I am going to add this as an interest question so I thought I would comment a little further.

The vertical axis is m/s   the horizontal axis is seconds.

When you multiply these together the seconds cancel out and you are left with metres which is distance.

When you find the area of a rectangle it might be metres * metres so the units will be m^2

When you find the area under these lines the units are  m/s and seconds so the resultant unit is metres.

That is why you can find the distance travelled by finding the area under the curve.

If you have any comments or questions please post here. This is a really interesting and important concept.

According to wolfram alpha, it is zero.

We observe that:

infinity^(-infinity)= 1/(infinity^infinit) 

Now, infinity^infinit must be considered to be quiet a lot. The inverse of this should be etremely small, i.e. very close to zero. 

It's important to remember, though, that infinity isn't a number, but an abstract concept.

Anonymous who has just joined up and is now AlexM has asked me to look over his answer.   

Hi Alex, I will look at your answer now.  I have copied it here so I can look and give feedback  both at the same time.   

let's start with cracking the two problems that already have an answer so we can understand how to solve0,5s + 3t. 

2s - 2 = 7

2s - 2 = 7 is an expression that says "the value of 2s minus 2 equals 7". That must mean that the original value of 2s was9, because 7 plus 2 is 9.

That must mean that 1s equals 4.5, because 2s equals 9.     GOOD

 3s + 5t = 10

We then move on to the next problem, 3s + 5t = 10. We know that 1s equals 4.5, so 3s must equal 4.5 * 3 = 13.5. Wait a second, 13.5 is above 10! What is this!? Well, 5t must be a negative value, with a total value of (-3.5). We use brackets to make it easier to read negative values. It's easy then! 13.5 + (-3.5) = 10! Actually, not as easy as someone may think, negative numbers involve in a bunch of pesky rules, that's why the answer is 10 and not 17. I recommend you to read about said rules in case you already haven't.

So, 5t equals (-3.5). How much is 1t? Let's simply just take (-3.5) and divide it by 5, like this: (-3.5) / 5 = (-0.7). 1t equals(-0.7).         GOOD

0.5s + 3t = ?

We now know that 1s equals 4.5 and that 1t equals (-0.7).

0.5s is half of the value of 1s. 0.5s = 4.5 / 2 = 2.25.

3t = (-0.7) * 3 = (-2.1).

 A simple, readable, version of the problem would then be 2.25 + (-0.7).

2.25 + (-2.1) = 0.15

 Finally, we have our answer, 0.5s + 3t = 0.15.       (YES this is the sames as CPhill's answer.)

 You have answered well Alex,  thank you.  

How many moles of atoms are there in 4.02 x 1023 atoms of Mg?

Did you mean 4,02* 10^23 atoms?

1 mol of something, Mg-atoms, water molecules or O3 molecules is about 6,022*10^23 particles. 

So 4,02*10^23 atoms of Mg is about 1 mol of Mg-atoms.

I assume you mean percentage (%)?

Percent means "per hundred" aka "out of one hundred". 23% means "23 out of 100". With other words 23% = 23/100. 

Often, one can read in the newspapers about round numbers such as 50%, 90% or 20%. Here it can be useful to remember that:

10% = 10/100 = 1/10 = 0,1

90% = 90/100 = 9/10 = 0,9

50% = 50/100 = 1/2 = 0,5

80% = 80/100 [ = 8/10 ] = 4/5

Also: 25% = 1/4 and 75% = 3/4 and 67% ≈ 2/3

The sentence "100% of all Norwegians were born in Norway" means that ALL Norwegians were born in Norway. If the price on a sweater is down 20%, it means that it is 1/5 cheaper. I.e. the new price is 4/5 of the original. If the price on gold has gone up 200%, the price has tripled (100% - original price + 200% - the price increase). To calculate what, say 27,56% of 23 is, you do the following:

27,56% of 23 = 27,56%*23 = (27,56/100)*23 = (27,56*23)/100 =

6,3388 

and if a=c    a=2/3b

then sin(a)=(2*square root of 2)/3       cos(a）=1/3.

Good job.it is my bad though.

I am exciting to study and solove problem with you guys.

You guys can understand and use the fomlua very well.That is really smart.

Let N be the number...so we have

3N - 9 = -12

Add 9 to both sides

3N = -3  divide both sides by 3

N = -1

5 = 2L + 2(.64L)                            (First simplify by multiplying 2 and .64)

5 = 2L + 1.28L                               (Next, simplify by adding 2L and 1.28L)

5 = 3.28L                                       (Finally divide both sides by 3.28)

L = 1.52 (approx)

I = k / R   (where k is the proportionality constant for this situation.

Given that I = 5 and R = 7:     5 = k / 7    --->     k = 35      (cross multiply)

So this formula is:     I = 35 / R  

                    --->     I · R = 35                    (cross multiply)

                    --->      R = 35 / I                    (divide)

Since tanA = opp/adj = 3/4   ....then angle A  must be  "1" in the diagram

For a right triangle, the tangent of the two acute angles is defined to the length of the opposite side divided by the length of the adjacent side.

tan = opp / adj

If tan A = 3/4, the opposite side is the 3 ft side, the adjacent side is the 4 ft side. The angle that fits this criterion is angle 1.

One formula for the area of a triangle is: Area = ½·a·b·sinC

where C is the angle between the two sides a and b.

In this problem, a = 100, b = 53.2, and C = 40°.

Area =  ½·100·53.2·sin40°     -->      Area = 1700 (rounded)

(-7/2)(2x+6/7)-3      distribute the -7/2 over the terms in the parentheses

(-14/2)x - 42/14 - 3  =

-7x - 3 - 3 =

-7x - 6

The area of the park is given by    (1/2)(100)(53.2)sin(40°) = about 1709.8 square yards.

If he starts with $34.25 and ends up with $5.25, he must have spent  ($34.25 - $5.25) =   $29.00

8% means that or every 100 ft of horizontal distance, the hill rises vertically 8 ft.  So,  8% = 8/100 = 2/25

So we need to use the inverse tangent to find the angle

tan^-1 (2/25) = about 4.57°

The area of the scarf is given by:

A = (1/2)(14²)sin(110°)   = about 92.1 in²

google it stupid

 c is not equal to a. because in the equation of x :

a(1-x)^2+2bx+c(1+x^2)=2

a-ax^2+2bx+c+cx^2-2=0

(c-a)x^2+2bx+(a+c-2)=0

when the equation of ax^2+bx+c=0 have 2 ame soloution, it have b^2-4ac=0

in this case, a=c-a b=2b c=a+c-2,so

(2b)^2-4(c-a)(a+c-2)=0

4b^2-4(ac+c^2-2c-a^2-ac+2a)=0

b^2=c^2-2c-a^2+2a

b^2=c^2-2c+1-a^2+2a-1

B^2=(c-1)^2-（a^2-2a+1)

B^2=(c-1)^2-(a-1)^2

so if a=c then (c-1)^2=(a-1)^2, (c-1)^2-(a-1)^2=0， b=0

a side of a triangle is always bigger than 0

so a not equal to c

i also alologize for the question should be a(1-x^2)+2bx+(1+x^2)c=0

i am really sorry about that. I typed it in a wrong way

Good job melody and heureka!

i think the answer to the pearl one would be 5000, 2500 of white, and 2500 of black. Since you said they must be equal in draw, this game is impossible to win entirely because the amount of pearls begins uneven, but the way to win maximum money is to draw 5000. (hopefully you don't have to draw them one at a time, otherwise this wouldn't work. :D)

The square root of  √1233897849484858694978004   is  1110809546900.3040104263997245.

You find 'x' by isolating it. That means have 'x' on one side and everything else on the other.

In this case, you would find x by subtracting 5 to get rid of the 5 on the side of the 'x'. However, what happens on one side also has to happen on the other. Therefore, you would also subtract 5 from 6.

x + 5 - 5 = 6 - 5

x = 1

In this case, 'x' would equal 1

You would find x by subtracting 6-5. 6-5=1 

1+5=6

Therefore, x=1.

-12, -√2 , -3/6 etc.