Answer:
x + 4/3x^3
Step-by-step explanation:
y=1/2x^2-2/3x^-2
dy/dx=1/2(2x)-2/3(-2x^-3)
=x+4/3 x^-3
=x+4/3x^3
Answer:
![[11.5-(2.5*3)]^2=16](https://tex.z-dn.net/?f=%5B11.5-%282.5%2A3%29%5D%5E2%3D16)
Step-by-step explanation:
We want to evaluate ![[11.5-(2.5*3)]^2](https://tex.z-dn.net/?f=%5B11.5-%282.5%2A3%29%5D%5E2)
Let us evaluate within the parenthesis first:
![[11.5-(2.5*3)]^2=[11.5-(7.5)]^2](https://tex.z-dn.net/?f=%5B11.5-%282.5%2A3%29%5D%5E2%3D%5B11.5-%287.5%29%5D%5E2)
![\implies [11.5-(2.5*3)]^2=[11.5-7.5]^2](https://tex.z-dn.net/?f=%5Cimplies%20%5B11.5-%282.5%2A3%29%5D%5E2%3D%5B11.5-7.5%5D%5E2)
We again subtract within the bracket to obtain:
![[11.5-(2.5*3)]^2=[4]^2](https://tex.z-dn.net/?f=%5B11.5-%282.5%2A3%29%5D%5E2%3D%5B4%5D%5E2)
This finally gives us:
![[11.5-(2.5*3)]^2=16](https://tex.z-dn.net/?f=%5B11.5-%282.5%2A3%29%5D%5E2%3D16)
Answer:
The initial velocity of the particle is
v' = -6 - 6.2 = -18 ft/s
at t = 5s, the velocity is v = -18 + 6.5 = 12 ft/s
the position is

the total distance traveled is
