Homework questions are welcome as long as they are asked honestly, explain the problem, and show sufficient effort. Please do not use this as the only tag for a question. For the answers on homework questions, helpful hints or instructions are preferred to a complete solution. Please do not add ...

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-2
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0answers
22 views

IB Math Help: grade Nine

Does anybody who has been or is in grade 9 IB program know what sort of material they put on the entrance tests. Just a brief list of the math topics covered in the examination. Only answer if you are ...
0
votes
0answers
16 views

Describing an open interval I centered at c, $I \subseteq (a, b)$

Entire question: Let (a,b) be an open interval of Real numbers and let $c \in (a,b).$ Describe an open interval I centered at c such that $I \subseteq (a,b)$ I didn't quite get where I should've ...
1
vote
1answer
18 views

Ambiguous Limits in Area Determination

I am to find the centroid of the area bounded by the curve $y=8x^3-24x+11$, the $x$-axis and the line $x=-1$. Now I know that the centroid requires me to find the area under the curve first. I have ...
2
votes
1answer
23 views

Parametrizing to Calculate Flux

Evaluate the flux of $\mathbf{f}$ across the oriented surface $\Sigma$ by computing the surface integral $\iint_{\Sigma} \mathbf{f} \cdot d\sigma$, where $\Sigma$ is the surface $z=xe^y$ for $0 \leq x ...
0
votes
0answers
29 views

Help with math steps, chain rule.

I'm trying to to understand the math steps to go from Eqn. (1) to Eqn. (2). $$\tag{1} q(x,t)=\frac{-V_t(1+\delta f(c,g))}{P(x,t)}\cdot \left(\frac{dP_o}{dt}\right)$$ $$\tag{2} \frac{-V_t ...
4
votes
1answer
14 views

Solving Differential equations with Laplace transform

$\displaystyle y''+4y'+3y=e^{-t}$, given $\displaystyle y(0)=y'(0)=1$ My Attempt: Taking Laplace transforms on both sides $\displaystyle $ $\displaystyle [s^2\bar y-sy(0)-y'(0)]+4[s\bar ...
2
votes
1answer
26 views

Please check my proof on: $\sim$ is an equivalence relation $\Leftrightarrow S<G$

Problem: Let $\emptyset\ne S\subset G$, where $G$ is a group, and define a relation on $G$ by $a\sim b\Leftrightarrow ab^{-1}\in S$. Show that $\sim$ is an equivalence relation if and only if $S$ is a ...
0
votes
1answer
26 views

Find the number of positive integer $a \leq n$ such that $(a,n) = (a+1,n) = 1)

For every positive integer $n$, let $$A_n = \{a \in \mathbb{N} \mid 1 \leq a \leq n \mid gcd(a,n) = gcd(a+1, n) = 1\}$$ Evaluate $\mid A_n\mid$ Assume that $n$ has the factorization ...
3
votes
1answer
38 views

Area of a Curved Surface

Find the area of the part o the surface $z=xy$ that lies within the cylinder $x^2+y^2=1$. I'm not sure how to set up the surface integral to compute this.
0
votes
2answers
33 views

Number of open sets in a metric space

I have got the following question which I could not solve: can a metric space have exactly 36 open sets? I believe if the metric space is finie, then it has to be discrete and so the number of open ...
1
vote
2answers
22 views

How to introduce flat cost of flow over a node using mixed integer programming.

In the set up for the program we have a graph where we are trying to minimize the cost of sending flow over the arcs. I have formulated the following linear program. \begin{array}{ll} \text{minimize} ...
0
votes
0answers
5 views

Transform gradient to reference element

Minimal example of the problem My attempt I think this is not a linear solution like \begin{equation} \nabla u = \nabla A_K x + \nabla b_K \end{equation} which must be wrong because $A_K$ is a ...
0
votes
0answers
7 views

Convergence of this priori error in FEM?

Problem My attempt I think h is the size of the mesh. C is a constant which probably depends on the size of the mesh, I think. I think the error converges linearly and dependent on the size of ...
1
vote
1answer
25 views

rearrange $t - (m-q)^2 = v - (m-p)^2$ for quadratic formula form $ax^2 + bx +c = 0$ solving for $q$

I have the equation $t - (m-q)^2 = v - (m-p)^2$ which I would like to rearrange to be able to apply the quadratic formula, and solve in terms of $q$. Accordingly, it needs to be in the form: $ax^2 ...
0
votes
1answer
22 views

shortest point on a line segment from point out side the line

from the above pic I found the value x from line (p1,p2) and point a using y=mx+b and imaginary red line which is perpendicular to black line having slope -1/m and the intersecting point x. the ...
2
votes
2answers
50 views

Decompose a real symmetric matrix

Prove that, without using induction, A real symmetric matrix $A$ can be decomposed as $A = Q^T \Lambda Q$, where $Q$ is an orthogonal matrix and $\Lambda$ is a diagonal matrix with eigenvalues of $A$ ...
1
vote
3answers
37 views

solve $-(x_m - x_q)^2 = -(x_m - x_p)^2$ in terms of $x_q$

I have an equation, $-(x_m - x_q)^2 = -(x_m - x_p)^2$ which I want to solve in terms of $x_q$. I can see (by using a number line) that $q$ can have two solutions: $x_q = x_p$ or: $x_q = 2x_m-x_p$ ...
-2
votes
0answers
27 views

Birthday Problem [on hold]

This is an extension of birthday problem, please help In a class of 85 students, let X be the number of students who share a birthday with at least two other members of the class. a) ...
-1
votes
2answers
22 views

Geometric distribution related probability questions [on hold]

I am learning Probability, and I have this problem. Suppose $X\sim {\cal Geom}(p_1)$ on $\{1,2,3,...\}$, $Y\sim {\cal Geom}(p_2)$ on $\{1,2,3,...\}$, and $X, Y$ are independent. Let $S=X+Y$. ...
0
votes
3answers
44 views

If $a^2=b^2+c^2$ and $0<n<2$ prove $a^n<b^n+c^n$

If $a^2=b^2+c^2$ and $a,b,c$ are positive real numbers, prove (a) if $n>2$ then $a^n>b^n+c^n$, (b) if $0<n<2$ then $a^n<b^n+c^n$. Part (a) was easy to prove: $a^2=b^2+c^2$ and ...
0
votes
1answer
24 views

Linear Maps from a finite space to an infinite space

Suppose V is finite dimensional with dim V > 0. Prove that if W is infinite dimensional then $L(V, W)$ is infinite dimensional. Help? I really have no idea how to go about this one? I'm assuming I ...
0
votes
0answers
29 views

Linear maps and linearly independent sets

Suppose $v_1,...,v_m$ is a linearly dependent list of vectors in $V$. Suppose also $W \neq \{0\}$. Prove there exist $w_1,...,w_m$ in $W$ such that no $T\in L(V, W)$ satisfies $Tv_j = w_j$ for $j = ...
0
votes
2answers
14 views

Quick question on the basis of subset of polynomals

Let U = {p $\in$ $P_4(F)$: $p(2) = p(5) = p(6)$} Find a basis of U. So the way I did this problem was by writing out $p(2) = p(5)$ and $p(5) = p(6)$, then I made a system of equations and solved for ...
2
votes
2answers
35 views

Dimension of the sum of three subspaces

So I was doing practice problems in my textbook and I'm really stuck on this one: We know that $$\dim(U_1 + U_2) = \dim U_1 + \dim U_2 - \dim(U_1 \cap U_2)$$ if $U_1$ and $U_2$ are finite dimensional ...
2
votes
4answers
63 views

Proof involving linear maps

Suppose $V$ is a vector space and $S,\ T \in L(V)$ such that range $S \subset$ null $T$. Prove that $$(ST)^2= 0$$ I have no idea how to go about this could someone maybe explain it in English or ...
-1
votes
0answers
35 views

How does this method work? [on hold]

Let $n=16$ for an example: step 1: get set of prims from $1$ to $\sqrt{2n}: \{2, 3, 5\}$, step 2: get set of $n \mod 2, n \mod 3, n \mod 5: \{0, 1, 1\}$, setp 3: from $0$ to $n-3$, ...
0
votes
1answer
24 views

Rank Nullity Theorem application

Show that {T $\in$ $L(R^5, R^4)$: dim null T > 2} is not a subspace of $L(R^5, R^4)$ I have no idea how to show this isn't a subspace the farthest I have gotten is to show that dim range T < 3 ...
0
votes
3answers
61 views

Find $dy/dx$ where $(7x+2y)^2=6x^4y^3$ [on hold]

Find $\displaystyle\frac{\mathrm{d}y}{\mathrm{d}x}$ where $$(7x+2y)^2=6x^4y^3$$ This is on my homework but book has different examples so I don't know what side to start on.
2
votes
1answer
92 views

Evaluate the limit $\lim \limits_{x \to \infty} \frac{1}{x(x+1)}$ [on hold]

How can I evaluate the limit $$\lim_{x \to \infty} \frac{1}{x(x+1)}$$
1
vote
5answers
61 views

How to evaluate the limit $\lim_{x \to \infty} \frac{2^x+1}{2^{x+1}}$

How to evaluate the limit as it approaches infinity $$\lim_{x \to \infty} \frac{2^x+1}{2^{x+1}}$$
3
votes
1answer
113 views

An arithmetic sequence whose members do not contain the digit ‘9’

There is a non-constant arithmetic progression made of natural numbers only; none of them contains the digit $9$. Prove that such an arithmetic progression has no more than $72$ terms.
0
votes
1answer
23 views

Area of a Paraboloid inside a Cylinder

Find the area of the part of the paraboloid $x=y^2+z^2$ that is inside the cylinder $y^2+z^2=9$. I'm not sure how to set up the integral to compute this. Thanks.
1
vote
2answers
54 views

Which set of points are defined by the relation $x/|x|=y/|y|$?

Which set of points are defined by the relation $x/|x|=y/|y|$? I think the answer is a straight line bisecting the first and third quadrants through the origin ( ie the line x=y). However wolfram ...
0
votes
4answers
67 views

Questions about solving inequality: $2 < \frac{3x+1}{2x+4}$

Solve the inequality: $2 < \frac{3x+1}{2x+4}$ Step 1: I simplified $\frac{3x+1}{2x+4}$ into: $3x+1-2x-4= x-3$. Step 2: $2>x-3$ Here I subtracted $2$ from both sides into: $x>-5$ or ...
1
vote
2answers
25 views

Equation of a Tangent Plane

Find the equation of the tangent plane to the given surface at the given point. $x=u^2, y=v^2, z=uv$ at $u=1, v=1$ How would you find the tangent plane when the surface is in this format? Thanks.
2
votes
2answers
19 views

Question on Green's Theorem

Consider the vector field $\textbf{f}(x,y)=(ye^{xy}+y^2\sqrt{x})\textbf{i}+(xe^{xy}+\frac{4}{3}yx^{\frac{3}{2}})\textbf{j}$. Use Green's Theorem to evaluate $\int_C\textbf{f} \dot d\textbf{r}$, where ...
2
votes
4answers
174 views

Line Integral Around a Triangle

Let $R$ be the interior of the triangle with vertices $(0,0), (4,2),$ and $(0,2)$. Let $C$ be the boundary of $R$, oriented counterclockwise. Now evaluate the integral below. $$\int_C(y+e^\sqrt{x}) ...
1
vote
0answers
34 views

Evaluating an improper integral with limits $_{-\infty}^\infty$

When evaluating an improper integral with limits $_{-\infty}^\infty$, why do we need to separate the integral into $\int\limits_a^{\infty} \text{ and } \int\limits_{-\infty}^a$? My homework asked ...
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votes
0answers
13 views

Maths incomes and expenditures [on hold]

1.) Explain the difference between an income-and-expenditure statement and a budget. 2.) You wrote down your own income and expenses for one month: ...
1
vote
2answers
65 views

True or False? $\int\limits_0^2(x-x^3)dx$ represents the area under the curve $y=x-x^3$ from 0 to 2.

True or False? $\int\limits_0^2(x-x^3)dx$ represents the area under the curve $y=x-x^3$ from 0 to 2. I said true but my textbook says false. Why? (Stewart: Concepts and Contexts p424 q13)
1
vote
1answer
19 views

Galerkin Orthogonality in this FEM?

Problem Galerkin orthogonality is but I am not sure if it is in the right form. How can you use this orthogonality here? I think I should expand the last inequality first somehow.
1
vote
2answers
50 views

Inequality - Find what value of $t$ satisfies: $ (t/24) - (t+1) + (3t/8) < (5/12) (t+1)$

Inequality - Find what value of $t$ satisfies: $(t/24) - (t+1) + (3t/8) < (5/12) (t+1)$. Step 1: I multiplied both sides by $24$ and divided to get: $t-24(t+1)+9t < 10+24(t+1)$. Step 2: I ...
2
votes
2answers
31 views

Possible ways of 8 digit numbers using 1,2 and 3 such that the number has atleast one digit for each 1,2,and 3

How many 8 digit numbers can be formed using the digits 1,2 and 3 so that the number contains at least one of each of these three digits?
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votes
0answers
22 views

Need a solution to find the locus of an equation. [on hold]

Find the equation of the locus of a point which moves so that its distance from $(a,0)$ is equal to its distance from the $y$-axis. The answer is $$y^2 - 2ax + a^2 =0$$ Please can someone find the ...
1
vote
4answers
1k views

What's wrong with my aproach to solving this equation with multiple logarithms?

A question I was faced with asked "For which $x$ is $\log_{10}(x)^{\log_{10}(\log_{10}(x))}= 10,000$?" My instincts tell me I can say $$\log_{10}(x)=10$$ and $$\log_{10}(\log_{10}(x))=4$$ However, ...
0
votes
0answers
24 views

Please help me check this derivative work

I have $$ J_{\theta}(X) = - \frac 1 m \cdot \left[ y \cdot ln( h_{\theta} (X ) ) + ( 1 - y) \cdot ln ( 1 - h_{\theta}(X) ) \right] $$ I need $\frac d {d\theta} J_{\theta}(X)$. I tried many time, and ...
1
vote
0answers
27 views

Rapidly Decreasing Functions

Can someone explain the notion of a rapidly decreasing function? Namely, a function in the Schwartz space: $$\mathscr{S}(\mathbb{R}^n):= \{ f \in C^{\infty} (\mathbb{R}^n) : ||f||_{\alpha, \beta} ...
0
votes
2answers
32 views

Splitting a segment with a ratio

I came across the homework question that I attempted to do. After looking at the answers, and getting it wrong I didn't understand why. I'm specifically lost at why we would get a fraction of 2/5 ...
0
votes
0answers
9 views

Determining Moving-Average Representation of AR(2) Process

Consider a stationary $AR(2)$ process given by $$X_{t} - X_{t-1} + 0.25X_{t-2} = 5 + a_{t}$$ where $a_{t} \sim WN(0,1)$ (white noise). I am interested in obtaining the causal representation of ...
2
votes
0answers
52 views

Ordinary differential equation­

$$\dfrac{dy}{dx}-\dfrac{\tan y}{1+x}=(1+x)e^x\sin y$$ I tried $\sin y=t$ but failed. It seems to immune to methods I know of or I am just unable to make the right substitution... Wolfram alpha ...