How do I do these maths equations?

You don't have to answer them all but if you can it'd be a great help!

1. Rationalise the denominator of

18

--------------------

square root 3

and simplify your answer.

2. Some plasticine is used to make a solid cylinder of base radius r cm and height h cm.

The plasticine is then split in half and used to make two identical cones.

Each cone has base radius 2r cm and height H cm.

Explain H in terms of h. Give your answer in it's simplest form.

3. A rectangle measures (x-1) cm by (x+1) cm.

The diagonals of the rectangle are each 10cm long.

Find the area of the rectangle.

Finally, 4: Show that x^2 - 8x + 19 can be written in the form (x+a)^2 +b for all values of x. State the value of a and the value of b.

Thanks in advance!

3 Answers

Relevance
  • ?
    Lv 7
    9 years ago
    Favorite Answer

    1.

    18/√3

    = 18√3 / (√3√3)

    = 18√3/3

    = 6√3

    --------------------

    2.

    Volume of cylinder = π r² h

    Volume of 2 cones = Volume of 1 cylinder

    2 * 1/3 π (2r)² H = π r² h

    2/3 π * 4r² H = π r² h

    8/3 π r² H = π r² h

    8/3 H = h

    H = 3/8 h

    --------------------

    3.

    Using Pythagorean theorem, we get:

    (x−1)² + (x+1)² = 10²

    x² − 2x + 1 + x² + 2x + 1 = 100

    2x² + 2 = 100

    2x² = 98

    x² = 49

    x = 7

    Area = (x−1) cm * (x+1) cm

    . . . . = 6 cm * 8 cm

    . . . . = 48 cm²

    --------------------

    4.

    x² − 8x + 19

    = (x² − 8x + 16) − 16 + 19

    = (x − 4)² + 3

    a = −4, b = 3

    Mαthmφm

  • 9 years ago

    1. 18/ r3 where r stands for root.

    18 r3

    ---- * ---

    r3 r3

    you end up with,

    18 * r3

    ---------

    3

    => 18 *r3

    -------

    3

    => 6 r3

    i.e 6 root 3 is your answer.

    3.Area of the rectangle is l*b.

    they have given the diagonal which forms a right angle triangle whose hypotenuse length is 10cm.

    so, (x+1)2+(x-1)2=102.

    I hope you can simply further. By finding x. you can find length and breadth.

  • Anonymous
    9 years ago

    Q1 times both sides by square root three so you end up with

    8 square root three

    ------

    3

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