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151 results.

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 1
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $\log_{a}(x+b)- \log_{a}(x+c)=d$
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 3
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $\log(ax+b)-\log(cx+d)=s$
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 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).
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 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 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 $\operatorname{gcd}(n_1,n_2,n_3)=1$
Find eigenvalues, characteristic polynomial and a normalised eigenvector of a 3x3 matrix
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$ .
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 $x$ : $\displaystyle \frac{s}{ax+b} = \frac{t}{cx+d}$
Solve a second order ODE with repeated roots,
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$ . (Equal roots example).
Second order ODE with constant coefficients and boundary conditions
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$ .
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.
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 $x$ .
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
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle \frac{a} {bx+c} + d= s$

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