hielly's maths thread

[Flaming_Arrow]

lol thanks, when i was typing it up i figured how to do it, and then i deleted my post but you were too quick you solved it already

[Hielly]

Swifts Creek Soccer Team has played 54 matches over the past three seasons. They have
drawn one third of their games and won twice as many games as they have lost. How many
games have they lost?

drawn one third of their games-
 1/3 *54 = 18
so they drawed 18 games.

won twice as many games as they have lost-
umm 2x=36 (54-18)

help ..thanks

[Flaming_Arrow]

lost 1/3 = 18 games

so 36 games they either lost or won

it says they won twice as many games as they lost

2x+x = 36
x = 12

so they lost 12 games

[Hielly]

Temperatures of Fahrenheit (F ) can be converted to
Celsius (C) by the formula
C =5/9(F − 32)
Find the temperature which has the same numerical value in both scales.

i dont get when it says 'the same numerical value in both scales'
thanks

[Flaming_Arrow]

let F= C

[Flaming_Arrow]

im not sure about the circle one ill let someone else have a crack at that

[TrueTears]

I think i got the circle gimme a sec...

[TrueTears]

ok this question might seem weird at first glance but it's quite easy once you get the logic behind it.

Let the radius of the smallest circle be r

so we know the total area of the largest circle is =

Just consider you're splitting the largest circle into 3 equal parts, (don't even worry about what the shape of the area that you're working out, because all you need is 3 equal parts in that larger circle right?). So this yields

HOWEVER, we know that one of the equal parts is coincidentally the area of the smallest circle, this yields

Now solve for r gives you or -. But obviously you can't have a negative radius so answer is

[TrueTears]

Basically, the larger circle is split into 3 equal parts, 2 of the equal parts are not circles right? If you draw a diagram 2 parts are just the outskirts of a circle. However there is 1 part which happens to be a full circle and thats the smallest circle inscribed in the larger circle. And this just happens to be the radius of the circle that we are looking for. So just equate and solve for r.

[Hielly]

hey thanks truetears! i get it now!

need help on this question
2. Sam’s plastic dinghy has sprung a leak and water is pouring in the hole at a rate of
27 000 cm3 per minute. He grabs a cup and frantically starts bailing the water out at a rate
of 9000 cm3 per minute. The dinghy is shaped like a circular prism (cylinder) with a base
radius of 40 cm and a height of 30 cm.
c. Find an expression for the depth of water, h cm, in the dinghy after t minutes.

i've found out that the volume is 150796cm^3
and 18000 is how fast the dinghy is filling up per minute.

not sure what else information i need to find.

thanks

[Over9000]

I shall attempt this question 

[Over9000]

Ok, so we know that the volume of the cylinder is 150796 cm^3
And we know it fills at a rate of 18000cm^3

So to find out the total percentage of the dinghy that is filled up per minute we can use , we get 12% from that. Now we know the height of the dinghy is 30 cm. So 12% of 30 cm is 3.6 cm. So that means that every minute, the water level in the dinghy rises by 3.6cm.
Lets find a suitable equation now.

so every minute, the water level rises by 3.6cm
Hope that helps.

[Hielly]

your explanation makes sense. i checked the answer and it says h=45t/4pie

[Over9000]

Thats interesting, maybe I will have to go back to the drawing board 

[Over9000]

oh ,k lol
I get it, what happened was u gave me total volume is 150796, which is right (but not exact answer), so my calculations werent using exact values. If you check on your calculator, is 3.58, which is quite close to my answer