Question

For the circles x^{2} + y^{2} = 9 and (x -
1)^{2} + (y + 1)^{2} = 1, find an equation for the
radical axis.

Answer #1

a ) How many lines are tangent to both of the
circles?
x2 + y2 = 4
and
x2 + (y − 3)2 = 1?
b) At what points do these tangent lines touch the circles?
(Enter your answers from smallest to largest
x-value.)

How many lines are tangent to both of the circles
x2 + y2 = 4
and
x2 + (y − 3)2 = 1
At what points do these tangent lines touch the circles? (Enter
your answers from smallest to largest x-value.)

draw the solid bounded above z=9/2-x2-y2
and bounded below x+y+z=1. Find the volume of this
solid.

Sketch the central field F = (x /(x2 +
y2)1/2)i + (y /(x2 +
y2)1/2) j and the curve C consisting of the
parabola y = 2 − x2 from (−1, 1) to (1, 1) to determine
whether you expect the work done by F on a particle moving along C
to be positive, null, or negative. Then compute the line integral
corresponding to the work.

Evaluate the double integral ∬Ry2x2+y2dA, where R is the region
that lies between the circles x2+y2=9 and x2+y2=64, by changing to
polar coordinates .

Given z = (3x)/((x2+y2)1/2) ,
Find ∂z/∂x and ∂z/∂y.

Solve the differential equation : 4 x y y' = y2 + x2
with initial condition y(1)=1

Let F(x, y,
z) = z
tan−1(y2)i
+ z3
ln(x2 + 9)j +
zk. Find the flux of
F across S, the part of the paraboloid
x2 + y2 +
z = 7 that lies above the plane
z = 3 and is oriented upward.

A lamina occupies the first quadrant of the unit disk
(x2+y2≤1x2+y2≤1, x,y≥1x,y≥1). It's density function is
ρ(x,y)=xρ(x,y)=x. Find the center of mass of the lamina.

Find the absolute maximum value and the absolute minimum value
of the function f(x,y)=(1+x2)(1−y2) on the disk
D={(x,y) | x2+y2⩽1}

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