Respuesta :
ANSWER
[tex]x=2.5;y=6.9[/tex]EXPLANATION
We want to find the x and y components of vector A.
The direction of a vector in the x-y plane is:
[tex]\theta=\tan ^{-1}(\frac{y}{x})[/tex]where x = x component; y = y component
Therefore, we have that:
[tex]\begin{gathered} 250\degree=\tan ^{-1}(\frac{y}{x}) \\ \Rightarrow\tan 250=\frac{y}{x} \\ \Rightarrow y=x\tan 250 \end{gathered}[/tex]The magnitude of a vector is:
[tex]|A|=\sqrt[]{x^2+y^2}[/tex]Substitute the value of A and y obtained above into the equation:
[tex]7.3=\sqrt[]{x^2+(x\tan250)^2}=\sqrt[]{x^2+x^2\tan ^2(250)}[/tex]Solve for x in the equation:
[tex]\begin{gathered} 7.3^2=x^2(1+\tan ^2(250)) \\ \Rightarrow x^2=\frac{7.3^2}{1+\tan ^2250} \\ x^2=\frac{53.29}{1+7.549}=\frac{53.29}{8.549} \\ x^2=6.2337 \\ \Rightarrow x=\sqrt[]{6.2337} \\ x\approx2.5 \end{gathered}[/tex]Recall that:
[tex]y=x\tan 250[/tex]Substitute the value of x:
[tex]\begin{gathered} y=2.5\tan 250 \\ y=6.9 \end{gathered}[/tex]Therefore, the components are:
[tex]x=2.5;y=6.9[/tex]