The force F acting on a particle constrained to move along the x - axis is given by the fucntion F ( x ) = a x ( b − c x 2 ) [ a = 8.97 , b = 7.83 , c = 5.65 ] Find the three equilibrium points x 1 , x 2 , and x 3 , and enter them in order of ascending x ‑coordinate.

— 1.177

0

1.177

Explanation:

Given that,

F(x) = ax(b — cx²)

Given that,

a = 8.97

b = 7.83

c = 5.65

F(x) = ax(b—cx²)

F(x) = abx — acx³

F(x) = 8.97 × 7.83x — 8.97 × 5.65x³

F(x) = 70.2351x —50.6805x³

Then, For a body to be in equilibrium the sum of forces acting on the body is zero. i.e. F(x) = 0

0 = 70.2351x —50.6805x³

70.2351x —50.6805x³ = 0

x(70.2351 —50.6805x²) = 0

For the multiplication of two number to be zero, it is either one of the number is zero or both of the number is zero

Therefore,

x = 0 OR 70.2351 —50.6805x² = 0

x=0

70.2351 — 50.6805x² = 0

50.6805x² = 70.2351

x² = 70.2351/50.6805

x² = 1.38584

x = √1.38584

x = ± 1.177

Then, the equilibrium position is

- 1.177, 1.177 and 0

So, the ascending order of the equilibrium position is -1.177, 0, 1.177

The correct answer could be A. or C. but most likely i'm going with c because if a beaver family blocked off a part of a river using a dam it would most likely result in a drought on side (X) of the river. But how you say, a dead tree could have fallen and blocked the water allowed behind the dam, and when the tree is removed the water that flows back towards the dam would destroy it because of the water pressure from the blocked tree being moved