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Solve for y given the equation y = sqrt( x - x) and x=45.

Mathematics

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Answer

y = 0\text{y = 0}

Graph of y = √(x − x)

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Key points of y = √(x − x)
Pointxy
y-intercept00

Step-by-step solution

3 steps
  1. Substitute the given value of xx into the equation.

    We are given the equation y=sin⁡x−cos⁡xy = \sqrt{\sin x - \cos x} and x=45x=45. We assume xx is in degrees.
    Substitute x=45∘x=45^\circ:

    y=sin⁡(45∘)−cos⁡(45∘)y = \sqrt{\sin(45^\circ) - \cos(45^\circ)}
  2. Evaluate the trigonometric functions for 45∘45^\circ.

    We know that sin⁡(45∘)=22\sin(45^\circ) = \frac{\sqrt{2}}{2} and cos⁡(45∘)=22\cos(45^\circ) = \frac{\sqrt{2}}{2}.

  3. Substitute these values into the equation and simplify.

    y=22−22y = \sqrt{\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}} y=0y = \sqrt{0} y=0y = 0

    The calculated value of yy for x=45∘x=45^\circ is 0. The problem states "given that x=45,y=90x=45, y=90", which is inconsistent with our calculation. Based on the equation and x=45∘x=45^\circ, the value of yy is:

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