Value Definition and 1000 Threads

Here is the question: Is it true that the value of K depends on the amounts of reactants and/or products that are mixed together initially? Explain. This is my explanation: The reaction always shifts left or right given any initial reactant and product amounts to attain equilibrium. Thus, the...

If E(X1)>E(X2), does it mean that E(1/X1)<E(1/X2)? Thanks!

How can I find Cauchy principal value. of this integral \[ n(x) = \int_{a}^{b} \frac{d \omega}{\omega ' ^2 - x^2} \] Where $ a<x<b $ I case $a = 0, b = 3, x = 1$ We get \[ n(1) = \int_{0}^{3} \frac{d \omega}{\omega ' ^2 - 1^2} = −0.3465735902799727 \] The result shown is the Cauchy...

##X_1## and## X_2## are uniformly distributed random variables with parameters ##(0,1)## then: ##E \left[ min \left\{ X_1 , X_2 \right\} \right] = ## what should I do with that min?

Is it true that ##\frac{|a|}{|b|} = |\frac{a}{b}|## and ##|a| < |b| = a^2 < b^2##?

Summary:: The price of a house is uniformly distributed between 0 and 1000 but we do not know its exact value. If we place a bid higher than the value, then we obtain the house, but if our bid is lower then we get nothing. If we know we can sell the house on to another person (guaranteed) for...

Dear Everyone, I have a question about how to solve for x near the end of the problem: \[ 1+2\sinh^{2}(z)=0 \] Here is the solution and work: \[ 1+2\sinh^2(z)=0 \\ \sinh^2(z)=\frac{-1}{2}\\ \sqrt{\sinh^2(z)}=\pm \sqrt{\frac{-1}{2}}\\ \sinh(z)=\pm i\frac{1}{\sqrt{2}}\\ \] Then we can split...

I'm having a bit of trouble getting a clear picture of what is going on here, so if anyone can shed any light, it will be greatly appreciated. 1. I can see how the metric coefficients provide the six numbers per spacepoint, but it can't always be possible to transform the metric into a diagonal...

Where have I gone wrong? According to the key, the right option is a.

368 Solve the IVP $y'=2(1+x)(1+y^2),\quad y(0)=0$ $\begin{array}{ll} \textit{separate variables}& \displaystyle \left(\dfrac{1}{1+y^2}\right)\ dy =2(1+x)\ dx\\ \textit{integrate thru}& \arctan \left(y\right)=2x+x^2+c\\ \textit{plug in x=0 and y=0}& \arctan 0=0+c\\ &0=c\\ \textit{thus the...

I have a formula for cost calculation that contain x and y two variable. I have to find the value of (x,y) where that formula will gives minimum value as cost should not be equal to zero, it has some minimum value. I took 1st partial derivative with respect to x and then with y and found the...

Solve the initial value problem $y'=\dfrac{1+3x^2}{3y^2-6y}, \quad y(0)=1$ Solving analytically $3y^2-6y\ dy = 1+3x^2 \ dx$ so far hopefully...

After getting the values of ψ₀(x) and ψ₁(x), I put them in the expression of ϕ(x) to get: ϕ(x) = (mw/πℏ)^(1/4) * exp[-(mw/2ℏ)x^2] * [α + βx√(2mw/ℏ)] Now when attempting to find the value of <x> by ∫xϕ(x) dx, I am having trouble determining the limits, as I am getting nothing useful by...

First, I try to define the function in the figure above: ##V(t)=100\left[sin(120\{pi}\right]##. Then, I use the fact that absolute value function is an even function, so only Fourier series only contain cosine terms. In other words, ##b_n = 0## Next, I want to determine Fourier coefficient...

Solve for y: $\quad |y+3|\le 4$ a.$\quad y \le 1$ b.$\quad y\ge 7$ c.$\quad -7\le y\le1$ d. $\quad -1\le y\le7$ e. $\quad -7\ge y \ge 1$ Ok I think this could be solved by observation but is risky to do so...

In Resnick halliday book during finding capacitance of isolated sphere they used equation of spherical capacitor[4πε₀(ab)/b-a,where a is inner radius and b is outer radius.] And took b common and equation becames 4πε₀(a)(1-a/b) and then they put radius of outer sphere infinity and then a/b...

Let: equation 1 : sin A + sin B = 1 equation 2 : cos A + cos B = 0 Squaring both sides of equation 1 and 2 then add the result gives me: cos (A - B) = -1/2 Then how to proceed? Thanks

For quadratic equation to have two real roots: b2 - 4ac > 0 (-2 (2a + 1))2 - 4 (2) (a (a - 1)) > 0 4 (4a2 + 4a + 1) - 8a2 + 8a > 0 16a2 + 16a + 4 - 8a2 + 8a > 0 8a2 + 24 a + 4 > 0 2a2 + 6a + 1 > 0 Using quadratic formula, I get a < (-3 - √7) / 2 or a > (-3 + √7) / 2Then how to know if a...

Let $a$ and $b$ be real numbers and $r,\,s$ and $t$ be the roots of $f(x)=x^3+ax^2+bx-1$ and $g(x)=x^3+mx^2+nx+p$ has roots $r^2,\,s^2$ and $t^2$. If $g(-1)=-5$, find the maximum possible value of $b$.

My guess is that g(x) = x? The limits of integration should be 0 to a, since after a the cup flows over. If I put these in, I get the solution (I've doubled checked with wolfram alpha that it's correct): $$E(Y) = ln(a+1) + 1/(a+1) - 1$$ The textbook solution is just ln(a+1). I'm super new to...

I write p(k) as: $$p(k) = 1/6, k = 2,3,4,5$$ $$p(k) = 2/6, k = 6$$ Is that wrong? Because then the expected value becomes $$1/6 * 4 + 2/6 * 6 = 8/3$$ While my book says 11/3

How to show that$E[N]=\displaystyle\sum_{k=1}^\infty P{\{N\geq k\}}=\displaystyle\sum_{k=0}^\infty P{\{N>k\}}$ If any member here knows the answer, may reply to this question.:confused:

Abs Pressure: Gauge press: 1 bar G = 100,000 Pa = 0.987 atm 0.1 bar G = 0.0987 atm Atm press = 101.3 kPa = 1 atm Hydrostatic press: average CO2 occurs 2.5m up the vessel (9.81 ms-2)(1010kgm-3)(5/2) = 24,770.25 Pa 1 Pa = 9.869x10^-6 atm 24,770.25 Pa = 0.2445 atm Abs press= 0.0987 atm + 1 atm...

Hello! (Wave) We suppose that the propositions $p,q$ are propositions such that the proposition $p \to q$ is false. Find the truth values for each of the following propositions: $\sim q \to p$ $p \land q$ $q \to p$ I have thought the following: Since the proposition $p \to q$ is false...

In its flip a lid contest, a coffee chain offers prizes of 50,000 free coffees, each worth \$1.50; two new TVs, each worth \$1200; a snowmobile worth \$15 000; and sports car worth \$35 000. A total of 1 000 000 promotional coffee cups have been printed for contest. Coffee sells for \$1.50 per...

https://www.physicsforums.com/attachments/9838 well not sure why we need 3 different coins other than confusion also each toss at least 2 coins have to have the same face frankly not sure how any of these choices work didn't want to surf online better to stumble thru it here and learn it better...

One of the maths groups I'm apart of on Facebook posts (usually) daily maths challenges. Typically they act as small brain teaser for when I wake up and I can solve them without much trouble. However, today's was more challenging: (Note: blue indicates a variable and red indicates a constant)...

it's late so I'll just start this \[ \dfrac{dy}{dx}=\dfrac{2\cos 2x}{3+2y} \] so \[(3+2y) \, dy= (2\cos 2x) \, dx\] $y^2 + 3 y= sin(2 x) + c$

So far I've got the real part and imaginary part of this complex number. Assume: ##z=\sin (x+iy)##, then 1. Real part: ##\sin x \cosh y## 2. Imaginary part: ##\cos x \sinh y## If I use the absolute value formula, I got ##|z|=\sqrt{\sin^2 {x}.\cosh^2 {y}+\cos^2 {x}.\sinh^2 {y} }## How to...

Hi, I have this formula, What I want is to find the value of "x" (without trying all possibilities) so that the result of the formula will be the lowest possible value under the constraint when x !=0, and x<n. Here, values of A,B,C, Q, R,n are already known and fixed...

I can not solve this problem: However, I have a similar problem with proper solution: Can you please guide me to solve my question? I am not being able to relate Y R (from first question) and U (from second question), and solve the question at the top above...

Find the solution of the give initial value problem $\displaystyle y^\prime - \frac{2}{t}y =\frac{\cos{t}}{t^2}; \quad y{(\pi)}=0, \quad t>0$$u(t)=e^{2 \ln{t}}$then $\displaystyle e^{2\ln{t}}\, y^\prime - \frac{2e^{e^{2\ln{t}}}}{t}y = \frac{e^{2\ln{t}}\cos{t}}{t^2}$not sure actually!

I make a theoretical calculation and then compare the calculation result and the median of the corresonding measured dateset. The difference between them is very slight, so I state that the theoretical model is right and good. However one expert has suspended whether the median is typical...

I want to use Q -test to truncate the data. But I have number of data 180 ( n = 180 ) How can i find Q critical value at 95 % Confidence ,When number of data equal to 180 ?

How to solve these two absolute value problems? 1. ##|3x - 5| > |x + 2|## My attempt: From what I read in my textbook, the closest properties of absolute value is the one that uses "equal" sign ##|3x - 5| = |x + 2|## ##3x - 5 = x + 2## ##3x -x = 5 + 2## ##2x = 7## ##x = \frac{7}{2}## ##|3x -...

1. Is it because the initial formula start the series from ##n = 2##? 2. If the initial formula is used, can I find ##S##, which $$S=\lim_{n\to\infty} \frac{2}{n^2-1}=\frac{2}{\infty}=0$$? Why that answer is different if the formula is changed.

So I started by checking the options.I substituted the value of friction in the equations I got by making free body diagrams.I got different value of Tensions.For 1 and 3 Tension came to be 38 N.For 2 Tension came out to be 42N and for 4 Tension came out to be 40 N. Now I think that I will take...

import numpy as np def array_change(a,new_val): a=np.array([]) for i in range(a): if abs(i)<1: a[i]=new_val e=np.arange(-2, 2, 0.2).reshape(4,5) print(array_change(e,0)) I am not sure where I am going wrong exactly but I keep getting an error message. I came up...

Let $f:\mathbb R\to \mathbb R$ be a twice-differentiable function such that $f(x)+f^{\prime\prime}(x)=-x|\sin(x)|f'(x)$ for $x\geq 0$. Assume that $f(0)=-3$ and $f'(0)=4$. Then what is the maximum value that $f$ achieves on the positive real line? a) 4 b) 3 c) 5 d) Maximum value does not exist...

PhET: https://phet.colorado.edu/en/simulation/masses-and-springs Any information would be appreciated. Thanks in advance!

$10 min = \dfrac{h}{6}$ So $a(t)=v'(t) =\dfrac{\dfrac{(50-30)mi}{h}}{\dfrac{h}{6}} =\dfrac{20 mi}{h}\cdot\dfrac{6}{h}=\dfrac{120 mi}{h^2}$ Hopefully 🕶

Ok Just have trouble getting this without a function..

$\tiny{3.2.15}$ Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. Graph the function the secant line through the endpoints, and the tangent line at $(c,f(c))$. $f(x)=\sqrt{x} \quad [0,4]$ Are the secant line and the tangent line parallel...

I have calculated my own solution but I am struggling to work out how to use Pspice to compare my values. I am using simetrix for this - could anyone help with this part? My solution is: VGS = -IDS RS Av = Vo/Vi Vo= -gm VGS RL Vi = VGS (1+gmRS) gm= IDS/VGS so gm= IDS/-IDS RS = 1/RD = -1/100 =...

Recently I started wondering why there seems to be so few practical/engineering applications where you need to calculate the momentum of something. I must emphasize that I don't mean usage of the concept of momentum or the law of conservation of momentum, but the value of the quantity itself...

Hello there! This is my first post, so I apologise for any faux pas I am about to commit. I have recently bumped into a few situations where I'm uncertain about my uncertainties. Especially where the value is a product of multiple variables. Please see the attatched table, where g is a function...