### Work Done by Force Field Along a Helix

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The solution is attached below in **two** Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.
There are **two** ways to do this.

Mathematics / Calculus and Analysis » 37493

P-value and standard deviation
The average mpg usage for a 2004 Ford Expedition 2WD for a sample of 10 **tanks** of gas was 17.0 with the standard deviation of 0.8.

Statistics / Hypothesis Testing / Parametric Tests / Student's t-Test » 181528

Pressurized **tanks** are expensive, hard to maintain safely, and difficult to access. Thus, it cannot be stored like gasoline in underground **tanks** at refueling stations.

Earth Sciences / Environmental Studies / Energy and the Environment » 95940

28506 Laplace equation in **cylindrical** coordinates Laplace equation in **cylindrical** coordinates Hi there!
The solution is attached both in Word format and in pdf format (the last one for the benefit of the solution library).

Mathematics / Calculus and Analysis » 28506

(3) The thermometer with the **cylindrical** bulb will respond quickly because, the area of the **cylindrical** surface is greater than that of the spherical bulb, and the mercury in the bulb reaches the temperature of the surrounding faster.

Physics / Heat & Thermodynamics » 7553

150486 **Two** problems on capacitors **Two** problems on capacitors
Solution
1.

Physics / Electricity & Magnetism / Elements / Capacitors » 150486

The solution is attached below in **two** files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

Physics / Electricity & Magnetism / Electric & Magnetic Fields / Gauss' Law » 509360

The volume charge density on the inner solid **cylindrical** wire is = ks2.
Consider a **cylindrical** sell of radius s and infinitesimally small thickness ds.

Physics / Light, Vision & Optics / Intensity / Photometry / Flux & Flux Density » 224378

Now the equation for the paraboloid in **cylindrical** coordinates is
z = rho^2
so we have
tan(psi(rho)) = dz/drho = 2 rho
whence
sec(psi(rho)) = sqrt(1 + tan^2(psi(rho))) = sqrt(1 + 4 rho^2).

Mathematics / Calculus and Analysis / Real Analysis / Integrals » 427446

Hence, the volume of the **cylindrical** shell is:
dV=2πy[xmax −f(y)]dy
￼￼￼
And all that is left is to integrate between the **two** extreme values of y:
y = x3 ⇒ x = f (y)= y^1/3
ymax =8 ⇒ xmax =2 ymin =0
See attachment for rest of solution.

Mathematics / Calculus and Analysis / Real Analysis / Integrals » 99177