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Melody:
Walt:
To find the largest possible square that would fit into your garden, we would have to find the largest perfect square that will divide into 6912, which is the area of the garden. 256 is the largest perfect square to divide into 6912 and when you divide you get 27. This means that you could make 27 squares with equal areas that would fit inside your garden. Because a square's length and width are always the same, you just find the square root of 256 and you got your sides. So, 16 feet.

a garden measures 64 ft by 108 ft. the gardener wishes to subdivide the garden into congruent squares. what is the side length of the largest squares possible?

But Walt, 108 divided by 16 = 6.75 so there is not a 'whole' number of squares in the length.

For the moment, this question has got me stumped. I don't have a lot of time to think about it today, I definitely want to play with this question.

Sorry for the moment.
Melody.

Good point Melody, I failed to see this. Ok so I think this is the right way,
To find the side lengths of the largest possible squares then you would have to find the greatest common factor of both 64 and 108 which is 4. Here is the why:

Another way to look at the length and width of this rectangle is that it tells you that you could fit 64x108 tiny boxes, all with side lengths of 1, inside the rectangle. If the side lengths of your overall rectangle have a common factor that means you could group up the little unit boxes into bigger ones. The biggest boxes you could possibly group them into will have side lengths of your greatest common factor which in this case is 4. If you draw yourself a picture in your head you'll see how it all works out.

WaltJan 20, 2014

#12

+118725

+26

Another day done.
There were a couple of top answers posted by teach and Walt plus some others by one or more guests.
A big thank you to each of you

There were 2 questions that i have not done yet.
I think they were called "Measurement" and "Teacher trying to flunk me"
these were both difficult questions and I didn't have much time today. Maybe I will suceed tomorrow, or maybe one of you will beat me to it.
Most of you would have the skills needed, they are just difficult puzzle type questions.

I wrote an information post today on how to deal with negative indices. If these give you any grief you should take a look.
I put an i symbol next to it to help it stand out. I have decided to use that symbol for information posts.
That's all folks,
Good night.
Melody.

MelodyJan 20, 2014

+118725

Walt:
Given that f(x)+2f(8-x)=4 for all real x values find f(2).

What is the smallest positive integer with exactly 768 divisors.

Guest's answer.
the factorial of 768 should be the answer to your second question- enter 768! into a calculator

Our guest had a good theory, unfortunately
4 is the smallest positive integer with 3 divisors and it is not 1x2x3 so maybe the theory does not hold up under testing

I've had a quick look at both your questions and you could be right.
maybe your teacher does want to flunk you, but i think it is much more likely that your teacher wants to really extend you.
I assume you are one smart person.

I haven't succeeded yet. They both appear to be very difficult. I haven't had much time today. Maybe I'll get a chance to have a better look tomorrow.

MelodyJan 20, 2014

+118725

Vraces:
x/2 + x/3 = 10

Hi Vraces,

Walt gave you an excellent answer and i am quite sure that you do understand it.
If it was a straight simplifying question you would definitely do it that way.

Since it is an equation question there is another way that I think is just a little easier.

The lowest common denominator is 6.
So you can just multiply both sieds by 6, like this

6[ x/2 + x/3 ] = 6 * 10
6x/2 + 6x/3 = 60
3x + 2x =60
5x=60
x=12

MelodyJan 20, 2014

+118725

Anna:
An aero plane flies from airport A to B 90 km away on a bearing 070 degrees. From B to airport c, 100 km from B on a bearing 210 degrees . How far and on what course must the plane fly in order to return to A direct

Hi Anna,
This is what your vectors look like.
You can find the distance using the cosine rule
then
you can find the angle within the triangle using the sine or cosine rule followed by a little bit of deduction (to get the actual angle that you need)

Have fun.

140121 Vectors for Anna.jpg

MelodyJan 20, 2014

Dear Melody,

Thank you very much..

GuestJan 20, 2014

+118725

Yes, I believe that it is.

MelodyJan 20, 2014

+118725

Ashlee:
How do you evaluate expressions that have negative exponents

If this is about scientific notation then

3.0361 x 10 ^-4 is a really tiny number.
to convert it to a normal number
you will need to move the decimal point 4 places in a direction that will make the number smaller
it will become

0.00030361

Put in loops from where the decimal point was to where it is now. it has looped over 4 digits!

If you wanted to know about negative indices (exponents) in algebra, I have just posted an information post on the topic.
Take a look. I put an i in a circle symbol next to my information posts.

MelodyJan 20, 2014

+118725

lol:
3x^2 + 20x + 12 = 0

Determine the 2nd X of this equation

I don't know what this means. However
if you want to solve it without using the quadratic formula or the completing the sqares method you will need to factorise it!

To factorise 3x^2 + 20x + 12
you need to find 2 numbers that multiply to 3*12=+36
and add to +20
You get back to me with those numbers and then we will continue.

MelodyJan 20, 2014

Dear Melody,

Is this correct ?

a. -4.4Q + 396 = 0
-4.4Q = -396
Q = 90

b. P = 400 - 2Q
= 400 - (2 x 90)
= 400 - 180
= 220

c. Profit = - 2.2Q2 + 396Q - 400
= - (2.2 x 90 ²) + (396 x 90) - 400
= - 17820 + 35640 - 400
= 17420

Thank you very much..

GuestJan 20, 2014

+118725

MathPong:
Quadratic Functions

I need help with a question i got on my math book. It goes like this Solve the equation y = 0 graphically and algebrally. And i got a formula for this and it goes like: y = x*h and the h in the formula is 12 - x so i did this x(12-x) and i got this 12x-x^2. But its very confusing please help me its a Quadratic Function..

MelodyJan 20, 2014

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