Volume Definition and 1000 Threads

$\tiny{s6.12.4.35}$ $\textrm{Find the volume of theparallelepiped with adjacent edges $PQ, PR$, and $PS$.}$ \begin{align*}\displaystyle P(2,0,-1),& \, Q(4,1,0), \, R(3.-1.1), S(2,-2,2)\\ \end{align*} ok I know the problem is basically solved with \begin{align*}\displaystyle...

I know this is so vague as to be unanswerable - at least no answer better than I might come up with through a bit of experimentation - but it's late and I'm lazy. After having my new Smart TV with soundbar for several months now, it has spontaneously started doing something different. The new...

Say we have 2 cylinders with the same volume capacities, but different radii, and a plunger to 'squeeze' the contents. We apply the same force to each plunger. Will the cylinder with the larger radii lose volume faster? Or will they be equal?

The above is a circuit i found on the net regarding amplification of volume. I needed to know if increasing the potentiometer resistance (between "cold" and "wiper"; terminal 1 and 2?) in the circuit would increase "volume" Also, i could use a potentiometer resistance ( between "cold" and...

Hey guys. I could use some explanation since I am new to FM: So my problem is the following one: Fluid flows with an average velocity 8 m/s in a pipe with diameter 3m. What is the volume flow rate? Now, I think the formula I got to use is Q= v.A Yet, I found my solution from a formula I found on...

Homework Statement Find the volume of the region bounded by the curves y=3x-2, y=6-x, and the x-axis when the region is rotated around the y-axis. Homework Equations Volume using cylindrical shells: 2π∫r(x)h(x)dx The Attempt at a Solution I graphed the curves and then found the x-intercept...

Theres something that bothers me, We claim that electron is a point particle.From that, Can we assume the volume the electron is ##(l_{h})^3## ( where ##l_h## is Planck length ) ? We know that every information can be described in bits like volume is ##(l_{h})^3## so, In every bit of...

The density of ice is 920 kg/m3. Now let's calculate. m = 269 000 000 000 000 kg p = 920 kg/m3 ----------------------------- v=? V=m/p V=269 000 000 000 000 kg / 920 kg/m3 V = 292 391 304 347 m3 = 292 391 304.347 km3 v > 269 km3 *NOTE* I made a mistake in the title. I meant to write 269 km3...

Homework Statement 10.00 cm3 of 1.00 mol dm–3 sulfuric acid is fully neutralized by 20.00 cm3 of 1.00 mol dm–3 of sodium hydroxide. What is the concentration, in mol dm–3, of sodium sulfate solution produced by the reaction? A 0.33 B 0.50 C 0.67 D 1.00 Correct answer = A Homework Equations...

Use a triple integral to find the volume of the solid bounded by the graphs of the equations. z = 4 - x^2, y = 4 - x^2, first octant I need help setting up the triple integral for the volume. I will do the rest.

Use a triple integral to find the volume of the solid bounded by the graphs of the equations. x = 4 - y^2, z = 0, z = x I need help setting up the triple integral for the volume. I will do the rest.

Is a surface bounding a volume always a closed surface?

Hi, For a book that I’m writing, i need to know how to describe the following, if the situation described is ever possible, otherwise I'll have to come up with another scenario. A surge of high voltage electricity at a gas-insulated switchgear creates a flashover whose Breaker Current Failure...

A shipping box is filled with pastry boxes. Each pastry box measures 1 cubic foot. The shipping box is 3 feet high. The bottom layer of the shipping box can fit 6 pastry boxes. What is the volume of the shipping box? Do I simply multiply 1 by 3 by 6 to get 18 cubic feet?

Hi guys, I need to determine the performance of a single expansion ramp nozzle (SERN) from CFD results with different nozzle pressure ratios (NPR). For some NPR the nozzle is overexpanded and for some underexpanded. Now the impact of the control volume definition on especially the axial thrust...

Homework Statement The flux density in a single phase core type symmetric(length=breadth=height) transformer is B and flux is Φ. Can we find out the volume of core of transformer if the height of limb is h? Homework Equations Φ = B * Cross sectional area The Attempt at a Solution Can we say...

Homework Statement Find the volume in octane 1 enclosed. x + y + 2z = 2 2x + 2y +z = 4 ∫∫∫ dV Homework Equations - The Attempt at a Solution ∫∫∫ dv = [∫(0⇒2) [∫(2-2z)⇒(2-½z) [∫(2-2z-y)⇒(2-½z-y) dx] dy] dz] = [∫(0⇒2) [∫(2-2z)⇒(2-½z)...

I cannot understand the the relation between Reynolds Transport Theorem and Volume Calculation. Volume calculation is an simple, straightforward process which, I think, have much connection between Reynolds Transport Theorem. We calculate volumes in thermodynamics, heat transfer and fluid...

Hello! I encountered in a problem the terms heat capacity at constant volume and density (##n##) and heat capacity at constant chemical potential (##\mu##) and volume and I need to prove a relation between them. What is their definition? I thought that for the first one it would be...

g(x)= √(19x) = upper curve f(x)= 0.2x^2 = lower curve Firstly, I found the point of intersection, which would later give the upper values for x and y. x=7.802 y=12.174 Then I found the area under g(x) and took away the area under f(x) to get the area between the curves. 31.67 units^2 This is...

In a change of coordinate system we have ##dx^\mu = (\partial x^\mu / \partial \xi^{\kappa})d \xi^{\kappa}##, where the term in round brackets is the Jacobian. That notation implies a sum over all values that ##\kappa## can take. This don't tell us that it's an alternating sum for the case of...

What is the answer to this question. The surface area of a rectangular prism is 136 square units. Some edge measurements are 6 and 2.What is the volume?

Homework Statement Here we divide the mole balance by the volume ##4*\pi## ##*## r2##*##dr and take lim as dr->0(standard procedure) 1) How exactly he makes the transition from equation from 6 to 7? Exercise #2(see below please) Solution for Problem#2 2)Why does he divide here by...

Homework Statement For the vector field F(r) = Ar3e-ar2rˆ+Br-3θ^ calculate the volume integral of the divergence over a sphere of radius R, centered at the origin. Homework Equations Volume of sphere V= ∫∫∫dV = ∫∫∫r2sinθdrdθdφ Force F(r) = Ar3e-ar2rˆ+Br-3θ^ where ^ denote basis (unit vectors)...

Homework Statement (a) A rectangular gasoline tank can hold 39.0 kg of gasoline when full. What is the depth of the tank if it is 0.450 m wide by 0.900 m long? m (b) What is the volume of the tank? (It is suitable for a passenger car.) gal Homework Equations Density of gas=719.7=mass/volume...

Homework Statement I'm having a bit of trouble with this problem: "A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball (r≤R) is E(r)=r^4Emax/R^4. a. What is Emax in terms of Q and R? b. Find an expression for the volume charge density ρ(r)...

To find the surface area of a hemisphere of radius ##R##, we can do so by summing up rings of height ##Rd\theta## (arc length) and radius ##r=Rcos(\theta)##. So the surface area is then ##S=\int_0^{\frac{\pi}{2}}2\pi (Rcos(\theta))Rd\theta=2\pi R^2\int_0^{\frac{\pi}{2}}cos(\theta)d\theta=2\pi...

Given sphereRadius and piVal, compute the volume of a sphere and assign to sphereVolume. Use (4.0 / 3.0) to perform floating-point division, instead of (4 / 3) which performs integer division. public class SphereVolumeCalculator { public static void main (String [] args) { double piVal...

If you have two different containers filled with two different gasses at the same temperature, would they have less pressure when connected to each other? Dalton's law states that each of the gases behave independently when it comes to pressure as they fill the space as if they were the only gas...

Do neutron stars have a minimum volume? Anything "in the way" of perhaps baseball sized neutron star? Or would something like that be an impossibility? How neat to have one in a laboratory...or not lol

Morning all, I am working on a Air Cannon Project and have hit a stumbling block. I am trying to work out what tank pressure and volume I would need to project a 1.4kg mass to 83m/s when it leaves the barrel. The barrel the mass will travel down is 4 meters long and 6inch in diameter, would...

Homework Statement Consider a 10 meter long gas column. We interrogate the gas molecules with a HeNe laser (lambda=633nm) at the minimum possible gas volume. If we focus the beam tightly, it will eventually diverge and the sampled gas volume will increase. Consider a minimum beam diameter D...

I have known the interaction parameter of a certain liquid mixture which has the phase behaviour can be described by the lattice model. , is it possible for us to know the temperature at the critical point? Besides, if we know the temperature at the critical point, can the volume fraction of...

Homework Statement A sector with central angle θ is cut from a circle of radius R = 6 inches, and the edges of the sector are brought together to form a cone. Find the magnitude of θ such that the volume of the cone is a maximum. Homework Equations Volume of a Cone = ⅓ * π * r2 * h Area of a...

Homework Statement In the year 2004 the USA produced 1787 TWh of electrical energy in conventional thermal plants and 476 TWh in nuclear plants. Assuming 30% efficiency for nuclear plants and 40% for conventional thermal plants, determine the (annual) volume of cooling water required to cool...

I'm working on this: When I consider a disc with radius ##a## and total charge ##Q## uniformly distributed (placed in the XY plane and centered at the origin) and determine the volume charge density in cylindrical coordinates, I have assumed is of the form ##\rho=A \delta (z) U(R-r)##, (##U## is...

Homework Statement A torus is formed by revolving the region bounded by the circle ##x^2+ y^2= 1## about the line x =2 Find the volume of this “doughnut-shaped” solid. (Hint: The integral ##{\int_{-1}^1} \sqrt{1 -x^2} dx## represents the area of a semicircle.) 2. Homework Equations...

If I submerge a cup in a graduated cylinder filled with water, will the change of the water line show me the volume of the cup? Or is this not the case? I am in an argument with a friend, he believes that the volume of the cup could be found by holding the top of the cup right about the water...

Homework Statement Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y =4. $$y=\frac 3 {1+x},~ y=0,~ x=0,~x=3$$ Homework Equations $$V= \int_a^b ([R(x)]^2-[r(x)]^2)dx$$ The Attempt at a Solution I understand how to use the...

Homework Statement I am to calculate the density of a nucleus, say, of Iron, with mass 55.845 amu. Homework Equations see below The Attempt at a Solution I come to notice that all elements have the same value for the volume if I use the formula: $$mass=m=m_{amu}(1.66\times10^{-27}kg/1u)$$...

Homework Statement Determine the number of cubic yards of crushed rock necessary to make a roadbed with the cross-section shown below, if the road is to be 1/4 mile − long. Assume that the crown of the pavement is an arc of a parabola, with its vertex at the top center. Be careful with units...

New to forum Most air tanks are categorized on volume of air they hold . The question I have is this that a 5 gal air tank that holds 160 psi , is it equivalent to a tank that holds 2.5 gal of air at 320 PSI ? if not then is there a formula to figure this ratio . Thanks

Homework Statement My problem includes answers from previous problems that are to be used as data in this problem so I will state the previous problems and the answers but not their solutions because I have solved them and they are pretty clear to me. So, I will be only posting the solution to...

You often hear "most of everything is made up of empty space", referring to the idea that atoms only have mass in their nucleus. It seems to me that this is trying to explain physics in terms of everyday intuition, rather than the other way around. Specifically we have this intuitive notion of...

Hello everyone, I am having a problem with MCNP. My question is how to get number of secondaries in a certain volume. For example I have a neutron beam bombarded Pb target, and I want to count all of proton formed in the target. I considered tally F4, but the unit is 1/cm**2. Who can explain the...

Hi. If an ideal gas of ##N## particles is allowed to expand isothermically to double its initial volume, the entropy increase is $$\Delta S=N\cdot k_B \cdot \log\left(\frac{V_f}{V_i}\right)=N\cdot k_B \cdot \log\left(\frac{2V}{V}\right)=N\cdot k_B \cdot \log\left(2\right)\enspace .$$ This can...

Homework Statement Express volume expansivity (B) in terms of density (ρ) and its partial derivatives Homework Equations B = (1/V) (dV/dT) V = m/ρ The Attempt at a Solution I have only managed to substitute m/ρ into the expansivity equation. Don't really understand how to manipulate the...

Hi guys, 42 year old engine hobbyist here, not a student. I've had great luck figuring out my questions in this portion of the forum in the past and look forward to your input. Keep in mind that I'm not formally educated, so if it's possible to dumb something down a bit I'd appreciate it.1...

Hello everyone, 1. Homework Statement Question : Find the volume of the region which remains inside the cyclinder x 2 + y 2 = 2y, and is bounded from above by the paraboloid surface x 2 + y 2 + z = 1 and from below by the plane z = 0 Homework Equations The Attempt at a Solution This looks...

Hey ! i am having this question to be answered , i am new to the cosmology studies and still a bit confused about some formulas. the question is: (a) The greatest redshift known corresponds to the cosmic microwave background (CMB, CBR) at redshift z 1100 (although the redshift is obtained...