Recent content by jamesdocherty

Homework Statement Homework Equations Laplace Trasformations The Attempt at a Solution a. done b. f(t)= t -3*t*u(t-1) + 4*u(t-1) -3*u(t-2) -2*t*(t-2) c. 1/(s^2) - (3e^-s -2e^-2s)/(s^3) + (4e^-s -3e^-2s)/s d. 1/(s-1) * (1/(s^2) - (3e^-s -2e^-2s)/(s^3) + (4e^-s -3e^-2s)/s) These are the...

Homework Statement Let R be the solid region that is bounded by two spheres x^2 + y^2 + z^2=1 and x^2 + y^2 + z^2=2. Determine the moment of inertia of R around the x-axis if the mass density per unit volume of R is u=sqrt(x^2 + y^2 + z^2). Homework Equations Moment of Inertia around the...

yeah that makes sense, thanks for that, because of that i would only need to integrate once then and hence got x=3cost and y=3sint where -pi/2<t<2pi and then the integral: 9cos^2(theta) + 12sin(theta) dt where -pi/2<t<2pi and solving this would get you 45pi/4 -12, would this be correct or would...

i'm not sure to be honest i thought it would be a two-dimensional object as it would have both a x and y direction but i am probably wrong, if it is a one dimensional object, how would i go about solving this problem?, would it just be x=3cost and y=3sint where -pi/2<t<2pi and hence you would...

Homework Statement Let the path C traverse part of the circle or radius 3 at the origin, in a clockwise direction, from (0,-3) to (3,0). Calculate the total mass of a wire in shape C, if the mass density of the wire is u=x^2+4y Homework Equations mass of plate equation= double integral u(x,y)...

the answer in the question booklet is pi*sinh(2)/4 not pi*sinh(2)/4sqrt(15), do u think there could be an error in the question booklet?

Homework Statement evaluate the double integral of cosh(6x^2+10y^2) dxdy by making the change of variables x=rcos(theta)/sqrt(3) and y=rsin(theta)/sqrt(5) let D be the region enclosed by the ellipse 3x^2+5y^2=1 and the line x=0 where x>0. Homework EquationsThe Attempt at a Solution first I...

Hi, as the compressive strength of concrete formula is max load applied/ surface area, could you say that the compressive strength of concrete is inversely proportional to it's surface area or this would make no sense as the concrete with a smaller surface would have a smaller max load anyway...

thanks for the reply, doing that i got: ∇f(r)=(x/√(x^2+y^2+z^2),y/√(x^2+y^2+z^2),z/√(x^2+y^2+z^2)) but i am still confused as to prove ∇f=df/drR⃗, what is df/dr is that the f(r) function being derived in terms of r (the length) and then i have to multiply it by R vector. Thanks again...

Homework Statement let r (vector) =xi+yj+zk and r=sqrt(x^2+y^2+z^2), let f(r) be a C2 scalar function. 1. Prove that ∇f = dr/df * vector r 2. Using part 1, calculate ∇ cosh(r^5), check answer by direct calculation 3. Using Vector Identities, calculate ∇ X (cosh(r^5)*∇f...

hi, for a task at school i have to design a pump and water storage system that will be able to work with a wind turbine to supply water from a well to a small community of about 2000 people. i am having some trouble finding information regarding these topics: -flow rate of pump -power of...

hi, for a task at school i have to design a pump and water storage system that will be able to work with a wind turbine to supply water from a well to a small community of about 2000 people. i am having some trouble finding information regarding these topics: -flow rate of pump -power of...