Maths Questions Help!!! (1 Viewer)

[coolboy234]

howdy, im a new mem at BOS (YAY!), and just hoping you could assist me with some maths problems, here they are!:

1. A regular octagon has an area of 500 cm squared. How long to the nearest centimetre is one side of the octagon?

2. Ricky is on an island looking for some treasure. He starts at point X by the palm tree and walks 150m in a direction of 230 degrees north to point Y. He then walks 80m in a direction of 140 degrees north to point Z. At point Z he digs and finds the treasure.
How far in metres is point Z from point X?
(I added the colour to make it more visually exciting, though it may not be.)
http://community.boredofstudies.org/attachment.php?attachmentid=16757&stc=1&d=1216637673

3. A water cooler has cone-shaped paper drinking cups. The volume of a cone can be found using this formula: V = (Pi x radius squared x height) divided by 3
Anton pours water into a cup until it contains water to half of its volume.
What is the depth of the water, to the nearest millimetre, in the cup?
http://community.boredofstudies.org/attachment.php?attachmentid=16758&stc=1&d=1216635986

4. A car follows another car along a straight stretch of an open highway at 100 kilometres per hour. The cars are 150m apart. The cars approach a town. When each car reaches the town it slows down at the same rate to 30 kilometres per hour. Both cars travel through the town at 30 kilometres per hour.
How far apart will the cars be when they are both travelling at 30 kilometres per hour?

btw, soz bout the diagrams, i dont have flash 8 or a good scanner

 

[conics2008]

1) 500/2(1+root2) = x^2 hence each side is equal x= 10root5/root (2(1+root2))
2) use pyth root of 150^2+80^2 = distance from x to z ( you get 90 at y )
3) no measurments.

 

[Undermyskin]

1. 10cm?
2. 126.89 m?
3. 119mm?

 

[coolboy234]

1) 500/2(1+root2) = x^2 hence each side is equal x= 10root5/root (2(1+root2))
2) use pyth root of 150^2+80^2 = distance from x to z ( you get 90 at y )
3) no measurments.

there is a measurement, it is the diagram of the cone.










coolboy234

 

[coolboy234]

anyways, thanks undermyskin and conics for the 1st three questions, i'll check answers and solutions later, good luck for the fourth one =)














coolboy234

 

[bored of sc]

1) Area of equal isosceles triangle when octagon is divided into 8 congruent triangles = 500/8 = 62.5cm²

Area of angle of triangle taken from middle of octagon = 360/8 = 45^o

Other angles are equal so through area of triangle angles end up being = 67.5^o ((180-45)/2)

So since area of triangle = 62.5cm² you can use the area of triangle formula of Area = 1/2 ab sinC

But since the triangle is isosceles a = b.

So substituting in values you get:

62.5 = 1/2 a² sin 45

125 = a² sin 45

a² = 125/sin 45 = 176.7766...

a = root (176.7766...)

a = 13.3 (to 1.d.p)

Now since you have the two equal sides of the isosceles triangle as 13.3 you can use the sin rule to find the other side.

x/sin45 = 13.3/sin67.5

x = 13.3 sin45/sin67.5

x = 10.1793
= 10cm (to nearest cm)