Let T be the triangular region with vertices (1,0,0)(1,0,0),
(0,1,0)(0,1,0), and (0,0,1)(0,0,1) oriented with upward-pointing
normal...
Let T be the triangular region with vertices (1,0,0)(1,0,0),
(0,1,0)(0,1,0), and (0,0,1)(0,0,1) oriented with upward-pointing
normal vector.
A fluid flows with constant velocity field v=4i+6j m/sv=4i+6j
m/s. Calculate:
(a) The flow rate through T
(b) The flow rate through the projection of T
onto the xyxy-plane [the triangle with vertices (0,0,0)(0,0,0),
(1,0,0)(1,0,0), and (0,1,0)(0,1,0)]
Assume distances are in meters.
(a) ∬Sv⋅dS=∬Sv⋅dS=
(b) ∬Sv⋅dS
Find the mass of the triangular region with vertices (0, 0), (1,
0), and (0, 5),...
Find the mass of the triangular region with vertices (0, 0), (1,
0), and (0, 5), with density function ρ(x,y)=x2+y2
Find the mass of the triangular region with vertices (0, 0), (3,
0), and (0, 5),...
Find the mass of the triangular region with vertices (0, 0), (3,
0), and (0, 5), with density function (x,y)=x^2+y^2.
Find the absolute maximum and minimum values of
f(x,y)=2x^2+y^2-xy^2 on the triangular region shown with vertices...
Find the absolute maximum and minimum values of
f(x,y)=2x^2+y^2-xy^2 on the triangular region shown with vertices
(0,0), (0,4) and (4,4).
Find the absolute maximum value of the function
f(x,y)=x2-4xy+y3+4y on the triangular region
with vertices (-1,-1),...
Find the absolute maximum value of the function
f(x,y)=x2-4xy+y3+4y on the triangular region
with vertices (-1,-1), (7,-1) and (7,7).
2. Volume
(a) Compute volume of the solid whose base is a triangular
region with vertices...
2. Volume
(a) Compute volume of the solid whose base is a triangular
region with vertices (0,0), (1,0), and (0,1), and whose
cross-sections taken perpendicular to the y -axis are equilateral
triangles.
(b) Compute the volume of the solid formed by rotating the
region between the curves x=(y-3)^2 and x = 4 about the line y
=1
Integrate the function f over the given region
f(x,y) =xy over the triangular region with vertices...
Integrate the function f over the given region
f(x,y) =xy over the triangular region with vertices (0,0) (6,0)
and(0,9)
A thin plate covers the triangular region of the xy-plane with
vertices (0,0), (1,1), and (−1,1)....
A thin plate covers the triangular region of the xy-plane with
vertices (0,0), (1,1), and (−1,1). (Coordinates measured in
cm.)
(a) Find the mass of the plate if its density at (x,y) is
sin(y^2) kg/cm^2 .
(b) Find the mass of the plate if its density at (x,y) is
sin(x^2) kg/cm^2 .
Find the absolute maximum and minimum values of f(x,y)=4xy+x^2
on the triangular region D in the...
Find the absolute maximum and minimum values of f(x,y)=4xy+x^2
on the triangular region D in the xy plane with the vertices (4,0)
(0,3) and (2,4)
Find the absolute minimum and absolute maximum of
f(x,y)=10−3x+8y
on the closed triangular region with vertices...
Find the absolute minimum and absolute maximum of
f(x,y)=10−3x+8y
on the closed triangular region with vertices (0,0),(8,0) and
(8,12).
List the minimum/maximum values as well as the point(s) at which
they occur. If a min or max occurs at multiple points separate the
points with commas.