Question

Find the center of the sphere x^2 + y^2 + z^2 = 6x + 4y + 10z.

a) (-3,2,5)

b) Other answer

c) (3,2,5)

d) (3,-2,5)

e) (3,2,-5)

Answer #1

Complete the square to write the equation of the
sphere in standard form.
x^2+y^2+z^2+5x-2y+10z+21=0
Find the center and radius

X'= 6x-5y+e^5t
Y'= x+4y
Find the general solution using undetermined coefficients

Find the solution to the linear system of differential
equations
{x′ = 6x + 4y
{y′=−2x
satisfying the initial conditions x(0)=−5 and
y(0)=−4.
x(t) = _____
y(t) = _____

evaluate the double integral where f(x,y) = 6x^3*y - 4y^2 and D
is the region bounded by the curve y = -x^2 and the line x + y =
-2

For f(x,y,z) = sqrt(35-x^2-4y^2-2z) 1. Find the gradient of
f(x,y,z) 2. Evaluate delta f(x,y,z) 3. Find the unit vectors U+ and
U- , that give the direction of steepest ascent and the steepest
descent respectively.

Let F ( x , y , z ) =< e^z sin( y ) + 3x , e^x cos( z ) + 4y
, cos( x y ) + 5z >, and let S1 be the sphere x^2 + y^2 + z^2 =
4 oriented outwards Find the flux integral ∬ S1 (F) * dS. You may
with to use the Divergence Theorem.

find the volume between the cone z=sqrt(x^2+y^2) and the sphere
x^2+y^2+z^2=2az, if a=1

If z=(x+4y)ex+y,x=ln(u),y=v,z=(x+4y)ex+y,x=ln(u),y=v, find
∂z∂u∂z∂u and ∂z∂v∂z∂v. The variables are restricted to domains on
which the functions are defined.

Find the absolute maximum and minimum of the function
f(x,y,z)=x^2 −2x+y^2 −4y+z^2 +4z
on the ball of radius 4 centered at the origin (i.e., x^2 + y^2
+ z^2 ≤ 16). Lay out your work neatly and clearly show your
procedure.

differential equations solve
(2xy+6x)dx+(x^2+4y^3)dy, y(0)=1

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