Final answer:
To find R and theta given the components X = 9.213 and Y = -6.255, use the equations R = sqrt(X^2 + Y^2) and theta = atan(Y/X).
Step-by-step explanation:
To find R and theta given the components X = 9.213 and Y = -6.255, we can use trigonometry. Since X is the horizontal component and Y is the vertical component, we can use the equations R = sqrt(X^2 + Y^2) and theta = atan(Y/X) to calculate the magnitude and direction of the vector R.
Plugging in the values, we get R = sqrt((9.213)^2 + (-6.255)^2)
= sqrt(84.94)
≈ 9.22 and theta
= atan((-6.255)/9.213)
≈ -33.9°.