Thank you for your time, I'll try to add as much relevant detail to my question as I can (and finally state the given equation correctly). It is ##3x^3-45x^2+243x-525=0##, making ##a=3##, ##b=-45##, ##c=243##, ##d=-525##. I quadruple-checked this time!
The method we were taught was to take an...
Oh geez, that's my fault. The original equation is ##3x^3-75x^2+243x-525=0##. I gave one half with the 3 factored out and one half without the 3 factored out...
Homework Statement
Use Cardano's formula to find a real root for ##3x^3-45x^2+243x-525=0##. [Edited to correct mistake]
Homework Equations
$$x = u - \frac{b}{3a}$$
Depressed cubic: $$u^3=3pu+2q$$
Cardano's formula: $$u=\sqrt[3]{q+\sqrt{q^2-p^3}}+\sqrt[3]{q-\sqrt{q^2-p^3}}$$
The Attempt at a...
Homework Statement
When a rocket launches, it burns fuel at a constant rate of (kg/s) as it accelerates, maintaining a constant thrust of T. The weight of the rocket, including fuel is 1200 kg (including 900 kg of fuel). So, the mass of the rocket changes as it accelerates:
m(t) = 1200 - m_ft...
Homework Statement
Find the coordinates of each member of set S relative to B.
B = {1, cos(x), cos2(x), cos3(x), cos4(x), cos5(x)}
S = {1, cos(x), cos(2x), cos(3x), cos(4x), cos(5x)}
I am to do this using Mathematica software. Each spanning equation will need to be sampled at six separate...