Volume Definition and 1000 Threads

Region bounded by x^2-y^2=16, y=0, x=8, about y-axis Integrating with respect to y, my lower and upper bounds are $-4\sqrt{3}$ and $+4\sqrt{3}$, respectively. V=\pi \int_{-4\sqrt{3}}^{4\sqrt{3}} 64-(16+y^2)\,dy =2\pi \int_{0}^{4\sqrt{3}} 48-y^2\,dy =2\pi (192\sqrt{3}) =256\pi My textbook...

Folks, It's been a while since I've done calculations like this so I was wondering if someone can help me calculate the volume of a gas at a specific temperature as compared to its liquid volume when measured below its boiling point. I can't seem to find a phase diagram for this material, is...

Homework Statement find volume of the region bounded by x^2+2y^2=2;z=0;x+y+2z=2 The Attempt at a Solution I figure "slicing" in the z=0 direction would be the easiest the first issue I am having is the upper bound of z, it definitely seems to be 2 but but it's not making sense...

Homework Statement compute volume below z=x^2+y and above the rectangle R= [0,1]x[1,2] The Attempt at a Solution \int_{0}^{1}\int_{1}^{2} x^2+y dydx \int_{0}^{1} [x^2y+\frac{y^2}{2}]\Bigg|_{1}^{2} dx \int_{0}^{1} x^2+ \frac{3}{2}dx \frac{x^3}{3} + \frac{3x}{2}...

I'm an engineering student, and I'm making a formula for the volume of liquid in a cylinder that is cut in half diagonally. r is the radius, h is the height from the bottom to the top of the sloped flat bottom, and L is the height of the water within the cylinder. So when L = h you would expect...

Homework Statement show rectangular box of given volume has minimum surface area when the box is a cube [gotta show it with partial derivatives to minimize] Homework Equations surface area = 2(wl+hl+hw) volume = whl The Attempt at a Solution so this is the one I would be minimizing...

Why there no change in volume and enthalpy of solution when two components are mixed

I have very large data sets: coins & amount i.e. {10 & 11, 9 & 7, 8 & 9, 4 & 5, 3 & 1} graphed would show greater volume to the left side while {1 & 0, 2 & 3, 2 & 1, 4 & 6, 9 & 10} would reflect greater volume on the right, and {1 & 4, 2 & 3, 12 & 10, 4 & 4, 3 & 2} would reflect a surge in the...

Homework Statement The top of a rubber band bushing is designed to absorb vibrations in an automobile is the surface of a revolution generated by revolving the curve z = (0.5y^2) + 2 for (0<= y <= 3) in the yz plane about the z axis. use the shell method to find its volume...

Question: What volume of a 0.835 M solution of Na2SO4 do you have if there are 0.0534 mol of Na+ present in the solution? What I did: Since we have 0.0534 moles of Na+ ions in the Na2SO4 molecule, I used that for the equation. Since 0.0534 moles is in a 1:1 ratio with Na2SO4 I can conclude we...

Homework Statement according to the model ans, the volime of oxygen produced is 25x 24 dm^3 ... where does the 25 come from ?? or someone can show me other step of getting the ans ? thanks in advance! according to the model ans, the volime of oxygen produced is 25x 24...

Homework Statement A 1-cm3 air bubble at a depth of 141 meters and at a temperature of 4 degrees Celsius rises to the surface of the lake where the temperature is 13.1 degrees Celsius, to the nearest tenth of a cm3, what is its new volume?Homework Equations P1V1/T1=P2V2/T2The Attempt at a...

If a helium-filled balloon initially at room temperature is placed in a freezer, will its volume increase, decrease, or remain the same? The Attempt at a Solution If you decrease the T of a vessel filled with gas, its molecules will have less kinetic energy, and the pressure inside the...

From browsing this website I have formed an opinion that people in here don't like when someone brings up information that they heard in a movie.. Well this is more along the lines of a question that arose from watching a movie.. With Sandra Bullock, forgot the name.. Dialogue went something...

I am no english native speaker, sorry if something is a little confuse. I was swimming, and then I realized that when I let the air go our of my lungs I sink. I though this might be because of changes in the volume of my body while holding air or letting it go. So I hold as much air as I...

1.find tthe volume solid generated by revolving the region bounded y=sqrt x and the ;lines y=1, x=4 about the line y=1 2. using simpson rule witj n=4 to aproximate int from 0 to 1 1 over 1-x power 2 dx

The Volume of an atom comes from its electrons and mass of an atom comes from its nucleons. I don't understand why? Any one can explain it please? Thanks in advance

In 2 dimensions given a scalar field f(x,y) is possible to compute the line integral ##\int f ds## and area integral ##\iint f d^2A##. In 3D, given a scalar field f(x,y,z) is possible to compute the surface integral ##\iint f d^2S## and the volume integral too ##\iiint f d^3V##...

Y=x^(2/3) and y=x^2 rotated about the x=4. First I equate the equations giving me x=0,-1,1. The problem is I have exactly 2 graphs that are symmetric in respect to the y axis. N I have not encountered a problem in stewart dealing with this. I know that the volume on the right side of the...

Hey I am a physics student, and not so familiar with chemistry. I have a huge problem, because I have to find the following 3 values for liquid isopropanol: 1. The specific heat capacity at constant volume 2. The specific heat capacity at constant pressure 3. Volumetric Isobaric...

Say for example you have take a sample of 500ml from a bulk saline solution (NaCl and H20). If you know that for every 100 grams of water there is 10 grams of NaCl, can you calculate the amount of NaCl in 500ml of the final mixture?

Homework Statement A dam has a rectangular base 1500 meters long and 140 meters wide. Its cross-section is shown in the figure. (The Grand Coulee Dam in Washington state is roughly this size.) By slicing horizontally, set up and evaluate a definite integral giving the volume of material used...

Hello . I am in the end of my exams and i have to do a geometry figure like a pyramid ( view image ) below Now i should find the Perimeter, Volume and Surface of this figure . Lengths are all 5 cm, Can somebody find and write the Permiter,volume and surface for this figure please it's urgent...

Hi everyone, I'm a bit confused with this question. An airline demands that all carry-on bags must have length + width + height at most 90cm. What is the maximum volume of a carry-on bag? How do you know this is the maximum? [Note: You can assume that the airline technically mean "all carry...

calculate the volume obtained when the area bounded by y=e^x, x=1, y=1, is rotated around x=4. use shell method. Can I see your integral? My teacher gave me the first integral. I found the second one here: BUT: the two do not give the same numerical result: integral of pi((4-lnx)^2-9) FROM 1...

hi every body Consider we have a null hypersurface. how we can calculate volume element on it?

So this is the problem that I am working on. It is a woosh bottle where I am inputting 70% isopropyl alcohol, closing the top and waiting for the alcohol to evaporate. This mixture is then ignited to generate a flame. My job for this project is to calculate the maximum volume of 70% isopropyl...

Hi: I have been working in this Project for a while now and I would like to share the results with you. Still needs some improvements; but it appears to be working fine so far. Please let me know your suggestions and ideas. Thanks.

Homework Statement By using triple integral, find the volume of the tetrahedron bounded by the coordinate planes and the plane 2x+3y+2z=6.Homework Equations Volume= ∫vdv=∫∫∫dxdydz The Attempt at a Solution find intercepts of the plane on the axes, x-intercept=3 y-intercept=2...

Is this so? I cannot think of a counter-example and it is too general a statement to prove.

Homework Statement Find the volume of the region enclosed by z = 1 - y^2 and z = y^2 - 1 for x lying between 0 and 2 inclusive. Homework Equations The Attempt at a Solution I know that the y bounds are from -1 to 1, where the parabolas meet. x bounds are from 0 to 2. So would...

Homework Statement Find surface and volume charge densities. Deduce electric field. Homework Equations The Attempt at a Solution Volume charge density: \epsilon_0 \epsilon_r \nabla . \vec E = \rho_f Using ##\vec P = \chi \epsilon_0 \vec E = (\epsilon_r -1)\epsilon_0 \vec E##...

Hi, I have a book that makes the equality. \vec{B}dV = (\vec{e_1}B_1 + \vec{e_2}B_2 + \vec{e_1}B_2)dx_1 dx_2 dx_3 \\[1ex] = dx_1 \vec{e}_1(B_1 dx_2 dx_3 ) + dx_2 \vec{e}_2(B_2 dx_1 dx_3 ) + dx_3 \vec{e}_3 (B_3 dx_1 dx_2) = (\vec{B}\cdot d\vec{S}) d\vec{l}. I'm a bit confused as to how it...

Today in my chemistry class, the teacher said: Is it true? If yes I have a doubt. 0 vloume means the matter will demolish right? Then how will the mass of the demolished matter be conserved according to Law of conservation of mass?

Homework Statement A standard mercury thermometer consists of a hollow glass cylinder, the stem, attached to a bulb filled with mercury. As the temperature of the thermometer changes, the mercury expands (or contracts) and the height of the mercury column in the stem changes. Marks are made on...

A solid has a circular base of radius 3. If every plane cross section perpendicular to the x-axis is an equilateral triangle, then it's volume is I keep on getting 18 root 3. But the answer is 36 root 3. Could I get some help? Thanks.

Homework Statement Hello! English is not my native language so I hope the terminology is right. Q: Find the volume generated by the curve y=1/x+2, positive x- and y-axis and the line x=1. Calculate the volume obtained by rotation around the: a) x-axis b) y-axis Homework...

https://www.physicsforums.com/attachments/69284Homework Statement i have done the part a, for b , i use the key in the (circled part equation ) into calculator .. my ans is also different form the ans given. is my concept correct by the way? Homework Equations The Attempt at a...

Say that we have a salt solution does the volume of the solution change after when the salt is ionized and equilibrium is achieved ??

Homework Statement Use a double integral to find the volume of the indicated solid. Homework Equations The Attempt at a Solution I can't find what I did wrong, it seems like a simple problem... $$\int_0^2 \int_0^x (4-y^{2})dydx=\int_0^2 4x-\frac{x^{3}}{3}dx$$...

Homework Statement Let ##A\subset E^n## be a set with volume and ##f:A\to\mathbb{R}## a continuous function. Show that if the set ##\{x\in A:f(x)=0\}## has volume zero, then the set ##\{x\in A:f(x)>0\}## has volume. Homework Equations None The Attempt at a Solution A proposition...

1. The problem statement, all vbles and given/known data So I'm going throught the Nova Physics book and I'm wondering if there's a mistake in calculation. The question reads: How much volume does 0.4kg of oxygen gas take up at T= 27 degrees Celsius and P= 12 atm (gas constant R = 0.0821 L...

Homework Statement Let ##A\subset E^n## and let ##f:A\to E^m.## Consider the condition that there exist some ##M\in\mathbb{R}## such that ##d(f(x),f(y))\le Md(x,y)## for all ##x,y\in A.## Show that if the condition is satisfied, if ##m=n##, and ##\text{vol}(A)=0##, then...

Homework Statement Whats the stock solution volume required to prepare 100ml of a NaHCO3 solution 5g/L using a stock solution of NaHCO3 30g/L. Homework Equations M1*V1 = M2*V2 M = Molarity = mols/L The Attempt at a Solution NaHCO3 = 84g/mol 5g NaHCO3 = 0.0595238095238095mol 30g NaHCO3 =...

Homework Statement Here is the problem: You are worried that your -80C freezer is on the fritz. Unfortunately you do not have a thermometer. You do have a balloon. so, you blow up the balloon and measure that it has a diameter of 10cm when at 25C. you put it in the freezer, let it come to...

Homework Statement Find the volume enclosed by the cone x^{2}+y^{2}=z^{2} and the plane 2z-y-2=0. Homework Equations \int\int\int dV The Attempt at a Solution In the image Cono=Cone and Plano=Plane

Hello, I'm not sure if I'm approaching this the right way, but essentially I used the definition of volume expansivity and a result for the molar volume of an ideal solution to get my expression, so my result is that the claim is wrong. Am I going about this one correctly?

I do not know how to formulate formulas on this forum so I just wrote it neatly on a piece of paper and linked it. http://puu.sh/8fwXr.jpg Thankss.

1. estimate the fermi energy for lithium... the crystal structure of lithium is a bcc with a unit cell size of 3.5*10^-10 m [b]i need n, which equals N / V. if i divide by per atom, then i get (N/atom) / (V/atom) = valance / (V/atom). my question is how to get the volume per atom...

please tell me if i did this correctly: task: I'm trying to divide the differential dA by dV where.. dA = differential surface area of a sphere, dV = differential volume of a sphere dA=8\pirdr dV=4\pir2dr so then dA/dV= 2/r Also, if i treat this as a derivative, then would...