Maths- Gym for Brainiacs

Immortal Babun wrote:The first version then. In which class are you?

cheers babun

im studying economics at uni, but this assigment is for "business and economic statistics"

Nice thread

I Maths

can you guys help me out?Im having some trouble completing this equation

3^2x-6.3x+9=0

i know i have to transform 3x in y,but i cant figure out how to get the 3x out of 3^2x

Does 6.3 mean 6 X 3?

And do you have to solve for x?

yes its 6x3,we just do "." here in brazil to not get it confused with the X.

and yeah,i need x

Is it 3^(2.x) or (3^2).x or (3.x)^2?

Use Wolfram|Alpha. A must for students of mathematics.

http://www.wolframalpha.com/

Put "Solve," before the equation, and click on "Show steps," in the Result panel and it will briefly show the steps, though I don't think it's in much detail.

Oh, and use * for multiply.

Ganso wrote:can you guys help me out?Im having some trouble completing this equation

3^2x-6.3x+9=0

i know i have to transform 3x in y,but i cant figure out how to get the 3x out of 3^2x

Let 3^x = y

therefore you get y^2-3y+9=0
then solve using whatever you like (quad formula i think)
then simplify to its easiest form, then replace the 'y' with 3^x and you get your answer. Should be two answers.

Ganso wrote:can you guys help me out?Im having some trouble completing this equation

3^2x-6.3x+9=0

i know i have to transform 3x in y,but i cant figure out how to get the 3x out of 3^2x

Is it 3^2x -6*3^x +9 = 0 or 3^2x - 6*3x +9 =0 ?

For the first version, use what ausbaz said, you'll get x1= sqrt(3) and x2= -sqrt(3).

For the second version, I changed the equation to:

3^2x = 18x-9 / :9

3^(2x-2)=2x-1

I drew the graphs with my prog, the interception points are the ones you're looking for. The interception takes place at x=1.

its the second one

i canot use programs in my test lol and i have to somehow change 3^x into y.

@ausbaz:i have no idea what you did there mate lol i think you didnt get what i wrote


I'll just ask my teacher next week,thanks though

If you change 3^x into y, then it goes like this,

3^x = y
x * ln(3) = ln(y)
x = ln(y)/ln(3)

Then the equations becomes

y^2 - 17ln(y) + 9 = 0

Then i think you have to use some numerical approximation techniques to solve this.

what kind of equation is that lol

i have no idea what ln is

natural log

Ganso wrote:i have no idea what ln is

i guess the only way to solve this problem analytically is to use a natural logarithms or (logarithms with the base of 3) and considering u dont know what they are i think you should double check what ur looking for and how.

i dont even get the equation, nothing i've seen in my life and i have seen A LOT of equations

i know what logarithms are i just use log and not ln,and thats not how you're supposed to do it,as i said,you are supposed to turn that into a ax^2+bx+c=0 quadratic equation and get the solution(s)

btw i just checked the answer and babun's is right,its 1,but i have to figure out a way of doing it on paper.im sure its not using logs because my teacher didnt even review logs yet

RealGunner wrote:i dont even get the equation, nothing i've seen in my life and i have seen A LOT of equations

You see such equations as f(x) = x + ln(x) and these can be found while doing differentiation, integration, finding maxima, minima etc...

@Ganso, there is no way you can make that equation into a* (y^2) + b*y + c = 0.

Because, in your equation, the first term is 3^(2.x) and the second term is 18.x

So you can see that the first term has x in the exponent and the second term has x in the base. You have to use log or natural log.

Ganso wrote:its the second one

i canot use programs in my test lol and i have to somehow change 3^x into y.

@ausbaz:i have no idea what you did there mate lol i think you didnt get what i wrote


I'll just ask my teacher next week,thanks though

http://en.wikipedia.org/wiki/Newton%27s_method_in_optimization

This method is easy to use for school kids.

By the way, I didn't really look at the graph. One look is enough to see that the interception point is at x=1

3^(2x-2)=2x-1

The left term can't go negative, impossibru. So the first positive value I used on the right was 1 and tada it worked
You can't calculate the value without iterative methods, kiranr is right unless you wrote the question wrong. Numerical approach is needed.

Ganso wrote:i know what logarithms are i just use log and not ln,and thats not how you're supposed to do it,as i said,you are supposed to turn that into a ax^2+bx+c=0 quadratic equation and get the solution(s)

Maybe you're looking for 2x= 3^log3(2) x but it wouldn't help you to get rid of x

only way you can transform that equation into a polynomial of the 2nd order (a*x^2 + b*x +c) is if x=1, its not possible any other way.

1) One house is on top of a hill and the other three houses are at the base. All distances from each other is the same.

3.
topic: geometry
difficulty: easy
requirements: 8th grade

A sail has been stitched together out of 6 equally wide panels like in the picture. How long are the stitches which were needed to put the sail together?

kiranr wrote:
1) One house is on top of a hill and the other three houses are at the base. All distances from each other is the same.

You uncovered one of the possibilities. What's the other version?

Immortal Babun wrote:3.
topic: geometry
difficulty: easy
requirements: 8th grade

A sail has been stitched together out of 6 equally wide panels like in the picture. How long are the stitches which were needed to put the sail together?

kiranr wrote:
1) One house is on top of a hill and the other three houses are at the base. All distances from each other is the same.

You uncovered one of the possibilities. What's the other version?

Could work it out using similar triangles but couldn't be arsed

Did everybody give up? The questions aren't even hard :lol!:

2)

is it

2002 * 222 ?