Answer:
40
Step-by-step explanation:
b² - 4ac
= 16 - 4(3)(-2)
= 16 + 24
= 40
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Answer:
1/2
Step-by-step explanation:
The interior of the square is the region D = { (x,y) : 0 ≤ x,y ≤1 }. We call L(x,y) = 7y²x, M(x,y) = 8x²y. Since C is positively oriented, Green Theorem states that
Lets calculate the partial derivates of M and L, Mx and Ly. They can be computed by taking the derivate of the respective value, treating the other variable as a constant.
- Mx(x,y) = d/dx 8x²y = 16xy
- Ly(x,y) = d/dy 7y²x = 14xy
Thus, Mx(x,y) - Ly(x,y) = 2xy, and therefore, the line ntegral is equal to the double integral
We can compute the double integral by applying the Barrow's Rule, a primitive of 2xy under the variable x is x²y, thus the double integral can be computed as follows
We conclude that the line integral is 1/2
Answer:
15.15% probability that both months (different) have less than 31 days.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Also, the order of the months is not important. For example, picking July and August is the same as picking August and July. So the combinations formula is used to solve this problem
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
There are 12 months, of which February, April, June, September and November, that is, 5 of them, have less than 31 months.
Desired outcomes:
Picking 2 months from a set of 5(those with less than 31 days). So
Total outcomes:
Picking 2 months from a set of 12(all the months). So
Probability:
15.15% probability that both months (different) have less than 31 days.