Answer:
m<9=130 it also equal to 180 so 130-180 makes m<4= 50
Answer:
b = 15.75
Step-by-step explanation:
Lets find the interception points of the curves
36 x² = 25
x² = 25/36 = 0.69444
|x| = √(25/36) = 5/6
thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).
The area of the bounded region is given by the integral
![\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B5%2F6%7D_%7B-5%2F6%7D%20%7B%2825-36%20%5C%2C%20x%5E2%29%7D%20%5C%2C%20dx%20%3D%20%2825x%20-%2012%20%5C%2C%20x%5E3%29%5C%2C%20%7C_%7Bx%3D-5%2F6%7D%5E%7Bx%3D5%2F6%7D%20%3D%2025%2A5%2F6%20-%2012%2A%285%2F6%29%5E3%20-%20%2825%2A%28-5%2F6%29%20-%2012%2A%28-5%2F6%29%5E3%29%20%3D%20250%2F9)
The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.
![125/18 = \int\limits^{\sqrt{b}/6}_0 {(b - 36 \, x^2)} \, dx = (bx - 12 \, x^3)\, |_{x = 0}^{x=\sqrt{b}/6} = b^{1.5}/6 - b^{1.5}/18 = b^{1.5}/9](https://tex.z-dn.net/?f=125%2F18%20%3D%20%5Cint%5Climits%5E%7B%5Csqrt%7Bb%7D%2F6%7D_0%20%7B%28b%20-%2036%20%5C%2C%20x%5E2%29%7D%20%5C%2C%20dx%20%3D%20%28bx%20-%2012%20%5C%2C%20x%5E3%29%5C%2C%20%7C_%7Bx%20%3D%200%7D%5E%7Bx%3D%5Csqrt%7Bb%7D%2F6%7D%20%3D%20b%5E%7B1.5%7D%2F6%20-%20b%5E%7B1.5%7D%2F18%20%3D%20b%5E%7B1.5%7D%2F9)
125/18 = b^{1.5}/9
b = (62.5²)^{1/3} = 15.75
M and n are both numbers to this problem