Mathematics

The arithmetic sequence a, a+d, a+2d, a+3d, ...,a+(n-1)d has the following properties. When the first, third, fifth, and so on are added to and including the last term, the sum is 320 When the first, fourth, seventh and so on, terms are added, up to and including the last term, the sum is 224 What is the sum of the whole sequence?

Can someone explain to me how to solve for x in this example? ln(x-2)=3 Also, is there a difference between ln, lg, and log or do they all mean the same thing? Thanks

can someone please introduce me to Hyperplanes. thank you

I need to calculate the distance between postcodes to find out how far people travel.I have obtained details such as latitude and longtitude for each postcode and know it is possible to do this but how? example of the information held postcode x (in metres)y latitude longitude AB10 392900 804900 57.135 -2.117 AB14 383600 801100 57.101 -2.27 EX35 272400 148800 51.224 -3.828 EX36 274300 125700 51.016 -3.792 Anyone have any ideas? Thanks dave

Example: x = √3x+7-1 x+1 = √3x+7 (x+1)² = (√3x+7)² x²+2x+1 = 3x+7 Question: Why +2x? x²-6-x = 0 Question: Why -6-x? x = -2 OR x = 3 Question: How can you see the answer will be -2 or 3?

Hello! What I'd like to ask is, whether there is a mathematical theory of consciousness in development or any promising serious research projects in describing conscious process mathematically or physically with sufficient mathematical background

The famous Last Theorem of Fermat (proven by Andrew Wiles in the early 1990's) http://en.wikipedia.org/wiki/Andrew_Wiles says There are no positive integer solutions for [MATH]n>2[/MATH] to the equation [MATH]z^n=x^n+y^n[/math] We will not prove this theorem here (Wiles method is very advanced). But we will play around with the implications a bit. Something fun for us mortals to do si assume the negative of FLT and then start messing around a bit and see what happens. It remains entertaining only because some people believe Fermat actually solved it with only his knowledge of number theory and that someday the "real" proof will re-emerge. It see…

Ok this is my problem. I dont even know how to use this program but i need to plot graphs with it for a project. Where are you supposed to input all the data and stuff. eg. i have this y=x2 <--squared i dont know any button for it. Ok so y=x2 and then x has diffrernt values like -5 then the next bit -4 so on and so on..so can anyone help me or send me any links i really need help!

hey , i'm having a bit of trouble with this linear transformation problem. i am not really sure what or how they want me to show? so yeah, does anyone have some suggestions or advice? Cheers Sarah

Howdy. I've been working through this site called Calculus On the Web or COW. It's been a great site so far, but I have a question on the section entitled 'Trigonometric Identities' At the top of the page it shows the situation where x = cos a y = sin a Then at the bottom of the same page, in an example, it says that side B = tan a I don't understand this. In the example at the top, isn't side B = y coordinate = sin a how can side B = tan a? Unfortunately there is not a direct link to the page I'm talking about. You must go here : Calculus On the Web and then click on : Precalculus Book Functions Trigonometry Trig …

If I have x number of balls in a lottery, how many times will I have to draw a ball at random and replace it before I draw a ball that has already been drawn once before? I developed an algorithm to solve this, I think it works, not entirely sure. But I was wondering how to solve it algebraicly, here is my algorithm: t = number of balls in lottery x = 1 n = 0 while (x>0.5) { n = n + 1 x = x * (t - n + 1) / t } Answer = n

i was trying to make a trig chart for the complex plane and accindently found 0>1. at pi/4, the hypotenuse is 0, but the real leg is 1. how is that? imaginary trig must be fun. edit: at [math]\theta=\frac{\pi}{4}[/math], i got: sin=undefined cos=undefined tan=i csc=0 sec=0 cot=-i it is in the first quadrant and cot is negative...something is wonky

Well I know you guys closed out one of these but the concept is interesting. Ordinal numbers and cardinal numbers I know a bit but not everything and cardinal numbers are part of one of the most important math discoveries of the 20th century Paul Cohen's result on the continuum hypothesis. Any takers?

Hey guys! (I posted the same thread in physicsforums. To grasp a wider audience I decided to post it here too.) They say the best way to develop and train problem solving skills is by creating one's own problems. I'm still a "passive" problem solver but I'd like to learn solving problems in an "active" way. Could you give me some advice, name some guidelines on how to create new, own problems? Thanks in advance.

apparently the number "One" is the most frequently occuring in any set of data by 30%. is this True? and if it is, Why is it? I`ve searched the net for it and comeup with very little, but there is a mathematical explaination named after a guy with the 1`st letter "B" in his name (it was noisey and I didn`t catch all the info about it). can anyone help?

A sphere of radius 8 cm is circumscribed by a right circular cone. If the cone is to have a max volume, find the height of the cone and the radius of the base of teh cone... I need to relate the radius of the sphere to either the radius of the base or height of the cone, i can't find anything, any ideas people? Vol of Sphere = 4/3 TTr^3 Vol of Cone = 1/3 .TT.r^2.h

Anyone here know much about Mathcad, enough to help me set up a table with the erf and erfc functions? I can get the output, but need help figuring out how to make the table the way I want it.

I will try to introduce several methods here. There is security sensitivity to this topic but nothing we do here is likely to approach a real RSA caliber factorization method so we should'nt get visited by NSA.

Hey, i am stuck on this question, although i think i have done a bit of it already... here is what i have done so far.... we want an [math] N_\epsilon [/math] such that if [math] n \geq N [/math] then [math] |\frac{1}{x_n}-\frac{1}{x}| \leq \epsilon [/math] we know (by the denition of a limit of a sequence) [math] |x_n - x| < \epsilon_2 [/math] now [math] |\frac{1}{x_n}-\frac{1}{x}| = |\frac{x-x_n}{x \times x_n}| = |\frac{x_n-x}{x \times x_n}| = |x_n-x| \times |\frac{1}{x \times x_n}| [/math] so [math] |x_n-x| \times |\frac{1}{x \times x_n}| < \epsilon_2 \times \frac{1}{x \times x_n} [/math] but i am unsure of what to do next. …

Using a stopwatch, a stick, a ruler, and a shadow cast by my house and the sun, I estimated the apparent speed of the sun. Or so I thought. I ended up with a rough number of 75 mm in 5 minutes. Now, doing the math, we get 900 mm in and hour, and 21,600 in a day. That means the sun's light apparently travels 2,160 cm in a day, or 21.6 meters. This can't be right. Can anyone tell me what I did wrong?

Hey guys, well, my math problem is below and I need help on it: Determine the maximal subset of R(real numbers) on which the following functions are (i) defined (ii) continuous [math] [x] [/math] is a Gauss bracket of [math] x [/math]. Defined to be the greatest integer (Z) not greater than [math] x [/math]. Eg: x=1.7, [x]=1

OK, after reading books on linear algebra, and vector calculus, I have come to tensor transformations. Huzzah! However, I do not have any book to study from(!) so I am rather "sol". I do understand that covariant tensors have subscript lettering and contravariant tensors have superscipt lettering. How do I transform a given vector in covariant and contravariant tensor transformations? I googled it and there were a number terrible websites. Any help would be great!

hey, its been awhile since i could do these, could i have a little bit of help, if there is someone willing out there? Cheers Sarah

hi finding these questions impossible and was wondering if anyone knew how to answer them!!!.... 1) a linear transformation T:R^6 -> R^6 is known to have characteristic polynomial x^2(x+1)(x+5)^3 determine all possibilities for the minimum polynomial of T 2)let V be and inner product space over C with inner product <,> and let u,v be vectors from V which are orthogonal to each other. prove that ||au+bv||^2 = |a|^2||u||^2 + |b|^2||v||^2 for any complex numbers a and b thank you!!!

What exactly is infinity? Isn't it just a term to describe a number that is beyond our calculation ability? Since the numbers go on forever, wouldn't it be impossible to have a value that is too big to be a number?