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1591 results for "with".

Represent a linear map as a matrix with a given basis
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$ with coefficients in the real numbers.

Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:

$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$

Using the standard basis for range and domain find the matrix given by $\phi$ .
When is a sequence within d of its limit?
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$x_n=\frac{an+b}{cn+d}$ . Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| \le 10 ^{-r},\;n\geq N$ , $2\leq r \leq 6$ .
Apply Kruskal-Wallis test
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Kruskal-Wallis test with ties.
Calculate definite integral with a hyperbolic substitution
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$
Indefinite integral of improper polynomial fraction
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle\int \frac{ax^3-ax+b}{1-x^2}\;dx$ . Input constant of integration as $C$ .
Indefinite integral: polynomial fraction
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find the polynomial $g(x)$ such that $\displaystyle \int \frac{ax+b}{(cx+d)^{n}} dx=\frac{g(x)}{(cx+d)^{n-1}}+C$ .
Indefinite integration using standard integrals
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$ . Must input $C$ as the constant of integration.
Integration of fraction with power in denominator
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$\displaystyle \int \frac{bx+c}{(ax+d)^n} dx=g(x)(ax+d)^{1-n}+C$ for a polynomial $g(x)$ . Find $g(x)$ .
Integration: Definite Integration
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Evaluate $\int_0^{\,m}e^{ax}\;dx$ , $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$ .

No solutions given in Advice to parts a and c.

Tolerance of 0.001 in answers to parts a and b. Perhaps should indicate to the student that a tolerance is set. The feedback on submitting an incorrect answer within the tolerance says that the answer is correct - perhaps there should be a different feedback in this case if possible for all such questions with tolerances.
Integration: Indefinite integral
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$ .
Integration: Indefinite integral
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$ .
Integration: Indefinite integral
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$
Inventory analysis: single price break point
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given constant demand for a product, with a single break point on the price, calculate the economic order quantity, and the minimum cost per year.
How to enter functions - Getting Started
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Dealing with functions in Numbas.
Sampling with and without replaement - binomial, hypergeometric, and Poisson approximation,
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Three parts. A sample of size $n$ is taken from $N$ where $k$ of the items are known to be defective and the task is to find the probability that more than $m$ defectives are in the sample. First part is sampling with replacement (binomial), second is sampling without replacement, (hypergeometric) and the last part uses the Poisson approximation to the first part.
Find mean and standard deviation of differences between samples
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$ .
Is the given function a probability mass function?, , ,
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Determine if the following describes a probability mass function.

$P(X=x) = \frac{ax+b}{c},\;\;x \in S=\{n_1,\;n_2,\;n_3,\;n_4\}\subset \mathbb{R}$ .
Probability of not choosing any from a subset
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given subset $T \subset S$ of $m$ objects in $n$ find the probability of choosing without replacement $r\lt n-m$ from $S$ and not choosing any element in $T$ .
Solve an equation in algebraic fractions
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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
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle \frac{s}{ax+b} = \frac{t}{cx+d}$
Express given fractions with different denominators
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Questions testing understanding of numerators and denominators of numerical fractions.
Apply the cosine rule
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.
Apply the cosine rule
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always obtuse. A secondary application is finding the area of a triangle.
Apply the sine rule
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Two questions testing the application of the Sine Rule when given two angles and a side. In this question the triangle is obtuse. In one question, the two given angles are both acute. In the second, one of the angles is obtuse.
Apply the sine rule
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Two questions testing the application of the Sine Rule when given two sides and an angle. In this question, the triangle is always acute and one of the given side lengths is opposite the given angle.
Apply the sine rule
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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.
Differentiate product of binomial and exponential
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate the function $(a + b x)^m e ^ {n x}$ using the product rule.
Number of combinations without replacement - lotto ticket,
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

No description given
Number of ways of choosing subsets with a condition,
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

No description given
Pigeonhole principle - greatest number of people with birthdays in the same month,
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

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