Any Clever People can help with any of these problems?

Question

1. Convert into cartesian form

r(1 + sinANGLE) = a



2. Find the equation of the plane through the point (2,1,3) which is normal to the vector n = 2i +5j - 3k.



3. Find dy/dx at point x = π, y = π/2 where x and y are related through the equation

sin ( x + 2y ) + x^3 - 4x(y^2)


Any help on any questions would be appreciated, im a bit stuck.

Oh yeah the 3rd one is

sin ( x + 2y ) + x^3 - 4x(y^2)=0

cheers

Answer 1

whew this ones tough buddy. thats why im a film production major. =)

Answer 2

1) note that x = rcos Angle, y = r sin Angle
and that sin ( a ) = cos ( a + pi/2 )

2)the outer product of n and unknown normal = 0 solve that,
and then v = (2,1,3) + kunknown normal

3) rubish theis is not an equation but an expression
so this one is unsolvable with info given

Answer 3

The third looks like fun to me, except that you left off the = sign and it is not an equation. It will be, once you have decided where the = sign goes, a problem involving implicit differentiation.

Answer 4

1: x=rcos(A)
y=rsin(A)
r=Sqrt(x^2+y^2)
r+rsin(A)=a

r+y=a
y=a-r
y=a-Sqrt(x^2+y^2)
a-y=Sqrt(x^2+y^2)
a^2-2ay-y^2=x^2+y^2
a^2-2ay-2y^2=x^2
x=Sqrt[a^2-2ay-2y^2]

2)The general form of a plane is:
a(x-x0)+b(y-y0)+c(z-z0)=0
so: 2(x-2)+5(y-1)-3(z-3)=0

3) This is not an equation.