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
![\int\limits_C {L(x,y)} \, dx + {M(x,y)} \, dy = \int\limits^1_0\int\limits^1_0 {(Mx - Ly)} \, dxdy](https://tex.z-dn.net/?f=%5Cint%5Climits_C%20%7BL%28x%2Cy%29%7D%20%5C%2C%20dx%20%2B%20%7BM%28x%2Cy%29%7D%20%5C%2C%20dy%20%3D%20%5Cint%5Climits%5E1_0%5Cint%5Climits%5E1_0%20%7B%28Mx%20-%20Ly%29%7D%20%5C%2C%20dxdy)
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
![\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E1_0%5Cint%5Climits%5E1_0%20%7B2xy%7D%20%5C%2C%20dxdy)
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
![\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy = \int\limits^1_0 {x^2y} |^1_0 \,dy = \int\limits^1_0 {y} \, dy = \frac{y^2}{2} \, |^1_0 = 1/2](https://tex.z-dn.net/?f=%5Cint%5Climits%5E1_0%5Cint%5Climits%5E1_0%20%7B2xy%7D%20%5C%2C%20dxdy%20%3D%20%5Cint%5Climits%5E1_0%20%7Bx%5E2y%7D%20%7C%5E1_0%20%5C%2Cdy%20%3D%20%5Cint%5Climits%5E1_0%20%7By%7D%20%5C%2C%20dy%20%3D%20%5Cfrac%7By%5E2%7D%7B2%7D%20%5C%2C%20%7C%5E1_0%20%3D%201%2F2)
We conclude that the line integral is 1/2
Answer:b=7-2-=2
Step-by-step explanation:
Answer:
Step-by-step explanation:
The number of samples is large(greater than or equal to 30). According to the central limit theorem, as the sample size increases, the distribution tends towards normal. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 22199
σ = 5300
n = 30
the probability that a senior owes a mean of more than $20,200 is expressed as
P(x > 20200)
Where x is a random variable representing the average credit card debt for college seniors.
For n = 30,
z = (20200 - 22199)/(5300/√30) =
- 2.07
Looking at the normal distribution table, the probability corresponding to the z score is 0.0197
P(x > 20200) = 0.0197
Answer:
triangle cannot be right-angled and obtuse angled at the same time. Since a right-angled triangle has one right angle, the other two angles are acute. Therefore, an obtuse-angled triangle can never have a right angle; and vice versa. The side opposite the obtuse angle in the triangle is the longest.
Step-by-step explanation:
No; in a right triangle, the other two angles are complementary so they are both less than 90° CLASSIFYING TRIANGLES Copy the triangle and measure its angles.