Two vectors having magnitudes of 5.00 and 9.00 respectively. If the value of their dot product is 12.0, find the angle between the two vectors.

C = 74.53°

Explanation:

Let the magnitudes of 5.00 and 9.00 be vectors A and B respectively, hence the dot product of this vector is defined as

A.B = |A||B|cosC; let C be the angle between the vectors

12 = 5×9 cos C

Hence cos C = 12/45

C = cos^-1(12/45)

C = 74.53°

e) none of the above answers are correct

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 .