438 results for "solve".

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• Question

Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

rebelmaths

• Question
Formulate a recurrence relation (= difference equation) and solve this recurrence relation.
• Question

Solve for the internal force in three members of a truss.

• Question

Solve for the internal force in three members of a truss.

• Question
Use the method of joints to solve for the forces in a cantilever truss.
• Question
Solve for the internal forces at on a multipart frame.
• Question

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

• Couples in equilibrium
Question

Solve for an angle which will result in equilibrium for a triangle subjected to three couples.   A trial and error solution is recommended.

• Question

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

• Question

A hand truck on wheels.  Easiest to solve by rotating coordinate system.

• Question

Rigid body equilibrium problem.  Easiest to solve by replacing forces on the perimiter of the pulley with equivalent forces at the axle.

• Question

Two forces act on a bell crank. This problem has two unknown magnitudes and an unknown direction which makes it tricky to solve by the equilibrium equation method.

The solution is much simpler if three force body principle is used.

• Sine and Cosine rules
Question

Solve a random oblique triangle for sides and angles.

• Question

Some quadratics are to be solved by factorising

• Question

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

• Question

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

• Question 1
Draft
Question

Solve the equation  5x - 8 = 32

• Question

Some quadratics are to be solved by factorising

• Question in Archive

Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

rebelmaths

Question

Using BIDMAS rules to solve equations

• Question

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

• Question

Some quadratics are to be solved by factorising

• Question

Calculate a repeated integral of the form $\displaystyle I=\int_0^1\;dx\;\int_0^{x^{m-1}}mf(x^m+a)dy$

The $y$ integral is trivial, and the $x$ integral is of the form $g'(x)f'(g(x))$, so it straightforwardly integrates to $f(g(x))$.

• Exam (1 question)

Solve a system of linear equations using Gaussian elimination.

• Exam (2 questions)

Use the simplex method to solve a linear program.

• Question

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.

• Question

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 $\operatorname{gcd}(c_1,n_1)=1,\;\operatorname{gcd}(c_2,n_2)=1,\;\operatorname{gcd}(n_1,n_2)=1$

• Question

Solving an equation of the form $ax \equiv b\;\textrm{mod}\;n$ where $a$ and $n$ are coprime.

• Question

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.

• Question

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 $\operatorname{gcd}(n_1,n_2,n_3)=1$