||| - Official Maths / Science Thread - |||

[stev]

Guys like you almost always end up with girls though

is true...ah have ah padna who goin and get ah female football team just now.

lol

notice i say football...he go teach he daughters to kick balls instead of playin with a piece of wood and balls (cricket side)

[Ronaldo95163]

[neals]

so today the temperature is 0 degrees Celsius tomorrow its will be twice as cold- whats the temperature tomorrow? never did quite figure out that one

[Ronaldo95163]

A Circle is divided into 6 sectors in an Arithmetic Progression where the largest side exceeds the smallest by 3. Find all the angles.

[Corn Bird]

A Circle is divided into 6 sectors in an Arithmetic Progression where the largest side exceeds the smallest by 3. Find all the angles.

you perhaps mean that largest angle of the sectors exceed the smallest angle by 3. there is no 'side' on a circle.

this is an add math problem -- using an a.p. we have that the angles are represented by

a, a-d, a-2d, a- 3d, a-4d, a-5d


the sum of angles gives 6a-15d=360
the difference between the largest and smallest gives a-(a-5d)=3

solving these equations simultaneously gives a=58.5 d=0.6

so the six angles are

58.5, 57.9, 57.3, 56.7, 56.1, 55.5



you know (i hope) that there is a huge difference between this type of problem and the Riemman hypothesis

[Ronaldo95163]

A Circle is divided into 6 sectors in an Arithmetic Progression where the largest side exceeds the smallest by 3. Find all the angles.

you perhaps mean that largest angle of the sectors exceed the smallest angle by 3. there is no 'side' on a circle.

this is an add math problem -- using an a.p. we have that the angles are represented by

a, a-d, a-2d, a- 3d, a-4d, a-5d


the sum of angles gives 6a-15d=360
the difference between the largest and smallest gives a-(a-5d)=3

solving these equations simultaneously gives a=58.5 d=0.6

so the six angles are

58.5, 57.9, 57.3, 56.7, 56.1, 55.5



you know (i hope) that there is a huge difference between this type of problem and the Riemman hypothesis

I know I was just rattling off questions off the top of my head.

S6=350
a+5d = a+3
3=5d
5d=3
d=3/5

Sn = n/2(2a+(n-1)d)
S6= 6/2(2a+5d)=360
6a+15d = 360

Substituting d=3/5

6a+15d = 360
6a+15(3/5)=360
6a+9 = 360
6a=351
a=351/6
a=58.5 <------ So far you're correct


a, (a+d), (a+2d), (a+3d), (a+4d), (a+5d)
58.5, (58.5+3/5), (58.5+2(3/5)), (58.5+3(3/5)), (58.5+4(3/5)), (58.5+5(3/5))

Angles are:

58.5, 59.1, 59.7, 60.3, 60.9, 61.5

^ The answer supposed to be integers but I couldn't remember how much the last angle exceeded the first by though

I believe you're formula for the nth term was wrong though...it's:

Tn = a+(n-1)d

so the six angles are represented by:
a, (a+d), (a+2d), (a+3d), (a+4d), (a+5d)


I'll post some more questions later

[Corn Bird]

presented by

a, a-d, a-2d, a- 3d, a-4d, a-5d


the sum of angles gives 6a-15d=360
the difference between the largest and smallest gives a-(a-5d)=3

solving these equations simultaneously gives a=58.5 d=0.6

so the six angles are

58.5, 57.9, 57.3, 56.7, 56.1, 55.5

I believe you're formula for the nth term was wrong though...it's:

Tn = a+(n-1)d

so the six angles are represented by:
a, (a+d), (a+2d), (a+3d), (a+4d), (a+5d)


I'll post some more questions later

yes, i made a mistake (add maths teacher would not be pleased). my simult equations are correct

the sum of angles gives 6a-15d=360
the difference between the largest and smallest gives a-(a-5d)=3

but the my solutions of the simult eqs are wrong -- i got the correct answer for d=.6 but the wrong answer for a. correct answer is a=61.5

nothing is wrong with using

a, a-d, a-2d, ...

this still is an a.p.; only thing is the common difference is now -d instead of d. just a matter of notation.

[Ronaldo95163]

lol no scene :p

Common Difference btw

Since you brought up common ratio....

x+1,x-5,x+4.... are Three successive terms of a GP

Find:

The Common Ratio
The 9th Term
The sum of the first 20 terms

[nervewrecker]

oh...allyuh want to play:

What is the difference / relation of areas between 2 circles where 1 circles diameter is double the diameter of the other?

also,

What percentage of a squares area is a circle whose diameter is equal to that of a side on the square?

[Corn Bird]

lol no scene :p

Common Difference btw

Since you brought up common ratio....

x+1,x-5,x+4.... are Three successive terms of a GP

Find:

The Common Ratio
The 9th Term
The sum of the first 20 terms

think you mean the *first* three terms?? otherwise three successive terms could be located anywhere in the gp; can't see a way to get the first term (and therefore the 9 th term)

[Ronaldo95163]

lol no scene :p

Common Difference btw

Since you brought up common ratio....

x+1,x-5,x+4.... are Three successive terms of a GP

Find:

The Common Ratio
The 9th Term
The sum of the first 20 terms

think you mean the *first* three terms?? otherwise three successive terms could be located anywhere in the gp; can't see a way to get the first term (and therefore the 9 th term)

The question is actually:

x+1, x-3 and x-6 are three consecutive terms of a G.P

find:

The value of x
the common ratio

If x+1 is the 4th term find:
The first term
The sum of the first 5 terms to 3S.F

once again my bad with the question

[black start]

vramps, where you at dan?

what is math2240?

[Corn Bird]

perimeter of shaded region:



AC=OC as they are both radii

this implies triangle AOC is equilateral

so AC=5

so arc ABC is 5 x Pi/2

arc APC is 5 x Pi/3


perimeter is the sum of these which is 25 x Pi/6

[Ronaldo95163]

oh...allyuh want to play:

What is the difference / relation of areas of 2 circles where 1 is double the diameter of the other?

also,

What percentage of a squares area is a circle whose diameter is equal to that of a side on the square?

Let's say the length of a side of the Square = 2 units
It's area = 2^2 = 4 units squared

Length of side of square=diameter of circle
Therefore the diameter of the circle = 2 units
Therefore it's radius is = 1 unit

By saying
"What percentage of a squares area is a circle"

Im guessing that the circle is inside the square?

Area of circle = pi*radius^2
=22/7*1^2
=22/7 or 3.142857143 units squared

Percentage of squares area that circle occupies (EDIT-didn't multiply by 100)

= 3.142857143/4*100
=78.5%

approx. value: 80%


hope i'm not wrong

[Ronaldo95163]

perimeter of shaded region:



AC=OC as they are both radii

this implies triangle AOC is equilateral

so AC=5

so arc ABC is 5 x Pi/2

arc APC is 5 x Pi/3


perimeter is the sum of these which is 25 x Pi/6

I'll work it out and tell you what I get in a bit...

[black start]

brings math homework to trinituner to get it done by nerve, corn bird and gracen


*assignment done- like a troll*

[Corn Bird]

The question is actually:

x+1, x-3 and x-6 are three consecutive terms of a G.P

find:

The value of x
the common ratio

If x+1 is the 4th term find:
The first term
The sum of the first 5 terms to 3S.F

once again my bad with the question

(x-3)/(x+1)=(x-6)/(x-3)=r

(x-3)(x-3)=(x+1)(x-6)

x^2-6x+9=x^2-5x-6

x=15

r=12/16=3/4


ar^3=16

a= 1024/27


too lazy to get the sum for the first 5 terms

[nervewrecker]

oh...allyuh want to play:

What is the difference / relation of areas of 2 circles where 1 is double the diameter of the other?

also,

What percentage of a squares area is a circle whose diameter is equal to that of a side on the square?

Let's say the length of a side of the Square = 2 units
It's area = 2^2 = 4 units squared

Length of side of square=diameter of circle
Therefore the diameter of the circle = 2 units
Therefore it's radius is = 1 unit

By saying
"What percentage of a squares area is a circle"

Im guessing that the circle is inside the square?

Area of circle = pi*radius^2
=22/7*1^2
=22/7 or 3.142857143 units squared

Percentage of squares area that circle occupies

= 3.142857143/4
=0.8%


hope i'm not wrong

yuh wrong.

tackle the first question nah (with the 2 circles). HINT: pipe of double diameter can transmit how much more flow through it than first pipe (neglecting friction against the internal walls of both pipes etc).

[nervewrecker]

you a little off on the answer though, dont round off the numbers.

its 0.785, I didnt look at your working

easy way to find area of circle eh, 0.785 * diameter squared. tell meh ah wrong nah?

[Corn Bird]

What percentage of a squares area is a circle whose diameter is equal to that of a side on the square?

let x=length of side of square

circle has diameter equal to x. so area of circle is Pi (x/2)^2

ratio of circle area to square is Pi/4

percentage is 25Pi=78.54%

[nervewrecker]

you guys did good, now tackle the second question.

I hope allyuh didnt google that eh.

[Corn Bird]

brings math homework to trinituner to get it done by nerve, corn bird and gracen


*assignment done- like a troll*

nothing is wrong with a little maths

Romans 12:21: Be not overcome of evil, but overcome evil with good.

[Ronaldo95163]

Sorry I took so long...was doubting myself :/




Per of ABC = 5pi/2=7.85

per of segment = 2r+rtheta

=2(5)+5(pi/3)
=15.23-10 = 5.23

5.23+7.82 = 13.08

I have to double check this tho..

EDIT:

Found my mistake

When I was adding the arc lengths of APC and ABC....I forgot to find the radius for ABC

So for APC:

s=rtheta
=5(pi/3)
=5.23

For ABC

s=rtheta
= 2.5(pi/3)
=7.85

adding the two you get 13.08

[nervewrecker]

yes, double check it.

[nervewrecker]

nah, try it again.

[Ronaldo95163]

you a little off on the answer though, dont round off the numbers.

its 0.785, I didnt look at your working

easy way to find area of circle eh, 0.785 * diameter squared. tell meh ah wrong nah?

badman does round off he numbers normel normel

[nervewrecker]

those rounded off numbers does make a big difference eh. ah just saying.

[nervewrecker]

take for example:

pump A pumps 0.264 US gallons a second into a cylindrical tank of radius 5.563m & 1 meter high, how long before it is full.

[Ronaldo95163]

nah, try it again.

180 degrees is pi radians....

pi(2.5) =7.85



just punched 180->2ndf->pi*2.5 on calculator

[Ronaldo95163]

take for example:

pump A pumps 0.264 US gallons a second into a cylindrical tank of radius 5.563m & 1 meter high, how long before it is full.

Vol. of cylinder = pi*radius^2* height

=pi*5.63^2*1= 99.6m^3

idk how to convert US gallons to m^3

EDIT:

According to a converter .264 gals = 0.000999m^3

so it's 99.6/.000999

I'm sure my answer is wrong but idk how to convert US Gals to m^3