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Thanks a lot, CPhill! :)

1/4 + 2/5      the common denominator is 20...so we have

5/20  +  8/20   =   13/20

Thanks but I though hookes law is f= -kx, how do I know when its negative or positive.

.25 =  (1/4)

(1/4)^8  =  1 / 65536  

I'm sorry, but I'm too old to play video games, so I don't understand what your aim is!. All I can do is to give you the formula for nth. term in an arithmetic sequence, which is this:

nth term=First term +(No.of terms -1) X(constant of difference between terms). Good Luck.

Ok, let me explain what I'm trying to do, and hopefully that'll clear things up. This may sound weird but I'm trying to find out what the highest level of a pet on a game I'm playing can reach, I've already found out how much XP I can earn by figuring out all the math of when it will die, which is after 64 days, I can gain a max xp of 56 a day, which means over the pets lifespan it can get 3584 xp. for level 1 it takes 30 xp to level up to level 2, and each consecutive level requires 3 more xp, so I was trying to figure out the highest level it will reach. but the problem is that I really didn't pay attention in 8th grade math class which is when they taught us nth term problems, and how to solve, and word them. help?

I'm not sure if this is what you mean....but I think you have....

x / y =  4 / 7    and   y / z =   14 / 3

Note that the first fraction can also be expressed as  x / y =  8 / 14

So

[x + y ] / z  =   [8 + 14 ] / 3   =  22 / 3

Let's see how "guest" got this solution........

 x-2(x+4)=8     simplify on the left

x - 2x - 8  = 8    

-1x - 8   = 8     add 8 to both sides

-1x = 16     divide both sides by -1

x = -16

This cannot be be precisely determined ....to see why, we have

41 = A(-2)^2 + B(-2)  + C    →   41  = 4A - 2B + C   (1)

20 = A(5)^2  + B(5)  + C   →     20 = 25A + 5B  + C   (2)

But, we have more variables than equations......in this situation, we will have an infinite number of solutions

[We need one more point and function value at that point to obtain a solution ]

When R=1 then you have x=99

When R=10.......................x=0

When R=2.........................x=192

When R=-10......................x=0

0 / 0   is known as an "indeterminate" form......to see why, note that ......

a/b = c    implies that bc = a

So

0 / 0  might  equal  any number because  any number times 0  = 0

Thus.....we can't precisely determine what 0 / 0 might equate to.....!!!

Your answer is:

x=-16

Fv=13,000; i=0.05; PMT=500; n=?,

We have to assume a few things here: that i is compounded annually, that the $500 deposit is made annually and at the end of each year. If that is the case your answer n?, will be the number of years. If you change ANY one of them from the above, then the answer will be different.

So, given those provisions i just mentioned, then the answer will be:

n=17.0713 Years. Lets knows if they are monthly deposits......etc.

2= (1.009)n,

Divide both sides by 1.009,

2/1.009=n

n=1.9822

Square root of 256=16, because:

16 x 16=256

DIVIDING BY 0 IS NOT ALLOWED IN MATH, BECAUSE IT GIVES YOU INFINITY!!!!.

Your answer of 3584/(3n+30)=? doesn't make sense!!!. The way you have it written, there is NO SOLUTION for it!!. If you are trying to get the nth term of an arithmetic sequence, then you have to give the first term, the number of terms in the sequence, and the constant of difference between the terrms, then will be able to find the nth term. Check your numbers carefully.

sorry, i phrased it wrong, I meant to phrase it 3584/(3n+30)=? and how to solve that, so that I can actually do other equations like it, instead of just knowing the answer.

\(\cos \theta = 0.5 \) implies an angle of 60 deg, but the negative sign means that the angle lies in the second or third quadrant, (where cosine is negative).

So, \(3x=120 \text{ or } 240 \text{ deg, } \)or, more generally 120 \(\pm\) 360k or 240 \(\pm\) 360k deg, where k is any integer.

Dividing by 3,

\(x = 40 \pm 120k, \text{ or }80 \pm 120k.\)

So,

\(x = \dots -80, 40, 160, 280, \dots\)

or

\(x = \dots -40, 80, 200, 320, \dots .\)

Hooke'slaw says the force required is proportional to the extension, where the proportionality constant is the spring constant.  So here (knowing that the force is mass*gravitational acceleration) we have:

10*9.81 = 70*extension

extension = 9.81/7 m ≈ 1.4 m

Hooke's Law:

F=kx

F is the force on the spring. Force is the product of mass and acceleration, so it can written as follows.

ma=kx

k is the spring constant, which is given. x is displacement, which is what we're trying to find.

x=ma/k

By subsituting the variables in (9.81 = acceleration due to gravity):

x=10*9.81/70

x=1.40

The spring will stretch 1.4 metres.

This is an "arithmetic sequence", which means the difference between one term and the next must a constant. Since the 1st. term is 3 and the 3rd. term is 8, then,

8 - 3=5 / 2=2.50 appears to be the difference between the terms. Therefore, the 2nd.term should be

3 + 2.5=5.5.........so we have, 3, 5.5, 8, 10.5, 13, 15.50............and so on.

Here's the graph : https://www.desmos.com/calculator/7pvpj3imv9

Just hold down your left mouse button and drag your cursor along the line......you will find as many pairs as you want  !!!!

"Guest" might be correct.....it could be the Fibonacci Series......but let's assume that it's a regular arithmetic series....we can find the middle term by finding the common difference, thusly :

8 = 3 + d(3 -1)    simplify

5 = d(2)   divide both sides by 2

2.5  = d   this is the common difference....so....the second term is just 3 + 2.5   = 5.5

And the third term is just 5.5 + 2.5   = 8    as we might suspect  !!!

it could be the fibonacci sequence. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The nextnumber is found by adding up the two numbersbefore it. Similarly, the 3 is found by adding the twonumbers before it (1+2).