Trace the curve of x^3 - 6x^2 +11x - y = 6

What is geometry?

Solve for x

In the diagram below, a circle with centre O is given with diameter AB. The coordinates of A and B are (4 ; 4) and (2 ; -6) respectively. ya A(4; 4) B(2; -6)
a) Determine the coordinates of O, the centre of the circle.
b) Calculate the length of the radius of the circle.
c) Write down the equation of the circle in form:
${\displaystyle {(x-a)}^2+{(y-b)}^2=r^2}$
d) Write down the equation of the circle in form:
${\displaystyle a{x}^2+bx+c{y}^2+dy+e=0}$

Can a rectangle be a rhombus?

Given:
${\displaystyle \theta ={240}^{\circ }}$
Find the value of ${\displaystyle \theta }$ in radians (in terms of ${\displaystyle \pi }$)

The vertices of a tetrahedron correspond to four alternating corners of a cube. By using analytical geometry, demonstrate that the angle made by connecting two of the vertices to a point at the center of the cube is ${\displaystyle {109.5}^{\circ }}$, the characteristic angle for tetrahedral molecules.

A cylindrical hole of radius xis bored through a shere of radius R in such a way that the axis of the hole passes throiugh the centerof the sphere. Find the value of x that maximizes the complete surface area of the remaining solid. Hint: The area of a segment of height h on a shere of radius R is $2\pi Rh$