Volume Definition and 1000 Threads

This question has been bugging me and the more I think about it the more confused I get. N2O4 ⇔2NO2 Question: the reaction will shift to the right with all of the following changes except A. Addition of N2O4 B. an increase in volume at constant pressure C. A decrease in pressure at...

Homework Statement Find the volume of the solid generated by revolving the region bounded by the parabola y=x^2 and the line y=1 about the line y=1 Homework Equations V= integral of pi*r^2 from a to b with respect to variable "x" The Attempt at a Solution pi(integral of 1-(x^2-1)^2...

Homework Statement A box that is open at the bottom is lowered into the sea (density like water). The outer volume of the box and the air inside it is V_{out}=3 m^3. The moment the box touches the sea surface the air inside it gets trapped and has a volume at V_0=2.5 m^3 and a pressure at...

Homework Statement Find the volume of the solid formed by revolving the region bounded by f(x) = 2-x^2 and g(x) = 1 about the line y = 1. Homework Equations V = ∏∫(1-f(x))^2dx - ∏∫(1-g(x))^2dx The Attempt at a Solution I keep ending up with ∏∫(1-(2-x^2))^2dx - ∏∫(1-1)^2dx, on...

Hello. Homework Statement Basically I want to evaluate the integral as shown in this document: Homework Equations The Attempt at a Solution The integral with the complex exponentials yields a Kronecker Delta. My question is whether this Delta can be taken inside the integral...

Problem: Suppose in a tetrahedron ABCD, AB=1; CD=$\sqrt{3}$; the distance and the angle between the skew lines AB and CD are 2 and $\pi/3$ respectively. Find the volume of tetrahedron. Attempt: Let the points A,B,C and D be represented by the vectors $\vec{a}, \vec{b}, \vec{c}$ and $\vec{d}$...

Homework Statement Find the volume of the solid bounded above by the surface z = x^2 + y^2 and below by the triangular region in the xy-plane enclosed by the lines x = 0 , y = x , and x + y = 8. Homework Equations V = ∫∫ Height Base The Attempt at a Solution I first found...

I found this matrix in the wiki: https://fr.wikipedia.org/wiki/Vitesse_ar%C3%A9olaire#.C3.89valuation_en_coordonn.C3.A9es_cart.C3.A9siennes I think that it is very interesting because it express d²A not trivially as dxdy. So, I'd like of know if exist a matrix formulation for volume...

what are the dimensions of rectangular beam of volume maximum that can be cut from a trunk in diameter "D" and length "L", assuming that the trunk has the shaped of a straight circular cylinder shape? Answer Width =lenght

The sum of the length and the perimeter of base of a postal package to is 60 cm. find the maximum volume: when the package is cylindrical. The answer is 2547 cm3 V cilinder = pir2h and the sum L + L+H = 60 2L + H = 60 solving for H and putting it into the volume i don't get the answer Yeah...

Consider a sheet of length L and width W. Each corner is cut out (x by x corners removed). Detemine the value of x so when the corners are removed and flaps folded up, the five sided box formed will have maximum volume. SA \(= 1LW + 2 LH + 2WH\) and V \(= LWH\). I am not sure how to do this...

A tree trunk is shaped like a truncated cone it has 2 m of length and diameters of their bases are 10 cm and 20 cm. Cut a square straight section so that the axis of the beam coincides with the axis of the truncated cone. find the beam volume maximum that can be drawn from this form. answer...

I am trying to find the volume of a pyramid where the base has length \(L\) and width \(W\), and the pyramid has height \(h\). Let \(L\) be on the x-axis and \(W\) be on the y axis. In the x-z plane, we have the line \(z = -\frac{h}{L/2}x + h\), and in the y-z plane, we have the line \(z =...

Homework Statement Find the volume of an object bounded by x2 + y2 ≤ 1, x2 + z2 ≤ 1 and y2 + z2 ≤ 1. Homework Equations The Attempt at a Solution This stuff is very new to me (multiple integrals to find volume) so I am not entirely familiar with it. My first thought was to put...

Homework Statement Use cylindrical shells to find the volume of a torus with radii r and R. Homework Equations V= ∫[a,b] 2πxf(x)dx y= sqrt(r2 - (x-R)2) The Attempt at a Solution V= ∫ [R, R+r] 2πx sqrt(r2 - x2 - 2xR + R2) dx I feel like this isn't going in the right direction...

Hello! I just found this website and it looks amazing! I'm not a scientist or anything, but I love it (should've studied physics but oh well), so I think it will be fun and useful for me to join this forum. I am trying to solve a situation, where I'd like to know how much energy would be...

My E&M professor brought up this problem of considering a uniform charge density, rho, that is infinite in volume and then using Gauss's Law to find the electric field at a point. It's resulted in a lot of head scratching and I'd appreciate some help/discussion to guide me towards a resolution...

1. At Lagoon, there is a large granite rock ball that is supported by water pressure, so people can spin the rock. The diameter of the rock is 1.3m. Granite has a density of 2691kg/m^3. Let’s assume a water pressure if 50 lbs/in^2. Calculate the area of the ball that must be in the water...

So, I have this question, but I have no idea what constraint is and how to find a constraint for the length, height and width... and if i say the square wastage is x, then the width is 80-x but I don't know what the length would be with respect to x... , and how do we determine the dimensions..?

Homework Statement Homework Equations The Attempt at a Solution I understand what the question is asking. Both ways I should get the same answer. I'm having trouble figuring out the mathematics behind this question.

Homework Statement The problem is attached in this post. Homework Equations The problem is attached in this post. The Attempt at a Solution Disk method with the radius equal to x/((x^2+3)^5/4) For Trig Substitution √(x^2+a^2) -> x=atanθ a=√3 -> a^2=3 x=√(3)tanθ -> dx=√(3)sec^2(θ)...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement Find the volume of the solid of revolution obtained by rotating the area bounded by the curves about the line indicated. y=x2-2, y=0 about y=-1. Need only consider part above y=-1 Homework Equations V=∏a∫b[f(x)]2dx The Attempt at a Solution I'm mainly unsure of...

When we way that \frac{d^3p}{p_0}=\frac{d^3p}{\sqrt{m^2+\vec{p}^2}} is the invariant volume element, is that with respect to all Lorentz transformations or just proper orthochronous Lorentz transformations?

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement The problem is attached in this post. Homework Equations The problem is attached in this post. The Attempt at a Solution I've set up the integral via disk method: π∫(e^√x)^2 dx from 0 to 1 I've done integration by parts by don't know how to integrate the...

what volume does the "v" in pv denotes? say that in a system where pressure is constant Mg reacts with O2.when dealing with above reaction thermodynamically, HI=UI+PVI where H is the initial enthalpy of the system UI is the...

I am thinking about how to find the volume rotate around its function.Let f be a function of x in the interval [a,b] . The function could be any curve. And the curve is rotation around itself. Would there exist a volume of the curve? And how to find the volumeThank you CBARKER1

Hi all, I read The unit cell is the smallest structure that repeats itself by translation through the crystal. Some says premitive unit cells contains atoms only at the corners while a unit cell may contain extra atoms in between(like bcc or fcc). At one place I found this: For each...

Need someone to verify that my work is correct please. Consider the region bounded by $y = sin(x)$ and the x - axis from $ x = 0$ to $x = \pi$ a) Find the volume if the region is rotated about the x - axis. $$V = \int \pi (sin(x))^2 \, dx$$ $$ \pi \int^{\pi}_0 sin^2x \, dx$$ $$\pi...

I have the pipe size, flow rate, and a duration. How can I figure out the amount of fluid that was released from the pipe?

A triangle hypotenuse given rectangle is rotated around one of their legs to generate a right circular cone? find the cone of greater volume. resp V= (2Sqrt(3)pi L^3)/27 It says hypotenuse given but it has no value According to the answer you can name it L

From A circular sheet of RADIUS "R" a sector tie is cuts so that the coil Gets a funnel. Calculate the angle of the circular sector to cut back so of funnel has the maximum capacity. Answer tha angle is 2sqrt(6)pi/3

From two places equal of radio circular R It wants to build a buoy consists of two equal bass common cones Determine the radius of Ia base when the volume of the buoy is maximum. r=(sqrt of 6) R/3

Here is the question: I have posted a link there to this thread so the OP can view my work.

i have no clue as to how to proceed for the following three problems: #1 find the volume of the resulting solid by any method x^2 + (y - 1)^2 = 1, about the y -axis #2 use the cylindrical method to obtain the volume of a sphere of radius r #3 and a right circular cone of radius r and height h...

Homework Statement The problem is attached in this post. Homework Equations The problem is attached in this post. The Attempt at a Solution I used washer method and set my outer radius as 2+2+√(x-1) and my inner radius as 2. I set my upper limit as 5 and my lower limit as 2...

Homework Statement The problem is attached in this post. Homework Equations The problem is attached in this post. The Attempt at a Solution I used shell's method and set up my integral as 2π∫(4-x)(x^2)dx, from -2 to 2 and got an answer of 128π/3 which is incorrect. The actual answer is...

Homework Statement Two copper cylinders, immersed in a water tank at 30.3 °C , contain helium and nitrogen, respectively. The helium-filled cylinder has a volume twice as large as the nitrogen-filled cylinder. [SIZE="3"]a) Calculate the average translational kinetic energy of a helium...

Here is the question: I have posted a link there to this thread to the OP can view my work.

Homework Statement See the problem attached in this post. Homework Equations See the problem attached in this post. The Attempt at a Solution I set my limits of integration with respect to z axis and got an upper limit of 2 since that's the vertex point/height of the pyramid...

Homework Statement Find the volume of the solid using cylindrical shells: y=e-x^2 y=0, x=0, x=1, about y-axis. Homework Equations How do I integrate xe^(-x^2)? The Attempt at a Solution 2∏x∫0 to 1 xe^(-x^2) dx 2∏*-(e^(-1))/2)

3) Calculate the dimensions of the straight circular cone, smaller volume that can be circumscribed around a cylinder of RADIUS "R" and height "H". Answer is h = 3H and r= 3R/2

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement You are building a device for monitoring ultracold environments. Because the device will be used in environments where its temperature will change by 211°C in 2.99s, it must have the ability to withstand thermal shock (rapid temperature changes). The volume of the device is...

Homework Statement Find the volume obtained by rotating the region between the graph of y=0.5(sin(x^2)^2) and the x-axis (from 0 to squareroot pi) about the y-axis. The answer pi^2/4, but I don't understand how to get the answer, I can set up the integral but can't simplify it to that...

Homework Statement Find the volume of the first quadrant region bounded by x=y-y3, x=1 and y=1 that is revolved about the y-axis. 2. The attempt at a solution v=∏ ∫ from 0 to 1 of (y-y^3)^2 dy and doing this, I got the answer to be 8∏/105. Did I set up that integral...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement When pressure is applied to a liquid, its volume decreases. Assuming that the isothermal compressibility κ=-1/V(δV/δP) is independent of pressure, derive an expression for the volume as a function of pressure. Homework Equations The Attempt at a Solution I don't...

Homework Statement It asks to find the volume of the solid given these planes: z = x y = x x + y = 2 z = 0 It also asks to find the volume using 2 iterated integrals with different orders of x and y integration. Homework Equations The Attempt at a Solution I found...