1) Convert the point (x,y,z)=(−2,−3,−1) to cylindrical
coordinates. Give answers as positive values, either as
expressions, or decimals to one decimal place.
(r,θ,z) =
2) Convert the point (x,y,z)= (3,−2,−3) to spherical
coordinates. Give answers as positive values, either as
expressions, or decimals to one decimal place.
(ρ,θ,ϕ)=
3) Convert the equation ρ = 3 to rectangular coordinates and
write in standard form.
1.) Convert the following from rectangular coordinates to
cylindrical coordinates. Write your angles in degrees rounded to
one decimal point
(3, -7, 4)
2.) Convert the following from rectangular coordinates to
spherical coordinates. Write your angles in degrees rounded to one
decimal point
(3, -7, 4)
3.) Convert the following from cylindrical to rectangular
coordinates. Round your answer to one decimal place.
(3, 20o, -4)
4.) Convert the following from sphereical to rectangular
coordinates. Round your answer to one decimal...
Use spherical coordinates to find the volume of solid within the
sphere x^2 + y^2 + z^2 = 16 and above the cone 3z^2 = x^2 + y^2 and
lying in the 1st octant.
Use spherical coordinates to evaluate the triple integral
∭e^−(x^2+y^2+z^2)/(x^2 + y^2 + z^2) dV , Where E is the region
bounded by the spheres x^2 + y^2 + z^2 = 4 and x^2 + y^2 + z^2 =
9
Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are
all real numbers
(a) Derive an equation for a line tangent to both of these
parabolas (show all steps with a proof, assuming that such
a line exists)
(b) Assume that the doubly-tangent line has an equation y+Ax+B.
Find an example of values of a,b,c (other than the ones given here)
such that A,B ∈ Z
2. Use the equation of
exchange (Ms x V = P x Y) to answer the
following:
15 pts
If Ms rises what would the Keynesians say will happen, all other
things equal?
If the government cuts taxes to promote spending what would the
Keynesians say would happen, all other things equal?
If Y starts to fall then what would the Keynesians say would
happen, all other things equal?
3. Equilibrium
GDP is $5000 while full employment is $6000.
...
in C++
Write a definition for a class ‘point’ to describe a point with
coordinates (X,Y) in 2-D space. The private data members are the
coordinates X and Y of type ‘double’. The public member functions
are:
A default constructor (no parameters) to initialize X and Y to
zero.
An explicit value constructor with two parameters to initialize
the values of X and Y.
Two functions, one to set the X value and the other to set the
Y value...
a)
Let y be the solution of the equation y ′ =
(y/x)+1+(y^2/x^2) satisfying the condition y ( 1 ) = 0.
Find the value of the function f ( x ) = (y ( x ))/x
at x = e^(pi/4) .
b)
Let y be the solution of the equation y ′ = (y/x) −
(y^2/x^2) satisfying the condition y ( 1 ) = 1. Find the
value of the function f ( x ) = x/(y(x))
at x = e .
c)
Let y be the solution...
1-Use the (x,y) coordinates in the figure to find the value of
the trigonometric function at the indicated real number, t, or
state that the expression is undefined.
SIN 11π/6
2-Use the (x,y) coordinates in the figure to find the value of
the trigonometric function at the indicated real number, t, or
state that the expression is undefined.
COS π//6
3- Use the (x,y) coordinates in the figure to find the value of
tan 4π/3
or state that the expression...