a) Does the relation "is less than" have a transitive property b)\angle3 is acute while\angle4 is obtuse. State an inequality involving the measure of\angle3 and\angle4. c) Where points M and N are midpoints of AB and CD, respectively it is given that AM\congCN... State a conclusion regarding AB and CD.

If $1\le \alpha$ show show that the gamma density has a maximum at $\frac{\alpha -1}{\lambda }$.
So using this form of the gamma density function:
$g(t)=\frac{{\lambda }^{\alpha }{t}^{\alpha -1}{e}^{-\lambda t}}{{\int }_0^{\mathrm{\infty }}{t}^{\alpha -1}{e}^{-t}dt}$
I would like to maximize this. Now i was thinking of trying to differentiate with respect to t, but that is becoming an issue because if i remember correctly the denominator is not a close form when the bound goes to infiniti

Restriction Of Parametric Functions Domain
The problem I am working on is, "Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter."
$x=\sec \theta \text{ and }y=\cos \theta$
In the answer key, $0\le \theta <\pi /2$ and $\pi /2<\theta \le \pi$. What about the angle on the unit circle that are in the third and fourth quadrant?
Also, in the answer key, $|x|\ge 1$ and $|y|\le 1$. Why are x and y restricted in such a way?

Graph the sets of points whose polar coordinates satisfy the equations and inequalities ${\displaystyle 1\le r\le 2}$

Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor is necessary:
${\displaystyle 3m^3+12m^2+9m}$

Evaluate $\int \frac{4}{9}e^{6x}\tan (e^{6x}+4)\sec (e^{6x}+4)dx$.

Find all rational zeros of the polynomial, and write the polynomial in factored form.
${\displaystyle P\left(x\right)=2x^3-3x^2-2x+3}$