C

The iron support has the shape of the right triangle $ABC$ with the side $AB$ of the length $30\mathrm{cm}$ and the hypotenuse $AC$ of the length $50\mathrm{cm}$ (see the picture). The maximal allowed force $F_1$ on $AB$ is $270\mathrm{N}$. Find the maximal force $G$ allowed at the point $A$. Hint: The load $G$ at the point $A$ can be decomposed to the direction of the hypotenuse and the other side of the triangle as shown in the picture.

A pendulum constituted of a rope of the length $l$ and a body is displaced from it's equilibrium. The force due to gravity on the body $F_g=20\mathrm{N}$. The body is higher by $h=10\mathrm{cm}$ in the displaced position (comparing to the equilibrium position). The tension in the rope in the displaced position is $F_1=12\mathrm{N}$. Find the length of the rope $l$. Hint: Using a parallelogram, the force of gravity on the body can be decomposed into a force $F_1$ in the direction of the rope and $F_2$ in the perpendicular direction.

Divide the following two polynomials using long division. $$(6x^2-5x-6):(2x-3)$$

Divide the following two polynomials using long division. $$(4x^2-10x-1):(x-2)$$