Using the result of part (a), the volume is
c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is
and using the result of part (a) again, the volume is