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Geometry Trigonometry

1. http://postimg.org/image/cemtnweir/

2. The length of a diagonal of a square is 24 sqrt 2 millimeters. Find the perimeter of the square. If the answer is not a whole number, please leave it in simplified radical form.

And if possible, explain procedure.
I can’t really see the image you posted, so, perhaps, if you want, try submitting it again :)
For the second problem: we have to apply Pythagoras Theorem. I know. I know.
So, we can set like a generic value “k” for the side of the square. We can then say that the perimeter will be 4k, right?
Now we are applying Pythagoras, so we have that a^2+b^2=c^2.
But we also know that the figure we are considering is a square, therefore, a=b=k, and c=length of the diagonal, therefore 24√2
so we have 2(k^2)=(24√2)^2
so k^2=576
so k= √576= 24

WORDS: Short URL: http://tmblr.co/ZHU09u109vd5s
Anonymous
question: does 3^log3(-5)=-5? why or why not. (also the 3 before -5 is the base)

Hi (:

yes, it does!

Basically log3(-5) is saying, what number will equal -5 when it is set as the power of three. As you are then doing 3 to the power of this number it will simply equal -5.

-Sam

Anonymous
i'm wondering why can a graph have an infinite amount of x-intercepts?

Hi (:

Let us consider the graph $y=(-1)^x$

for every odd value of x we will have y=-1 and for every even x we will get y=1 such that the graph will literally be the same two points again and again as x increases! As one is a minus number and the other positive it will intercept the x axis everytime x increases by 1! As x will go on to infinity(also it will go to negative infinity at the other side) there will be an infinite amount of x-intercepts (: Hope this helped!

here’s the graph if you’re interested > http://www.wolframalpha.com/input/?i=y%3D%28-1%29%5Ex

-Sam

Source:
Short URL: http://tmblr.co/ZHU09u-jioyp
Anonymous
This is a really silly question but I'm in my first year of a maths degree and I've come to realise that while I'm great at picking up abstract concepts and the more complex (read: post high school level) stuff, my arithmetic skills are actually pretty poor. Ask me what 20+34 is and I'll probably count on my fingers. My girlfriend tells me that this isn't really an issue since I'll be expected to use a calculator for most things but how right is she? I don't want to end up struggling later on..

It really depends, but I am pretty sure you’ll be allowed a calculator :) Anyway, if you want to stop struggling, there is an excellent visualization method to make easy calculations even easier. Just picture 20  in two different colors (e.g. I use blue for the units, red for the tens, and green for the hundreds, but you can choose your own), so it should become 0 blue and 2 red. Now picture 34 the same way, like, 4 blue and 3 red. Now if you add the colors it should be much more immediate to do the calculation, because it will be more “descriptive”. Same goes for subtractions, multiplications and divisions, you’ll end up working more with colors and less with numbers, until it will become way easier!
Otherwise, if this wasn’t to work, you can always try picturing stuff with the numbers attached to them (plushes, pool balls, sheep, whatever comes to mind) and then just to the calculations you need! Of course, perhaps you have to make your own “tricks”, but these are the one who generally work for me!
If someone else has ideas, comments, tricks or hints please do feel free to share them!

Anonymous
Hi, could help me with this? Lim x-> -3 x^2 - 4x - 21/ 2x^2 + 7x + 3 thank you (:

Hi (:

First lets try putting x=-3 into the equation.

$\frac{(-3)^2&space;-&space;4(-3)&space;-&space;21}{2(-3)^2&space;+&space;7(-3)&space;+&space;3}$

If you work all this out you get 0 on both the top and the bottom, that’s not ideal for us! so we’re gonna have to find a different way to get the limit. Luckily we just figured out that (x + 3) is a factor of both the numerator and denominator!

Dividing top and bottom by (x+3) we get

$\frac{x-7}{2x+1}$

which if we put x=-3 into again we get:

-10/-5

=2

So it’s limit is two :D Hope this helps!

- Sam

Anonymous
how do you find the conjugate of a complex number?

Hi (:

Lets take an example complex number of: 5-4i

we know that i is also equal to $\pm&space;\sqrt{-1}$ so we can think of this complex number in two ways, when the root is positive and when the root is negative.

The complex conjugate is when the number’s root is the opposite sign to what it is now.

E.g. 5-4i has a complex conjugate of 5+4i

More examples: 6i has a complex conjugate of -6i

22i - 5 has a complex conjugate of -22i -5

Hope this helps!

-Sam

Anonymous
the sum of half a number and one sixth a number is 12 find the number and the value of a fraction and its numerator is 8 more than its denominator find the fraction

Just set it like this:

1/2x+1/6x =12 (supposing that they are fractions of the same number)
You find a first grade equation with one (or possibly two, if the numbers are different) incognitas.
so we know that 4/6x=12 -> 2/3x=12 -> x= 18.

Then you have to write down a fraction that is made by (18+8)/18 [have I understood correctly your question?]
So you have 26/18 -> 13/9

Thank you, we try our best! I hope this is soon enough:

1) Our substance has a molar mass of 115.8 g/mol.