Question:A ladder of length 5 m rests with its foot on horizontal ground and leans against a vertical wall. If the inclination of the ladder to the horizontal is `47^@` , find the distance of the foot of the ladder from the wall. 

If x meters, is the distance of the foot of the ladder from the wall.

cos `47^@` = `x/7`
`:.`    x = 5 cos `47^@`
          = `5 xx 0.6820`
          = 3.410
          = 3.41 (correct to 3 sig. fig.).
The foot of the ladder is 3.41 m from the wall.

Question:Divide `2x^2` + 7x + 6 by x+2 

x + 2)`2x^2` + 7x+6( 2x + 3
      `2x^2` + 4x
       ------------
              3x + 6
              3x + 6
             ----------
                 0

The quotient is 2x + 3

Question:Divide `4x^4` - `3x^3` +  `2x^2` -5x +6 by `x^2` - 3x - 1 

`x^2` - 3x - 1 ) `4x^4` -  `3x^3` + `2x^2` - 5x + 6 ( `4x^2` + 9x + 33
                       `4x^4` - `12x^3` -  `4x^2` 
                       ---------------------------------
                                    `9x^3` +  `6x^2` - 5x
                                    `9x^3` - `27x^2` - 9x
                                    -----------------------------
                                                  `33x^2` + 4x +   6
                                                  `33x^2` - 99x - 33
                                                  ---------------------
                                                               103x + 39 

The quotient is `4x^2` + 9x + 33; the reminder is 103x + 39.

Question:Divide `x^3` + 8 by x + 2. 

 `x^2` - 2x + 4
x + 2 ) `x^3`             + 8(
          `x^3` + 2`x^2`
           -----------------
                     - 2`x^2`
                     - 2`x^2` - 4x
                    -----------------
                                     4x + 8
                                     4x + 8
                                     --------

The quotient is `x^2` - 2x + 4.

Question:Define Parallelogram. 

A parallelogram is a quadrilateral with its opposite sides parallel.

\\begin{graph}

width=200;
line((-2,3),(3,3))
line((3,3),(2,-3))
line((-3,-3),(2,-3))
line((-3,-3),(-2,3))

\\end{graph}Properties(1) Both pairs of opposite sides are equal.(2) A diagonal bisect the area of a parallelogram.(3) Both pairs of opposite angles are equal.(4) The diagonals bisect each other.Theorem: The opposite sides of a parallelogram are equal; the opposite angles are equal; the opposite angles are equal; and a diagonal bisects the parallelogram.Theorem: The diagonals of a parallelogram bisect each other.Theorem: If the opposite sides of a quadrilateral are equal are equal, then the quadrilateral must be a parallelogram.Theorem: If the opposite angles of a quadrilateral are equal are equal, then the quadrilateral must be a parallelogram.Theorem: If the diagonals of a quadrilateral bisect each other,then the quadrilateral must be a parallelogram. Theorem: If one pair of opposite sides of a quadrilateral are equal are parallel, then the  other sides must be equal and parallel and the quadrilateral must be a parallelogram.

Question:What is Circle? 

A circle is the path traces out by point which moves in a plane so that it is always the same distance from a fixed point in that plane.
The fixed point is called the center of the circle and the distance of the point from the center of the circle is called the radius.
If the point could move anywhere in space and where not obliged to lie in a plane, it would trace out a sphere.

Question:Define diameter, chord, circumference, arc. 

Diameter: A diameter of a circle is a line through its center terminated at  each end by the circumference of the circle.  chord: A chord of a circle is a line joining any two points  on the circle.circumference: The circumference of a circle is the distance round the circle .Arc: An arc of a circle is a circle is part of the circumference. A major arc is an arc greater then half the circumference. A minor arc is an arc less than half the circumference.

Question:Find the circumference of a circle of radius  5 cm. 

C = 2`pi` r=2`pi xx`5 cm=10`pi`cm
                                        =31.42 cm
                                        =31.4 cm  (to 3 sig. fig)

Question:Taking `pi` to be `22/7`, find the radius of a circle whose circumference is 44 cm. 

C = 2`pi`r 

`:.` r = `C/(2pi)`

         = `44/(2 xx 22/7)`

         = 7.

The radius of the circle is 7 cm.

Question:Find the area of a circle of radius 7 cm. Take `pi` to be `22/7` . 

A = `pi r^2`

   = `22/7 xx (7)^2 cm^2`

   = 22 `xx 7 cm^2`

   = 154 `cm^2`