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Hyperbolic Functions 1
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Question in Bill's workspace by Bill Foster

Solve for $x$ : $a\cosh(x)+b\sinh(x)=c$ . There are two solutions for this example.
Solving equations
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $\displaystyle ax ^ 2 + bx + c=0$ .
Complete the square. (Video)
Draft
Question in Bill's workspace by Bill Foster

Find $p$ and $q$ such that $ax^2+bx+c = a(x+p)^2+q$ .

Hence, or otherwise, find roots of $ax^2+bx+c=0$ .

Includes a video which shows how to solve a quadratic by completing the square.
Interactive Newton-Raphson method
Should not be used
Question in Christian's workspace by Christian Lawson-Perfect and 1 other

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$ . If $x_0=1$ find $x_1$ .

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.
Solve three congruences with the Chinese Remainder Theorem
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving three simultaneous congruences using the Chinese Remainder Theorem:

$\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*}$ where $\operatorname{gcd}(n_1,n_2,n_3)=1$
Solve three congruences using Chinese Remainder Theorem
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving three simultaneous congruences using the Chinese Remainder Theorem:

$\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*}$ where $\operatorname{gcd}(n_1,n_2,n_3)=1$
Solve congruence in given range
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving an equation of the form $ax \equiv\;b\;\textrm{mod}\;n$ where $\operatorname{gcd}(a,n)|r$ . In this case we can find all solutions. The user is asked for the two greatest.
Solve a pair of congruences
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving a pair of congruences of the form
$\begin{align}x &\equiv b_1\;\textrm{mod} \;n_1\\x &\equiv b_2\;\textrm{mod}\;n_2 \end{align}$ where $n_1,\;n_2$ are coprime.
Solve a pair of congruences
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving two simultaneous congruences:

$\begin{eqnarray*} c_1x\;&\equiv&\;b_1\;&\mod&\;n_1\\ c_2x\;&\equiv&\;b_2\;&\mod&\;n_2\\ \end{eqnarray*}$ where $\operatorname{gcd}(c_1,n_1)=1,\;\operatorname{gcd}(c_2,n_2)=1,\;\operatorname{gcd}(n_1,n_2)=1$
Solve an equation in algebraic fractions
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle \frac{px+s}{ax+b} = \frac{qx+t}{cx+d}$ with $pc=qa$ .
Solve a linear equation
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle ax+b = cx+d$
Solve an equation with reciprocals
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle \frac{s}{ax+b} = \frac{t}{cx+d}$
Solving equations
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ and $y$ :
$\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$
Solve a pair of simultaneous equations
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ and $y$ :
$\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.
Solve a quadratic with the formula
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 2 others

Solve for $x$ : $\displaystyle ax ^ 2 + bx + c=0$ .

Entering the correct roots in any order is marked as correct. However, entering one correct and the other incorrect gives feedback stating that both are incorrect.
Solve an equation with a reciprocal
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle \frac{a} {bx+c} + d= s$
Solving equations
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle \frac{a} {bx+c} + d= s$
Solving equations
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle ax ^ 2 + bx + c=0$ .
Solving equations
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve $\displaystyle ax + b = cx + d$ for $x$ .
Solve an equation in logarithms
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$ .

Make sure that your choice is a solution by substituting back into the equation.
Expand brackets and solve an equation
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve $\displaystyle ax + b =\frac{f}{g}( cx + d)$ for $x$ .

A video is included in Show steps which goes through a similar example.
Solving log equations using exponentials
Ready to use
Question in Algebra by Ben Brawn

No description given
Interactive Newton-Raphson method
Ready to use
Question in Bill's workspace by Bill Foster

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$ . If $x_0=1$ find $x_1$ .

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.
Julie's copy of First order differential equations 4
Draft
Question in Julie's workspace by Julie Crowley

Find the solution of $\displaystyle \frac{dy}{dx}=\frac{1+y^2}{a+bx}$ which satisfies $y(1)=c$

rebelmaths
Rearranging equations by multiplying or dividing: One step
Ready to use
Question in Julie's workspace by Julie Crowley

Rearranging equations by multiplying or dividing: One step

rebelmaths
delete syntax checkinbg bryan's copy of MA4100 4.4 Gaussian Elimination
Ready to use
Question in bryan's workspace by bryan pearce

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.
Lois's copy of Simultaneous linear equations (variables)
Ready to use
Question in Algebra by Lois Rollings

Shows how to define variables to stop degenerate examples.
Solving equations 2
Draft
Question in Algebra by Lois Rollings

Solve for $x$ : $\displaystyle \frac{a} {bx+c} + d= s$
Solving a quadratic equation
Draft
Question in Algebra by Lois Rollings

Solve for $x$ : $\displaystyle ax ^ 2 + bx + c=0$ .
Solving linear equations: two step
Draft
Question in Algebra by Lois Rollings

Equations of type ax-b = c.

Includes advice.

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