Equilibrium of a particle, solution by rotating coordinate system.

Expanding two linear brackets multiplied together.

Expanding two linear brackets multiplied together.

Expanding two linear brackets multiplied together.

Expanding two linear brackets multiplied together.

Expanding two linear brackets multiplied together.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Given a point and a line, determine the distance between them.

MECE3930U: Heat Transfer Assignment 4

Please follow the Numbas guidance first if you did not attend the Numbas session.

This assignment is only to allow a maximum of 5 attempts.

Time to complete: unlimited

All answers should be provided without the units, but attention must be paid to the unit instructions in each question. For example, if your answer is 100.3 W/m2K, type 100.3 only.

Important Note: You have to submit your assignment to receive a mark!

A question to practice equation line and finding gradients

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Recovering original function given some information such as derivative and value at some point.

Determine frictional force acting on a block on an incline.  Coefficients of friction, weight and a horizontal force are given

Use integration to find the centroid of an area bounded by a parabola, a sloping line, and the y-axis.  

This question uses a Geogebra applet to solve a linear program with two variables using the graphical method. It contains three steps:

1. Construct the feasible area (polygon) by adding the constraints one by one. The students can see what happens when the constraints are added.
2. Add the objective function, and the level set of the objective value is shown, as well as its (normalised) gradient.
3. Compute the optimal solution by moving the level set of the objective around.

Classic problem of a vehicle parked on an incline.  Best solved by rotating the coordinate system.

Image Credit: https://svgsilh.com/image/34325.html  CC-0

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Given a linear programming problem in standard form, write down the dual problem.

Solving linear equations with unknowns on both sides

Solving equations of the form a(ex+b)=c(fx+d)

Solving equations of the form a(x+b)=c(x+d)

Solving equations of the form ax+b=cx+d where 2<|a-c|<13

Solving equations of the form ax+b=cx+d where |a-c|=2

Solving three step linear equations.

Solving two step linear equations including a division.

Covering 1-3 step linear equations but not introducing brackets or an unknown on both sides.

Solving two step equations.

One step equations - just multiplication.

One step equations - just division.

One-step equation solving - just adding.