<u>Solution-</u>
The two parabolas are,
By solving the above two equations we calculate where the two parabolas meet,
Given the symmetry, the area bounded by the two parabolas is twice the area bounded by either parabola with the x-axis.
![\therefore Area=2\int_{-c}^{c}y.dx= 2\int_{-c}^{c}(16x^2-c^2).dx\\=2[\frac{16}{3}x^3-c^2x]_{-c}^{ \ c}=2[(\frac{16}{3}c^3-c^3)-(-\frac{16}{3}c^3+c^3)]=2[\frac{32}{3}c^3-2c^3]=2(\frac{26c^3}{3})\\=\frac{52c^3}{3}](https://tex.z-dn.net/?f=%5Ctherefore%20Area%3D2%5Cint_%7B-c%7D%5E%7Bc%7Dy.dx%3D%202%5Cint_%7B-c%7D%5E%7Bc%7D%2816x%5E2-c%5E2%29.dx%5C%5C%3D2%5B%5Cfrac%7B16%7D%7B3%7Dx%5E3-c%5E2x%5D_%7B-c%7D%5E%7B%20%5C%20c%7D%3D2%5B%28%5Cfrac%7B16%7D%7B3%7Dc%5E3-c%5E3%29-%28-%5Cfrac%7B16%7D%7B3%7Dc%5E3%2Bc%5E3%29%5D%3D2%5B%5Cfrac%7B32%7D%7B3%7Dc%5E3-2c%5E3%5D%3D2%28%5Cfrac%7B26c%5E3%7D%7B3%7D%29%5C%5C%3D%5Cfrac%7B52c%5E3%7D%7B3%7D)
![So \frac{52c^3}{3}=\frac{250}{3}\Rightarrow c=\sqrt[3]{\frac{250}{52}}=1.68](https://tex.z-dn.net/?f=So%20%5Cfrac%7B52c%5E3%7D%7B3%7D%3D%5Cfrac%7B250%7D%7B3%7D%5CRightarrow%20c%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B250%7D%7B52%7D%7D%3D1.68)
Answer:
x = 2+1/3i or 2-1/3i
Step-by-step explanation:
The equation of interest can be written in vertex form as ...
9(x -2)² +1 = 0
so its solutions can be found by subtracting 1, dividing by 9, taking the square root, then adding 2.
x = 2 ± √(-1/9)
In the desired form, the zeros of the given expression are ...
x = 2 +1/3i or 2 -1/3i
Answer:
A. simpson's paradox
Step-by-step explanation:
The Simpson's paradox was named after Edward Simpson, the person who described this paradox for the first time in 1951. In this paradox, you find two contrary patterns. For example, a positive and a negative correlation, depending on how data is analyzed. The differences in the analyses are how data are grouped. This paradox is observed often in social researches. Most of the times, results are affected by the sample on each group or additional information related to the data.
Start by isolating the X.
1 :
x + 1 ¾ = 2 4/8
- 1 ¾ - 1 ¾
2 :
x = (2 4/8) - (1 ¾)
3 :
In order to subtract the fractions, you need to find a common denominator.
The common denominator can be found by multiplying the two denominators together.
4 x 8 = 32
4 :
Rewrite each fraction as an equivalent fraction with a denominator of 32.
4/8 —> (4 x 4)/(8 x 4) —> 16/32
¾ —> (3 x 8)/(4 x 8) —> 24/32
5 :
Subtract the numerators. Simplify the answer if needed.
16/32 - 24/32
16 - 24 = -8
-8/32 —> (-8/4)/(32/4) —> -2/4
-2/4 —> (-2/2)/(4/2) —> - ½
6 :
(2 - 1) - ½ —> 1 - ½ = ½
Final answer : X = ½ :)
