Answer:

Step-by-step explanation:
Given that:
![\int \int _R 4xye^{x^2 \ y} \ dA, R = [0,1]\times [0,7]](https://tex.z-dn.net/?f=%5Cint%20%5Cint%20_R%204xye%5E%7Bx%5E2%20%5C%20y%7D%20%5C%20dA%2C%20R%20%3D%20%5B0%2C1%5D%5Ctimes%20%5B0%2C7%5D)
The rectangle R = [0,1] × [0,7]
R = { (x,y): x ∈ [0,1] and y ∈ [0,7] }
R = { (x,y): 0 ≤ x ≤ 1 and 0 ≤ x ≤ 7 }




![\int \int _R \ 4xy e^{x^2 \ y} \ dA = \dfrac{4}{2}[e^y -1]^7_0 \ dy](https://tex.z-dn.net/?f=%5Cint%20%5Cint%20_R%20%5C%204xy%20e%5E%7Bx%5E2%20%5C%20y%7D%20%20%5C%20dA%20%3D%20%20%5Cdfrac%7B4%7D%7B2%7D%5Be%5Ey%20-1%5D%5E7_0%20%5C%20dy)
![\int \int _R \ 4xy e^{x^2 \ y} \ dA = 2 [(e^7 -7)-(e^0 -0)]](https://tex.z-dn.net/?f=%5Cint%20%5Cint%20_R%20%5C%204xy%20e%5E%7Bx%5E2%20%5C%20y%7D%20%20%5C%20dA%20%3D%20%202%20%5B%28e%5E7%20-7%29-%28e%5E0%20-0%29%5D)
![\int \int _R \ 4xy e^{x^2 \ y} \ dA = 2 [(e^7 -7)-1]](https://tex.z-dn.net/?f=%5Cint%20%5Cint%20_R%20%5C%204xy%20e%5E%7Bx%5E2%20%5C%20y%7D%20%20%5C%20dA%20%3D%20%202%20%5B%28e%5E7%20-7%29-1%5D)

Answer:
Slope: -1/4; Y-Intercept: 1.5
Step-by-step explanation:
Step 1: Find the slope. The best way to do this is to transform the two given points to y=mx+b form. When given two points, the best way to find the slope will be to do y2-y1/x2-x1. In this equation it would be -2-0/2+6, which is -2/8, simplified is -0.25 or -1/4. So we have the slope, which can determine the length of the line.
Step 2: Find the Y-Intercept. Finding the Y-intercept is so much simpler when given a graph, since all you have to do is find where the line goes through the y-axis, which in this case is (0,1.5), meaning that the y-intercept is 1.5 <em>(note: the y-intercept can also be found when x=0, for example (0,9).</em>
Hope this helped, good luck!
Answer/Step-by-step explanation:
Area of trapezium = ½*(AD + BC)*AB
Area = 42 cm²
AD = (x + 8) cm
BC = (x + 5) cm
AB = x cm
Plug in the values into the equation
42 = ½((x + 8) + (x + 5))*x
42 = ½((x + 8 + x + 5)*x
42 = ½(2x + 13)*x
Multiply both sides by 2
42*2 = (2x + 13)*x
84 = 2x² + 13x
2x² + 13x = 84
Subtract both sides by 84
2x² + 13x - 84 = 0
M/8 = 21/6
m = 8 *21 / 6
m = 28
answer
D . 28
Answer:
13.1868131868
Step-by-step explanation:
24 divided by 90 equals 0.26373626373, which then multiplied by 50, equals 13.1868131868.