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
The square root of 225 is 15. I hope that helped!
Answer:
$128
Step-by-step explanation:
1. We need to find how much 1 yard of material cost.
If needed, use a calculator*
120/75=1.6
2. Now we need to know how much 15 yards of material cost.
1.6 times 15=24
3. The buyer ordered an additional 90 yards. If we know how much 75 yards cost, and 15 yards, all you have to do is...
120+24=144
90 yards=$144
4. The additional cost is $144
(Note: the total cost would be $264 (120+144=264))
Answer:
(x - 2)² - 30
Step-by-step explanation:
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 4x
f(x) = x² + 2(- 2)x + 4 - 4 - 26 = (x - 2)² - 30
Answer:
One of the angles in the triangle might be 50.
AND
The length of the third side must be 11cm or smaller.
Step-by-step explanation:
-The triangle might be an equilateral triangle (having all the same sides and angles). False, since the triangle sum theorem states that all angles inside of a triangle must add up to 180, so an equilateral triangle would need to have all three angles at 60 degrees.
-One of the angles in the triangle must be 120 (false; it can be anything above 90, which is not only 120)
-The length of the third side must be 11cm or smaller. (True, Triangle Inequality Theorem)
-One of the angles in the triangle might be 50 (possibly, so very much true)
