Two forces whose resultant is 100N, are perpendicular to each other. if one of them makes an angle of 60° with the resultant, calculate it's magnitude

Calculate the absolute pressure of an ocean depth of 1200atm. Assuming the density of liquid is 1200kg/m^2amd that (pa=1.01×10^6pa N/m^2

Magnitude of the force = 50N

Explanation:

Let one force be X

And the second force be Y

Both the forces are perpendicular, so α = 90°

The resultant R of the two forces = 100N

Angle between resultant and 1 force, α = 60°

We know,

R² = X² + Y² + 2XYcos 90

100² = X² + Y²

If X makes an angle of Φ = 60°

Then, tan Ф =  Y sin α / X + Y cos α

Putting the values we find,

tan 60 = Y/X

Y  = √3X

Putting Y = √3X in equation 1 we get,

(X)² + (√3X)² = 100 X 100

4X² = 100 X 100

X² = 2500

X = 50N

Therefore, magnitude of the force = 50N

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 .

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