Finding the zero of a non-polynomial function

Find principal stresses by finding the eigenvalues of the matrix

Finding the arc length of a sector of a circle when given the radius of the circle and angle of the sector.

Finding the arc length of a sector of a circle when given the radius of the circle and angle of the sector.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant.

Find the sum of two couples in a plane.

Find the moment of a couple formed by two equal and opposite forces.

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Find the tension in a rope necessary to prevent a bracket from rotating by applying $\Sigma M = 0$.

Find the force required to balance a see-saw.

Homework set.  Find internal shear force, normal force, and bending moment at a designated point in a rigid body.

Homework set. Find the forces in truss members using the method of joints.

Homework set.  Problems require finding centroid, then Moment of Inertia about a centroidal axis.

Homework set.  Application of Parallel Axis Theorem to find area Moment of Inertia

Homework set.  Use integration to find the centroid of shapes bounded by functions.

Homework set.  Use integration to find the centroid of shapes bounded by functions.

Homework set.  Find centroids of shapes by dividing them into simple subshapes.

Find the tensions in two ropes supporting a weight.

Find reactions for a particle in equilibrium

Find forces required to hold a particle in equilibrium when subjected to a downward load.  Directions of the reactions are given.  

Find the sum of two 2-dimensional vectors, graphically and exactly using the parallelogram rule.

Given three vectors with integer components, find the corresponding magnitude and direction.

Find the magnitude and direction of a force given its scalar components.

Written for the Western Sydney University MESH numeracy preparation workshop for the LANTITE test (Australia). Students are given a proportion of staff who either have or haven't completed their reports. They are asked to find the complement, as a percentage. There are 6 different versions of this question. 

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Find the reactions of a simply-supported beam with a trapazoidal distributed load.

Find the reactions for a beam with a uniformly varying distributed load.

Find the reactions for a beam with a uniformly distributed load.