A10 kg shark swimming at 5m/s swallows an absent-minded 0.5 kg fish that is originally at rest. what is the speed of the large fish after eating the smaller fish?

The speed of the large fish after eating the small fish is 4.76 m/s.

We can apply the law of momentum conservation to calculate the speed of the large fish.

Let the velocity of the large fish after eating small fish is v.

According to law of momentum conservation

m1u1+m2u2=(m1+m2)v

here, m1 is the mass of the large fish, u1 is the initial speed of larger fish, ml is the mass of the small fish, u2 is the initial speed of small fish

10*5+0.5*0=(10+0.5)v

v=4.76 m/s

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .