a custodian pulls a vacuum 13.5 m with a 33.9 n force at a 55.0° angle, against a 14.1 n friction force…

Explanation:

Step1: Identify the formula for work

The work - done formula is $W = Fd\cos\theta$, where $F$ is the force applied, $d$ is the displacement, and $\theta$ is the angle between the force and the displacement.

Step2: Substitute the given values

We are given that $F = 33.9\ N$, $d=13.5\ m$, and $\theta = 55.0^{\circ}$. $W=(33.9)\times(13.5)\times\cos(55.0^{\circ})$

Step3: Calculate the value of $\cos(55.0^{\circ})$

$\cos(55.0^{\circ})\approx0.5736$

Step4: Calculate the work - done

$W = 33.9\times13.5\times0.5736$ $W=33.9\times7.7436$ $W\approx262\ J$

Answer:

$262$