An airplane is flying at an elevation of 20,000 feet and descends at a rate of 325 feet per minute for 8 minutes. What is the new elevation of the airplane?
Answer: 17,400
I put the explanation down below! Hope this helps!
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:
11 breads
Step-by-step explanation:
Note that:
1 bread recipe = 1 bread
From the above question, we know that:
2/3 cups of walnut = 1 bread
7 1/2 cups of walnut = x breads
Cross Multiply
2/3 cups × x breads = 7 1/2 cups × 1 bread
x breads = 7 1/2 cups × 1 bread/2/3 cups
x breads = 7 1/2 ÷ 2/3
x breads = 15/2 ÷ 2/3
x breads = 15/2 × 3/2
x breads = 45/4
x breads = 11 1/4 breads
Maximum full recipe = 11 breads.
Therefore, the MAXIMUM numbers of full recipe of walnut bread the baker can make is 11 breads.
833
Seravalle____________Chiesanuova______________San Marino
|---------------------------------------------------------------------|
982
so the distance from Chiesanuova to Serravalle is :
982 - 833 = 149 miles <==
When asked these kinds of problems you find the discriminate and use that to tell if you have one , two or zero real solutions.
The formula for the discriminate is b^2 - 4ac. I hope that looks familiar because it is the inside part of the quadratic formula. (the part under the radical)
so if your answer is greater than zero you have two solutions
if your answer is equal to zero you have one solution
if your answer is less than zero you have no real solutions it will be a complex solution.
So lets apply all that to your question:
5^2 - 4(1)(7) = -3
so your answer would be B no real-number solution.