Answer:
Using the quadratic formula to solve 5x = 6x^2 – 3, what are the values of x?
5x = 6x^2 – 3
Subtract 5x from both sides:
0 = 6x^2 – 5x – 3
a = 6, b = -5, c = -3
x = (-b ± √(b^2 - 4ac))/(2a)
x = (-(-5) ± √((-5)^2 - 4(6)(-3)))/(2(6))
x = (5 ± √(25 + 72))/12
x = (5 ± √(97))/12
Step-by-step explanation:
If you divide the original equation by "a", you have your answer.
30/a = (a*60)/a = 60*(a/a)
30/a = 60
Answer:
Her centripetal acceleration during the turn at each end of the track is ![0.432\, \frac{m}{s^{2}}](https://tex.z-dn.net/?f=0.432%5C%2C%20%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D)
Step-by-step explanation:
Total distance covered in one round , D= 400 m
Time taken to cover one round , T = 1 min 40 s = 100 sec
Speed of runner , ![V=\frac{D}{T}=\frac{400}{100}\, \frac{m}{s}= 4.0\, \frac{m}{s}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7BD%7D%7BT%7D%3D%5Cfrac%7B400%7D%7B100%7D%5C%2C%20%5Cfrac%7Bm%7D%7Bs%7D%3D%204.0%5C%2C%20%5Cfrac%7Bm%7D%7Bs%7D)
Now centripetal acceleration is given by
![a_c=\frac{V^{2}}{R}](https://tex.z-dn.net/?f=a_c%3D%5Cfrac%7BV%5E%7B2%7D%7D%7BR%7D)
where ![V= 4.0\frac{m}{s}](https://tex.z-dn.net/?f=V%3D%204.0%5Cfrac%7Bm%7D%7Bs%7D)
![Radius, R= \frac{Diameter}{2}=\frac{74}{2}m=37\, m](https://tex.z-dn.net/?f=Radius%2C%20R%3D%20%5Cfrac%7BDiameter%7D%7B2%7D%3D%5Cfrac%7B74%7D%7B2%7Dm%3D37%5C%2C%20m)
![\therefore a_c=\frac{4^{2}}{37}\, \frac{m}{s^{2}}=0.432\, \frac{m}{s^{2}}](https://tex.z-dn.net/?f=%5Ctherefore%20a_c%3D%5Cfrac%7B4%5E%7B2%7D%7D%7B37%7D%5C%2C%20%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%3D0.432%5C%2C%20%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D)
Thus her centripetal acceleration during the turn at each end of the track is ![0.432\, \frac{m}{s^{2}}](https://tex.z-dn.net/?f=0.432%5C%2C%20%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D)
Answer:
D. Keep track of the number of heads flipped in 50 flips. These represent the number of females born today. Repeat this 200 times.