Calculation Definition and 1000 Threads

So how can I calculate the energy of a volcanic eruption? If I know the VEI, total ejecta, duration and plume height would that be enough or would I need more variables?

My solution is: Let ##\lim_{ x \to 0}\left(\dfrac {1}{\sin^2x}-\dfrac1{x^2}\right)=L## Let ##x=2y## ##\lim_{ y \to 0}\left(\dfrac {1}{\sin^22y}-\dfrac1{4y^2}\right)=\lim_{ y \to 0}\left(\dfrac1{4\sin^2y\cdot\cos^2y}-\dfrac1{4y^2}\right)=L## ##=\dfrac14\lim_{ y \to...

TL;DR Summary: Question about fractions Hi All, I am currently going through my old maths school book and just finished fractions and decided to google some further questions online, but I am stuck on the following question. I include the image below with the provided answer from the...

I'VE SEEN MANY QUESTION WROTE C/m, WHAT IS C? CURRENT? Consider an insulating sphere with 10μC of charge uniformly distributed through its volume. The sphere is surrounded by a conducting spherical shell that has a total charge of −3μC. Outside the conucting shell is an insulating shell with...

Hi I have problems with the following task I now wanted to try to calculate the vector potential, which according to my professor's script is defined as follows: $$\mathbf{A}(\mathbf{x}) = \frac{1}{c} \int d^3\mathbf{x}' \frac{\mathbf{j}(\mathbf{x}')}{|\mathbf{x} - \mathbf{x}'|}$$ I have...

Number of neutrinos detected per kg of water = 12/3*10^6 kg = 4*10^-6 neutrinos Neutrinos detected by 1 eyeball = 4*10^-6 neutrinos * 0.01kg = 4*10^-8 neutrinos I am not sure how to scale this to get 400 neutrinos. I did try multiple ways but either ended up with 3.69*10^9 or 4*10^-8 neutrinos...

Hi I'm not sure if I calculated the magnetic field from task a) correct? for calculatin ##\vec{B}## i used, the formular ##\vec{B}=\vec{\nabla} x \vec{A}## $$\vec{B}=\left(\begin{array}{c} \frac{\partial}{\partial x_1} \\ \frac{\partial}{\partial x_2} \\ \frac{\partial}{\partial x_3}...

The answer should be around 39g. I keep getting around 45g. This is the calculation I tried Any feedback on what I am doing wrong ? Regards!

I have a question about how to solve the following integral: ##\int \frac 1 {x\sqrt{3x^2+2x-1}}dx##, I know how to get the right answer (which agrees with WolframAlpha and the book I got the question from) through substituting ##\frac 1u## for ##x##, completing the square and finally doing a...

For example ##(0,0,1,0,0,0,0,1,1,1,..)## is a subsequence? I think it is not a subsequence and a rule must be given? İs it true? Thank you.

1. How to get f’(1), f’(2), f’(3), and f’(5) 2. How to calculate average speed change of y to changes in x in the interval [0,6] 3. Estimate value of f’+(0) and f’-(6) pls help me about this graph, i dont know how to read this 🙏

I created a problem for myself, which I have documented in LaTeX. I hope it's acceptable that I included snapshots of my pages. I would like to calculate the Work W along curve C1. I have solved the problem as shown below. Is my solution correct (see Equation 1.11)? The pictures I included...

My problem is on how to arrive at ##d=\dfrac{mx-y}{\sqrt{1+m^2}}## My working steps are as follows; ##d^2=(x_1 - x)^2+ (y_1-y)^2## ##d^2=(\dfrac{y}{m} -x)^2+ (mx-y)^2## ##d^2=\dfrac{(mx-y)^2}{m^2} + (mx-y)^2## ##m^2d^2=(mx-y)^2(1+m^2)## ##d=\dfrac{mx-y\sqrt{1+m^2}}{m}## ...unless they...

Mass of honorite initially: 4.51 kg at 261.2 K Additional mass of honorite added: 3.75 kg at 261.2 K total mass of honorite is 4.51 kg + 3.75 kg = 8.26 kg Mass of liquid odium: 14.69 kg at 391.14 K Q melt = m honorite × L honorite Qmelt = 8.26kg × 15500J/kg Qmelt = 128030 J Q cool = (m odium)...

My answer disagrees with the textbook and I have a feeling it may be due to how I calculated the moment of inertia. Is there anything obviously wrong with my calculation? Any help is appreciated. ## I_{sphere} = \frac{2}{5}MR^2 + Md^2 ## ## I_{rod} = \frac{1}{3}ML^2 + Md^2 ## ## I_{sphere} =...

I want to calculate the K and L absorption edges for Niobium (Nb). Could anyone explain the steps to calculate these absorption edges? I don't know how to use the Moseley law to calculate those values: https://en.wikipedia.org/wiki/Moseley%27s_law For reference, Niobium has: Shielding...

I've written it as : The mentor indicated that this is incorrect. How can I write it correctly? My try: $$ \sigma = 1.07 \times 10^{-8}W.m^{-2}.k^{-4} \pm 0.0243 \times 10^{-8} W.m^{-2}.k^{-4} $$

source: https://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceIntegrals.aspx I am not sure why the question had to say "in front of the yz-plane". If I understand correctly, that means x >= 0. However, isn't this restriction already accounted for by saying "in the first octant" which means x...

I'll try and keep this as easy as I can. The Right Triangle above represents the forces acting through the trailing shoe of a automotive drum brake. Point A is the central position of the brake expander. When the foot brake is depressed, a force is created that pushes the brake expander piston...

I'm trying to solve it by 2 methods(screenshot below). However, I'm getting 2 different answers. I'm not able to find out the error in method 1. Method 2 gives the answer correctly. Kindly help. P. S: If the pics are not clearly visible enough, kindly let me know. I'll try to either improve the...

Hello, Great Minds and Fellow RPG Enthusiasts! I play and moderate a role-playing game and am seeking your brilliance. Can anyone provide me with a formula to calculate how far a person can throw and object based on how much they can lift and how much the object weighs? For example, if a...

My textbook says the correct answer for #79 is 1551 kg but I get 1600 kg. I just attempted to solve it using conservation of momentum. Can't see where the math is incorrect.

Is there an online source where I can learn how to calculate cross-sections and rates using CCC? More specifically, I want to calculate the dissociation rate of the molecular hydrogen ion due to electrons and ions, but I don't know how to do it numerically. Is there a resource available where I...

My interest is on how they arrived at ##r^2 \sin θ## My approach using the third line, is as follows ##\cos θ[r^2 \cos θ \sin θ \cos^2 ∅ + r^2 \sin θ \cos θ cos^2∅ ] + r\sin θ [r\sin^2 θ \cos^2∅ + r \sin^2 θ \sin^2 ∅]=## ##\cos θ[r^2 \cos θ \sin θ[\cos^2 ∅+ \sin^2 ∅]] + r\sin θ [r\sin^2 θ...

Can someone please explain me the steps of calculation of X1:X2 after putting in the lower value of W^2 in equation 9.9 in "Riley, Hobson, Bence - Mathematical Methods for Physics and Engineering 2006 - pg 319"? I have attached the page as a PDF file. Thank you.

My course has a module in mechanical engineering. The handout i was given for this one is: Effort = (Load x Load to fulcrum distance) / Effort to fulcrum distance my problem is memorising the formula, I am not used to formulas that use sentences to denote a variable. I am simply here to ask...

I am trying to solve (a) and (b) of this tutorial question. (a) Attempt: Since ##c'## is at ##c'(0) = 1##, then from the definition of continuity at a point: Let ##\epsilon > 0##, then there exists ##d > 0## such that ##|x - 0| < d \implies |c'(x) - c'(0)| < \epsilon## which is equivalent to...

I do not seem to understand why the ms answer is (C) 45 m unless i am missing something, In my working i have the longest piece being; ##x+0.5x+0.25x= 95## ##x=\dfrac{380}{7}= 54.28 ##m

How can i calculate the Energy required to bring 1 kg 1000 meter above the surface of the earth ?

I am stuck on part b) i). I understand that there is no normal force from the ground as the bin is on the point of being lifted off the ground, that is all fine. That leaves R, F and W. I know W is 40g, and I am required to calculate F, therefore it makes most sense to take moments about the...

Hi, I have problems with task b, more precisely with the calculation of the limit value: By the way, I got the following for task a ##f^{(n)}(x)=(-1)^{n+1} \frac{(n-1)}{x^n}## Unfortunately, I have no idea how to calculate the limit value for the remainder element, since ##n## appears in...

I'm really not sure. Obviously I can get the units right with Resistance * thickness, but I assume there's a correction factor here that I can't find anywhere?

I have done this problem three times now, and keep coming up with an answer that is a factor of 10 off from the answer in the solutions manual. The way I'm doing it is MUCH different than how they did it, so I can't use their method to see where I'm going wrong. I want to find out what I'm...

Did some calculations and with 3×-1 i Always get 5.is this correct?

Hello everyone, I've been brushing up on some calculus and had some new questions come to mind. I notice that most proofs of the fundamental theorem of calculus (the one stating the derivative of the accumulation function of f is equal to f itself) only use a limit where the derivative is...

$$Re(e^{2iz}) = Re(\cos(2z)+i\sin(2z))=\cos(2z)$$$$e^{i^3} = e^{-i}$$ $$\ln (\sqrt 3 + i)^3=\ln(2)+i(\dfrac {\pi}{6}+2k\pi)$$ Can't I simplify these more? Are they correct? Final one:## (1+3i)^{\frac 1 2}## Can I write in in term of ##\sin x## and ##\cos x## then use ##(\cos x+i\sin x)^n=\cos...

Need help in calculating the force required to flange a cylinder outwards around the perimeter by approx. 5mm. Cylinder is either Aluminum or standard Mild Steel. Thank you.

**EDIT** Everything looked good in the preview, then I posted and saw that some stuff got cropped out along the right edge...give me some time and I'll fix it. Hello all, I"m trying to calculate shaded area, that is, the area bounded by the curves ##x=y^{2}-2, x=e^{y}, y=-1##, and ##y=1##...

$$K_i + U_i = K_f + U_f$$ $$K_i = \frac 1 2 m(15)^2$$ $$U_i = 196m$$ $$U_f = 0$$ $$K_f = K_i + U_i - U_f$$ $$=\frac {15^2} 2 m + 196m$$ $$=\frac 1 2(15^2m + 98m)$$ $$=\frac 1 2m(15^2 + 98)$$ $$=\frac 1 2m(323)$$ $$=\frac 1 2m(17.97)^2$$ $$v=17.97 m/s$$ Not seeing where I'm...

The following images contain the question as well as my solution. I am not sure whether my solution is correct or not. Please help.

How can I calculate the absolute velocity of air at the outlet of a centrifugal compressor if I have: Diameter of impeller RPM Slip factor I've been reading for weeks and cannot seem to find the answer to this question. For anyone who is familiar with the subject, I'm sure you know about the...

Hi, I'm teaching Engineering (honors) and want to drill the students on series, parallel resistors in circuits and voltage dividers. does anybody a have a worksheet with lots of samples? Thanks!

I'm confused in the calculation for R/2. The author took in account that the charge will change by a factor 1/8. But how does it show that the coloumbic force will become 1/8th. The distance will also reduce by half shouldn't that also be taken into account? Or am I missing something here?

Hi need to calculate 240v/315v motor size attached to reduction gearbox (reduction unknown) to lift a weight of 100kg on cable drum .8mtr/sec. Drum dia not determined yet. motor size not determined yet. any help is greatly appreciated as this seems to be out of depth of many motor drum winch...

My solution was that the final velocity of the fly is equal to the mass of the elephant divided by the mass of the fly, and then multiplies by the delta in the elephant's velocity. My teacher said it was the wrong answer and that the calculations are presumably pretty long

Hi all, I've made errors in my calculations and need help. I'm trying to calculate the volume of a layer above sea level to the height of Flight Level 300 i.e. 30,000 feet. Next, I want to subtract the volume of land within that layer. Here are my calculations. Purely for the sake of my...

hi, how do we calculated the number of atoms at the start of universe i.e, after big bang?

Can't figure it out, here's a screenshot with better typography.

Alleyway kick The kicker weighs approximately 64kg or 140lb and the gentlemen holding the air shield is approximately 73kg or 160lb. How far does the kickee travel before hitting the chair and boxes and what speed is he travelling at? The practice kick prior to the actual kick puts the men...