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121 results.

Julie's copy of Second order differential equations 1
Draft
Question in Julie's workspace by Julie Crowley

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$ .

rebelmaths
José's copy of Lois's copy of Simultaneous linear equations (variables)
Ready to use
Question in Jos's workspace by Jos Klenner

Shows how to define variables to stop degenerate examples.
José's copy of Solve simulatenous equations. (Video)
Ready to use
Question in Jos's workspace by Jos Klenner

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.
Gauss elimination to solve a system of linear equations.
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 2 others

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.
Logarithms: Solving equations 5
Ready to use
Question in Bill's workspace by Bill Foster

Given $\rho(t)=\rho_0e^{kt}$ , and values for $\rho(t)$ for $t=t_1$ and a value for $\rho_0$ , find $k$ . (Two examples).
Jessica's copy of Solving equations
Draft
Question in Jessica's workspace by Jessica Ryan

Solve $\displaystyle ay + b = cy + d$ for $y$ .
Solving equations
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $\log_{a}(x+b)- \log_{a}(x+c)=d$
Solving equations
Draft
Question in Bill's workspace by Bill Foster

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.
Solving equations
Draft
Question in Bill's workspace by Bill Foster

Solve $\displaystyle ax + b = cx + d$ for $x$ .
Solving equations
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $\displaystyle \frac{a} {bx+c} + d= s$
Solving equations. (Video)
Draft
Question in Bill's workspace by Bill Foster

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

A video is included in Show steps which goes through a similar example.
Logarithms: Solving equations 3
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $\log(ax+b)-\log(cx+d)=s$
Logarithms: Solving equations 6
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $c(a^2)^x + d(a)^{x+1}=b$ (there is only one solution for this example).
Logarithms: Solving equations 2
Draft
Question in Bill's workspace by Bill Foster

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.
Logarithms: Solving equations 4
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ each of the following equations: $n^{ax+b}=m^{cx}$ and $p^{rx^2}=q^{sx}$ .
Logarithms: Solving equations 1
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $\log_{a}(x+b)- \log_{a}(x+c)=d$
Hyperbolic Functions 1
Draft
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 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 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 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 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 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.
Do three given vectors form a spanning set and are they linearly independent?
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given the following three vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3$ Find out whether they are a linearly independent set are not. Also if linearly dependent find the relationship $\textbf{v}_{r}=p\textbf{v}_{s}+q\textbf{v}_{t}$ for suitable $r,\;s,\;t$ and integers $p,\;q$ .
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 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 an equation with reciprocals
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle \frac{s}{ax+b} = \frac{t}{cx+d}$
Apply the sine rule
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

A question testing the application of the Sine Rule when given two sides and an angle. In this question the triangle is obtuse and the first angle to be found is obtuse.

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