Question

the magnitude of impedance, or z, can be determined using the pythagorean theorem, where r is the ac resistance and x is the total reactance.

z = \sqrt{r^{2}+x^{2}}

which can be rewritten as follows as well:

z^{2}=r^{2}+x^{2}

find x when z = 13 and r = 10.

(you do not need to include the units. only enter the number value for an answer. round to the nearest tenth if necessary.)

review the linked section of the prealgebra textbook for problem help

Explanation:

Step1: Substitute the given values into the formula

Given \(Z = 13\) and \(R = 10\), substitute into \(Z^{2}=R^{2}+X^{2}\). So, \(13^{2}=10^{2}+X^{2}\).

Step2: Simplify the equation

Calculate \(13^{2}=169\) and \(10^{2} = 100\). The equation becomes \(169=100 + X^{2}\).

Step3: Solve for \(X^{2}\)

Subtract 100 from both sides: \(X^{2}=169 - 100\). So, \(X^{2}=69\).

Step4: Solve for \(X\)

Take the square root of both sides: \(X=\sqrt{69}\approx 8.3\)

Answer:

\(8.3\)