Q2 : Water waves in a shallow dish are 6cm long. At one point water moves up and down at a rate of 4.8 oscillation per second. What is the speed of water waves? What is the period of water waves? What is the frequency of water waves?

v = 0.3 ms⁻¹

Frequency = 4.8 Hz

T = 0.21 sec

Explanation:

The rate of oscillation is 4.8 oscillation/second

Let's see frequency's definition " no. of vibration/oscillation per unit time"

So,

Frequency = 4.8 Hz

Now

Time period is the reciprocal of frequency

T = 1/f

T = 1/4.8

T = 0.21 sec

Now

Using formula

v = f λ

f = 4.8 Hz , λ = 6 cm (But we need to convert it in a standard form)

So, λ = 0.06 m

Putting in formula

v = (4.8)(0.06)

v = 0.3 ms⁻¹

the independent variable, or the one that is intentionally manipulated is the speed.

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 .