# 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

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square root 3

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.

Relevance

1.

18/√3

= 18√3 / (√3√3)

= 18√3/3

= 6√3

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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

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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

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4.

x² − 8x + 19

= (x² − 8x + 16) − 16 + 19

= (x − 4)² + 3

a = −4, b = 3

Mαthmφm

• 1. 18/ r3 where r stands for root.

18 r3

---- * ---

r3 r3

you end up with,

18 * r3

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3

=> 18 *r3

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3

=> 6 r3

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

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3