Homework Statement
find all complex roots of z^8=81i
Homework Equations
The Attempt at a Solution
let the angle=x
z^8=r^8(cis8x)
we know
81i=81 (cis pi/2)
threfore
z^8=81(cos pi/2 + i sin (pi/2) )
8x= pi/2 + 2kpi
x = pi/16 + kpi/4 kEz
therefore...
Homework Statement
Determine if the congruence has solutions. If it does, determine the complete solution
x^11 + 3x^10 + 5x ≡ 2 (mod 11)
Homework Equations
The Attempt at a Solution
i know that 11 | x^11 + 3x^10 + 5x -2
and where ax≡c (mod m) has a solutioon iff...
Homework Statement
conssider the system of equations
a + b = 2m^2
b+c=6m
a+c =2
Determine all real values of m for whcih a<=b<=c
Homework Equations
The Attempt at a Solution
tried subtracting the equations
got a-c = -4m
a= -6m +2
i have no idea what I am trying...
This is a question pertaining to a lab we did. Ill try to describe it the best i can. What we pratically did was attach a rubber stopper to an end of a string, put the string to a hollow tube (like a torn apart pen), and tied a mass on the bottom. We had to hold on the tube and start swinging...
Homework Statement
I need to express V in terms of Z and A.
i know
V= (3/5)Y + (2/5)Z
given
y=2A-3X
X=(1/6)Z + (5/6)Y
Homework Equations
The Attempt at a Solution
ok. my first attempt was to isolate y in the second equation, and let the two equations equal...
Find the coordinates of the point on the curve f(x)=3x^2-4x, where the tangent is parallel to the line y=8x.
Ok i know the slope of the tangent is 8.
and i know the formula is m=[f(a+h)-f(a)]/h
i need a hint please
Limit question
Find the coordinates of the point on the curve f(x)=3x^2-4x, where the tangent is parallel to the line y=8x.
Ok i know the slope of the tangent is 8.
and i know the formula is m=[f(a+h)-f(a)]/h
i need a hint please
The question states
Rationalize each of the following numerators to obtain and equivalent expression.
(sqroot(h^2+5h+4) -2 ) / h
How do i rationalize the numerator here.
I don't remember
thanks