Answer:
![x = \frac{ - 3b}{4} \: or \: b](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%203b%7D%7B4%7D%20%20%5C%3A%20or%20%5C%3A%20b)
Step-by-step explanation:
![\frac{1}{b + x} = \frac{3b}{2 {x}^{2} } - \frac{1}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bb%20%2B%20x%7D%20%20%3D%20%20%5Cfrac%7B3b%7D%7B2%20%7Bx%7D%5E%7B2%7D%20%7D%20%20-%20%20%5Cfrac%7B1%7D%7Bx%7D%20)
![= > \frac{1}{b + x} = \frac{3b - 2x}{2 {x}^{2} }](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20%20%5Cfrac%7B1%7D%7Bb%20%2B%20x%7D%20%20%3D%20%20%5Cfrac%7B3b%20-%202x%7D%7B2%20%7Bx%7D%5E%7B2%7D%20%7D%20)
![= > 2 {x}^{2} = (b + x)(3b - 2x)](https://tex.z-dn.net/?f=%20%3D%20%20%3E%202%20%7Bx%7D%5E%7B2%7D%20%20%3D%20%28b%20%2B%20x%29%283b%20-%202x%29)
![= > 2 {x}^{2} = 3 {b}^{2} - 2bx + 3bx - 2 {x}^{2}](https://tex.z-dn.net/?f=%20%3D%20%20%3E%202%20%7Bx%7D%5E%7B2%7D%20%20%3D%203%20%7Bb%7D%5E%7B2%7D%20%20-%202bx%20%2B%203bx%20-%202%20%7Bx%7D%5E%7B2%7D%20)
![= > 2 {b}^{2} = 3 {b}^{2} + bx - 2 {x}^{2}](https://tex.z-dn.net/?f=%20%3D%20%20%3E%202%20%7Bb%7D%5E%7B2%7D%20%20%3D%203%20%7Bb%7D%5E%7B2%7D%20%20%2B%20bx%20-%202%20%7Bx%7D%5E%7B2%7D%20)
![= > 3 {b}^{2} + bx - 4 {x}^{2} = 0](https://tex.z-dn.net/?f=%20%3D%20%20%3E%203%20%7Bb%7D%5E%7B2%7D%20%20%2B%20bx%20-%204%20%7Bx%7D%5E%7B2%7D%20%20%3D%200)
![= > 3 {b}^{2} + 4bx - 3bx - 4 {x}^{2} = 0](https://tex.z-dn.net/?f=%20%3D%20%20%3E%203%20%7Bb%7D%5E%7B2%7D%20%20%2B%204bx%20-%203bx%20-%204%20%7Bx%7D%5E%7B2%7D%20%20%3D%200)
![= > b(3b + 4x) - x(3b + 4x) = 0](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20b%283b%20%2B%204x%29%20-%20x%283b%20%2B%204x%29%20%3D%200)
![= > (3b + 4x)(b - x) = 0](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20%283b%20%2B%204x%29%28b%20-%20x%29%20%3D%200)
Hence,
![x = \frac{ - 3b}{4} \: or \: b](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%203b%7D%7B4%7D%20%20%5C%3A%20or%20%5C%3A%20b)
Answer:
H. 1/9.
Step-by-step explanation:
The area of a circle is calculated by solving for π
.
The smallest circle has an area of π
= π * 1 = π.
The middle ring will then have an area of π
- π = π * 4 - π = 4π - π = 3π.
The largest ring will then have an area of π
- π
= 9π - 4π = 5π.
5π + 3π + π = 9π
So, the probability of hitting the innermost circle will be π / 9π = 1 / 9.
Your answer is H. 1/9.
Hope this helps!
Answer:
R/Z
Step-by-step explanation:
Three rational numbers between 1/3 and 1/2 making the denominator same: 1/3=8/24(equivalent fraction) 1/2=12/24(also equivalent fraction). Three rational numbers between 8/24 and 12/24 are: 9/24,10/24,11/24. Hope this helps!