Suppose you are driving a car around in a circle of radius 212 ft, at a velocity which has the constant magnitude of 43 ft/s. A string hangs from the ceiling of the car with a mass of 1.8 kg suspended from it. What angle (in degrees) will the string make with the vertical

To solve this problem we will apply the concepts related to dynamic equilibrium. The vertical component of the tension is equivalent to the centripetal Force while the horizontal component of the tension is equivalent to the weight, therefore we will have the two equations,

Our values are,

Therefore if we divide both equation we have,

Replacing,

Therefore the angle required is 15.18°

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 .