Answer:
![y=\pm i \sqrt{7}](https://tex.z-dn.net/?f=y%3D%5Cpm%20i%20%5Csqrt%7B7%7D)
Step-by-step explanation:
Given equation is ![\frac{y}{\left(y-4\right)}-\frac{4}{\left(y+4\right)}=\frac{3^2}{(y^2-16)}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B%5Cleft%28y-4%5Cright%29%7D-%5Cfrac%7B4%7D%7B%5Cleft%28y%2B4%5Cright%29%7D%3D%5Cfrac%7B3%5E2%7D%7B%28y%5E2-16%29%7D)
Factor denominators then solve by making denominators equal
![\frac{y}{\left(y-4\right)}-\frac{4}{\left(y+4\right)}=\frac{3^2}{(y^2-16)}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B%5Cleft%28y-4%5Cright%29%7D-%5Cfrac%7B4%7D%7B%5Cleft%28y%2B4%5Cright%29%7D%3D%5Cfrac%7B3%5E2%7D%7B%28y%5E2-16%29%7D)
![\frac{y}{\left(y-4\right)}-\frac{4}{\left(y+4\right)}=\frac{9}{(y+4)\left(y-4\right)}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B%5Cleft%28y-4%5Cright%29%7D-%5Cfrac%7B4%7D%7B%5Cleft%28y%2B4%5Cright%29%7D%3D%5Cfrac%7B9%7D%7B%28y%2B4%29%5Cleft%28y-4%5Cright%29%7D)
![\frac{y\left(y+4\right)-4\left(y-4\right)}{\left(y-4\right)\left(y+4\right)}=\frac{9}{(y+4)\left(y-4\right)}](https://tex.z-dn.net/?f=%5Cfrac%7By%5Cleft%28y%2B4%5Cright%29-4%5Cleft%28y-4%5Cright%29%7D%7B%5Cleft%28y-4%5Cright%29%5Cleft%28y%2B4%5Cright%29%7D%3D%5Cfrac%7B9%7D%7B%28y%2B4%29%5Cleft%28y-4%5Cright%29%7D)
![y\left(y+4\right)-4\left(y-4\right)=9](https://tex.z-dn.net/?f=y%5Cleft%28y%2B4%5Cright%29-4%5Cleft%28y-4%5Cright%29%3D9)
![y^2+4y-4y+16=9](https://tex.z-dn.net/?f=y%5E2%2B4y-4y%2B16%3D9)
![y^2=9-16](https://tex.z-dn.net/?f=y%5E2%3D9-16)
![y^2=-7](https://tex.z-dn.net/?f=y%5E2%3D-7)
take squar root of both sides
![y=\pm \sqrt{-7}](https://tex.z-dn.net/?f=y%3D%5Cpm%20%5Csqrt%7B-7%7D)
![y=\pm i \sqrt{7}](https://tex.z-dn.net/?f=y%3D%5Cpm%20i%20%5Csqrt%7B7%7D)
Hence final answer is
.
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:
We have to use the formule to calculate the vertex which is: V(-b/2a;4ac-b^2/4a)
A) y=x+7 where a=1 b=0 and c=7
By replacing we have: V(0;28/4) V(0;7)
B) y=-x where a=-1 b and c=0 so V(0,0)
Answer:
74.958
Step-by-step explanation:
Because 57.66 added 30 percent is equal to 74.958
Answer:
4/7 as a decimal is 0.57142857142857.