Mathematical!

What exactly is Pi? 

Pi is the ratio of the circumference of a circle divided by its diameter.

π = C/d

It just so happens that this ratio is infinite and none repetitive, which makes it an irrational number.

π=3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609...

oooooor 

A factorial symbol (!) at the end of a number means the number is multiplied by the factorial of its predecessor. This can also be said as, the number is multiplied by all the numbers before it. All of this starting from the notion that 0! = 1

Ex:

0! = 1

1! = 0!*1 = 1*1= 1

2! = 1!*2 = 1*2 = 2

3! = 2!*3 = 1*2*3 = 6

4! = 3!*4 = 1*2*3*4 = 24

I hope your semester/trimester/quarter/work or whatever applies is going well. Personally mine is just starting which is why I'm still not posting daily updates. I'll start posting soon. Posts may include GRE prep work. 

Sorry I've been away, I was finishing my semester/travelling. For this upcoming year I'm going to try to expand from number based help to words as well! Specifically Spanish help. As always what I post depends on what you ask so bombard my inbox if need be!

For the first picture: 

The first derivative lets you know if the slope increases (positive) or decreases (negative). If the first derivative is 0 The second derivative lets you know if the curve is concave up (u: positive) or concave down (n: negative). If the second derivative is 0: the point can be a maximum or a minimum. Example:

Knowing this give the problem a try if you still can't do it feel free to come back :) 

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As for the second picture: 

The equation can be rewritten as: 

(3-x^3)^(-1/3) using the chain rule: (derivative of the outside time the derivative of the inside)

-1/3 * (3-x^3)^(-4/3) * -3x^2

x^2 * (3-x^3)^(4/3)

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csca=1.45 it lies in the first quadrant us a cofunction identity to determine angle a to two decimal places. My textbook tells me the answer I just need to learn how to get there. (Can you tag this as anonimath It will be easy/quicker for me to find that way. )

To find a mean or average you have to add all your values and divide them by the amount of values there are.

Example: 

1,2,3,4,5,6

mean = (1+2+3+4+5+6)/(6)

To find the standard deviation you use the following formula:

Region I:

mean = 1387.3

s1 = 498.3

Region II:

mean = 1039.3

s2 = 346.7

Cofunction of csc is sec

csc a = sec (pi/2-a)

1.45 = sec (pi/2-a)

solving for a we have: (i used a handy dandy software)

which is equal to: 

When you make a plot that has values y = x it means that your graph is a straight line that has a slope of 1. This means that all the points in your graph have the same value.

For example: (1,1), (2,2), (935,935) 

The plot will look like: 

An inverse function means that y = 1/x

When plotting this function you have two different asymptotes (an invisible line the graph will not touch) when y = 0 and when x = 0. This occurs because there are no real numbers that can satisfy those values. This means that your plot will look like this: 

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To plot something you simply give different values to the independent variable (in your case x) and it will give you a corresponding value of the dependent variable (in your case g(x)). 

I suggest you make a table of values of x and the subsequent value of g(x) you will get

Example:

x = 0  —-> g(x) = 4/3

x = 1 —-> g(x) = 7/3 = 2.33

and so on

Tip: When plotting you have basic movements a plot does according to how the equation is written. Since you have g(x) = x + 4/3 this means it’s the same plot as y=x except it moves 4/3 up from the origin. If you compare the two it should look like: 

where the blue (lower) line is y = x and the red (top) line is y = x + 4/3

How do you solve equations correctly? 

My 8th grade math teacher made sure we got this memorized by using colours. Red, green, blue then purple. The colour association works wonders and to this day in my 4th year in university I still run the colours through my mind. 

1) Red = parenthesis and radicals (from inwards out)

If you have an equation that looks like the following

1 + (6 * (4 * (5+1))) = ? 

Solve the most inner parenthesis first then the next one and so on until you reach the final parenthesis. If you have more than one same degree of deep parenthesis go from left to right. 

2) Green = exponents

Yup, just exponents. From left to right as above.

3) Blue = multiplications and divisions

From left to right, whether it's multiplication or division it's what ever comes first from left to right

4) Purple = addition and subtraction

 (Again) From left to right, just as above

*If you have a parenthesis with several operations inside make sure you still follow the order of the list. The rules apply the same way.*

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mathanon te puede brindar ayuda tanto en inglés como español

cualquier duda o pregunta que tengan con matemáticas sometanlas a mi inbox y los ayudaré como pueda

An easier way to say this is: Solve for z

Solving for z will give you a complex number that makes your equation true.

Here’s how we do it: 

1) multiply both sides by the denumerator and simplify. you should end up with the following

z = (1+i) (1+z)

2) expand the right side then simplify

z = 1 + i +z + zi

0 = 1 + i +zi

3) solve for z

-zi= 1 +i 

- z = -i + 1

z = -1 + i

And there you go! You now have a complex number z that when plugged in to your equation will give you 1 + i.

to solve functions you create an x/y table or in your cases x/g & t/h tables. What you do is you give the x or t a value and then you substitute the value until you have a final number.

Ex.

g(x)=2x-3

if x = 0

g(0) = -3

if x = 1

g(1) = 2(1)-3 = -1

and so on. Once you have at least 7 values (from -3 to 3) you can have a trustworthy plot. 

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To solve function compositions I’ll explain with an example:

g(h(t)) is the g(x) function except the x is your h(t) function. In other words substitute your x for the function on the inside. 

I can help you tackle your number troubles away

Feel free to follow and ask and I'll do my best to help you out