Two violinists are trying to tune their instruments in an orchestra. One is producing the desired frequency of 440.0 hz. The other is producing a frequency of 448.4 hz. By what percentage should the out-of-tune musician change the tension in his string to bring his instrument into tune at 440.0 hz?

Percentage change in tension is 3.8%

Explanation:

We have given initially frequency = 440 Hz

Let tension in the string at this frequency is

Now second frequency is

Frequency in string is given by

From the relation we can say that

Percentage change in tension is equal to

%

So percentage change in tension is 3.8%

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 .

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle