-1
votes
0answers
15 views

Moments (deducing the range of values for x)

A uniform rod AB has length 4 m and weight 150 N. The rod rests in equilibrium in a horizontal position, smoothly supported at points C and D, where AC=1m and AD=2.5m as shown in the diagram above. A ...
0
votes
0answers
37 views

What is $(k+1)^2[(k+1)+1]^2$ in factored form?

What is $(k+1)^2[(k+1)+1]^2$ in factored form? I'm a bit confused as to what the term "factored form" means in this context. Thank you.
1
vote
3answers
79 views

$2 \cos^2 x − 2 \cos x− 1 = 0$ Find the solutions if $0^\circ \le x < 360^\circ$

Find the solutions of $$2 \cos^2 x − 2 \cos x− 1 = 0$$ for all $0^\circ ≤ x < 360^\circ$. For $0^\circ \le x < 360^\circ$, I'm getting $x=111.5^\circ$ and $x=248.5^\circ$. Is this ...
8
votes
5answers
290 views

Why does $n^0 = 1$?

Why is it that $n^0 = 1$? I understand how $n^2 = n*n$ and how $n^1 = n$ but I can't understand why $n^0 = 1$.
3
votes
3answers
82 views

Why do we use $cm^2$?

I can't seem to wrap my head around why we should use $cm^2$ for area. According to my textbook we use it for converting units of area but I don't understand how $1cm$ is any different from $1cm^2$. ...
0
votes
1answer
71 views

Parabola problem. How far from the vertex is the focus?

A spotlight has a parabolic cross section that is 8 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? I'm getting 8/5 ft. Is this correct? Appreciated!
0
votes
1answer
128 views

A Ferris Wheel Word Problem (Trigonometry)

Please help, will give me an idea how to do more of these. A Ferris Wheel called Colossus has a diameter of 158 feet. Using the figure as a model, find the distance traveled by someone starting at ...
1
vote
0answers
23 views

Strange conundrum involving mean and variance of numbers.

Given $n$ numbers $a_1<a_2<...<a_n$ how would we find a $m$-element subset ($m \leq n$), with the smallest variance? If I knew what the optimal mean for the smallest variance is I could just ...
0
votes
1answer
55 views

Calculating $\lim\limits_{x \to 0} \frac{10^x - 2^x - 5^x + 1}{x \cdot \tan x}$ [duplicate]

I am trying to solve this limit without using Taylor expansions to explain it to a secondary school student $$\lim_{x \to 0} \frac{10^x - 2^x - 5^x + 1}{x \cdot \tan x}.$$
1
vote
2answers
20 views

Getting the Amps from Watts, Amps and the voltage of a line

What amperage capacity should the supplied wired be rated for a refrigerated fixture which has a 208V power supply and the following loads? 4 Evaporator fan motor rated at 9W each 4 Evaporator fan ...
5
votes
4answers
773 views

Solve without a calculator: What is the possible value of 2*((1+1/100)^100)?

What is the possible value of $2·((1+\tfrac{1}{100})^{100})$? Google will give $2·((1+\tfrac{1}{100})^{100}) = 5.40962765884$. How can I find the possible value without Google or a calculator? How ...
4
votes
3answers
353 views

Most useful books for a math undergrad

What are the most useful books an undergraduate in math should read? I found Alock's "How to study as a math major" and "how to study for a math degree" very useful. Are there any other good readings ...
0
votes
0answers
30 views

Need help with expected value and variance of Chebyshev's Inequality [duplicate]

Let X1,X2,...,Xn and Y1,Y2,...,Ym be independent exponential distributed random samples with mean θ. Let T_α=αx¯+(1−α)y¯, where 0<α<1. a) Find E[T_α] and var(T_α) b) Show that, for any ϵ>0, ...
0
votes
1answer
237 views

Determine sin cos and tan from slope? NON CALCULator

I am used to finding this by drawing the triangle and knowing the angle measurement. With the angle measurement i can find sin cos and tan. But i dont have angle all I have is line. I have put a ...
1
vote
1answer
23 views

The right angled triangles ABD and BCD?

AB=5cm BD=4cm and angle ABD=x Find the exact value of cos(ABC) this is the trangle...: https://twitter.com/JxstyBiebs/status/432919494466752514
1
vote
4answers
51 views

The graph of the function is $g(x)=x^3-2x^2+x+1$ and the tangent to the curve is at $x=2$?

a) Find the equation of the tangent to the curve at $x=2$ HELP and then b) Determine the angle that this tangent makes with the positive direction of the $x$-axis Please help I really need to ...
0
votes
1answer
52 views

Mean and Variance Statistics

$X_1, X_2, \dots , X_n$ ~ i.i.d $U[0,1]$ a) Find the mean and variance of $lnX_1$. b) Let $0\le a \lt b$. Find the $\lim_{n \to \infty} P(a \le (X_1,X_2, \dots ,X_n)^{(n^ -0.5)}*e^{ ( n^{0.5})}\le ...
0
votes
0answers
18 views

Jacobian, Independence, and expectation [duplicate]

Let $Y_1,Y_2,\dots Y_n \tilde{} exp(θ)$ be i.i.d. random samples. If $Y_i$'s are sorted in ascending order, the ordered random variables $X_1,X_2,\dots,X_n$ with the join pdf: $$ ...
0
votes
1answer
134 views

Can any one help solving this puzzle of digits (Puzzle : Strike off any digit from each number in seven rows … )

Q) Strike off any digit from each number in seven rows (need not be at same place) and combine the same operations with 3 digit numbers to get the same addition. After this strike off another digit ...
0
votes
1answer
78 views

Linear Transformation Brief Question

$T:P_{3}\rightarrow P_{3}$ defined by $T(p(t))=tp'(t)+p(0)$ is a linear transformation. Determine whether $T$ is invertible. If yes, find $T^{-1}(q(t))$, where $q(t)$ is a polynomial of degree at ...
3
votes
2answers
303 views

What is the distance between the line and plane if it is parallel?

So far, I've gotten that the line is parallel to the plane $x = 2 + t$, $y = -3 + 2t$, $z = 1 + 4t$ With the vector of that being $U$ is $(1,2,4)$ and the plane $2y-z = 1$ with the vector $V$ being ...
9
votes
4answers
416 views

Middle school number theory

Find at least three numbers that satisfy all three conditions: (1) there is a remainder of $1$ when the number is divided by $2$; (2) there is a remainder of $2$ when the number is divided by $3$; ...
1
vote
3answers
88 views

Integrating a school homework question.

Show that $$\int_0^1\frac{4x-5}{\sqrt{3+2x-x^2}}dx = \frac{a\sqrt{3}+b-\pi}{6},$$ where $a$ and $b$ are constants to be found. Answer is: $$\frac{24\sqrt3-48-\pi}{6}$$ Thank you in advance!
3
votes
3answers
1k views

Find the shortest distance from the point $P(0,1)$ to a point on the curve $x² - y² = 1$ , and find the point on the curve closest to $P$.

Find the shortest distance from the point $P(0,1)$ to a point on the curve $x² - y² = 1$, and find the point on the curve closest to $P$. What I did so far is : plot the y var from $x^2-y^2=1 ...
1
vote
3answers
101 views

what are the rules/rationale for “simplifying” negative denominators

So I'm losing my mind trying to understand the rules and rationale behind "simplifying" expressions and equations in Algebra. It's been decades since I've had to study for it (going back and ...
1
vote
1answer
126 views

The volume of a cylinder [closed]

A metal conduit will be used as a pathway for wiring through a concrete block. The conduit is a 5 foot long rod with an outer diameter of 2.2 inches and an inner diameter of 2 inches. What is the ...
1
vote
1answer
182 views

Question about the greatest lower bound of sets.

Let $A$ and $B$ be sets of real numbers. Define a set $A+B$ by $A+B =\{a+b|a \in A, b \in B\}$. Show that if $A$ and $B$ are bounded sets, then $g.l.b.(A+B) = (g.l.b. A)+(g.l.b.B)$. (The g.l.b. ...
4
votes
1answer
149 views

Skip count “starting at one”

My daughter is taking a second grade math class and they are learning to "skip count" I am guessing this means to count by [n]. The directions say "Start at 1. Skip count by 2." and the worksheet has ...
0
votes
1answer
2k views

Accounting Question: Computing Break-even #'s

The Lake Shore Inn is trying to determine its break-even point. The inn has 50 rooms that are rented at $60 per night. Operating costs are as follows: ...
0
votes
1answer
793 views

Accounting Question: Computing margin of Safety Ratio

Smith Company produces desk lamps. The information for June indicated that the selling price was $\$25$ per unit, variable costs were $\$15$ per unit, fixed costs totaled $\$6,000$, and the margin of ...
1
vote
4answers
331 views

Which discussion board is good for homework questions?

I'm a CompSci university student and i want some help for my math questions. Therefore i am looking for a good discussion board for math homework questions. I don't know any (good), because I come ...