584 results for "point".

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• Question
Instructional "drill" exercise to emphasize the method.
• Question

Calculate reactions and shear and bending moment at a point for an overhanging beam with a constant or uniformly varying distributed load.

• Question

$f(x)= ae^{-bt}+c$ is given and plotted. A few points are plotted on the curve. $x$-coordinates are provided for two of them and $y$-coordinate provided for third. Student is required to determine other coordinates.

• Question

Determine the internal shear force, normal force, and bending moment at a specified point.

• Question

Calculate the moment of a force about three points using the definition of a Moment.  All forces and points are in the same plane.

• Question

Determine the moment of a force about a point by using $M= F d_\perp$ or $M = F_\perp d$.

• Question

Calculate the moment of a force about three points using Verignon' theorem.  All forces and points are in the same plane.

• Question

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

• Question

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

• Question in Archive

No description given

• Question in Archive

Drag points on a graph to the given Cartesian coordinates. There are points in each of the four quadrants and on each axis.

• Question

Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

Question

Points of intersection

• Question

An applied example of the use of two points on a graph to develop a straight line function, then use the t estimate and predict. MCQ's are also used to develop student understanding of the uses of gradient and intercepts as well as the limitations of prediction.

• Min_max_v1
Draft
Question

Calculate the local extrema of a function ${f(x) = e^{x/C1}(C2sin(x)-C3cos(x))}$

The graph of f(x) has to be identified.

The first derivative of f(x) has to be calculated.

The min max points have to be identified using the graph and/or calculated using the first derivative method.  Requires solving trigonometric equation

• Question in Demos

Give the student three points lying on a quadratic, and ask them to find the roots.

Then ask them to find the equation of the quadratic, using their roots. Error in calculating the roots is carried forward.

Finally, ask them to find the midpoint of the roots (just for fun). Error is carried forward again.

• Numbas demo: video
Question in Demos

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

• Question in How-tos

A line with random $x$- and $y$- intercepts is plotted, and you have to drag two dots over the points where the line crosses the $x$ and $y$ axes.

• Question in How-tos

A couple of different ways of asking the student to enter a large number, to get around the floating point imprecision problem.

• Question in How-tos

Construct a line in a GeoGebra worksheet by writing its definition string by hand.

This isn't a very neat way of doing this. It's easier to define two points in GeoGebra, then make a line through those points. You can set the positions of the points from Numbas using vectors.

• Question in How-tos

Construct a line through two points in a GeoGebra worksheet. Change the line by setting the positions of the two points when the worksheet is embedded into the question.

• Question

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.

• Question

Parametric form of a curve, cartesian points, tangent vector, and speed.

• Cartesian equation of a plane
Has some problems

A plane goes through three given non-collinear points in 3-space. Find the Cartesian equation of the plane in the form $ax+by+cz=d$.

There is a problem in that this equation can be multiplied by a constant and be correct. Perhaps d can be given as this makes a,b and c unique and the method of the question will give the correct solution.

• Find minimum distance between a point and a line in 3-space. The line goes through a given point in the direction of a given vector.

The correct solution is given, however the accuracy of 0.001  is not enough as in some cases answers near to the correct solution are also marked as correct.

• Find the angle between planes
Has some problems

Find angle between plane $\Pi_1$, given by three points, and the plane $\Pi_2$ given in Cartesian form.

The calculation of $cos(\alpha)$ at the end of Advice has fractionNumbers switched on and so the result is presented as a fraction, which can be misleading. Best if calculation is followed through without using fractionNumbers.

• Question

Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

• Question

Find the coordinates of the stationary point for $f: D \rightarrow \mathbb{R}$: $f(x,y) = a + be^{-(x-c)^2-(y-d)^2}$, $D$ is a disk centre $(c,d)$.

• Question

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Inputting the values given into the partial derivatives to see if 0 is obtained is tedious! Could ask for the factorisation of equation 1 as the solution uses this. However there is a problem in asking for the input of the stationary points - order of input and also giving that there is two stationary points.

• Given a pair of 3D position vectors, find the vector equation of the line through both.  Find two such lines and their point of intersection.