\frac{\mathbb{F}_2[X,Y]}{(Y^2 + Y + 1,X^2 + X + Y )}

Fitting a ballistic trajectory to noisy data where both spacial and temporal domains observations are noisy
Fitting a curve to noisy data is somewhat trivial. However it generally assumes that data abscissa is fixed, and the error is computed on the ordinate.
In my setup, I have 3D spacial observations of ballistic trajectories (that I model with a simple parabola), but the observations time are also noisy.
Therefore, I have to estimate the initial position ${\displaystyle y_0,y_0,z_0}$ and initial speed ${\displaystyle v_{x_0},v_{y_0},v_{z_0}}$, based on 4D (noisy) observations ${\displaystyle (X_i,Y_i,Z_i,T_i),i\in [0,N]}$, such that they fit the following model:
$\{\begin{array}{rl}x\left(t\right)& =x_0+v_{x_0}t\\ y\left(t\right)& =y_0+v_{y_0}t\\ z\left(t\right)& =z_0+v_{z_0}t-\frac{g}{2}{t}^2\end{array}$
with t monotonically increasing with i.
I'm not sure how to formulate such optimization problem because I have 6 parameters to estimate, but also 4N variables with only 3N equations… My intuition tells me there's only one single parabola that minimizes the error (MSE for example), but I can't formulate the problem.

Determine whether g(x)= x lxl is even or odd or neither function.

Let a and b be coprime integers, and let m be an integer such that a | m and b | m. Prove that ab | m

. The average credit card debt for a recent year was $9205. Five years earlier the average credit card debt was $6618. Assume sample sizes of 35 were used and the population standard deviations of both samples were $1928. Find the 95% confidence interval of the difference in means

say if this statement is true or false with justification

$\forall x \in \mathrm{ℝ}, x<2 \Rightarrow x^2<4$