MattMayD

Wanna hop in on the pi discussion and add your thoughts? :)

That, my friend, is one beautiful question and I will try to answer it as best as I can in as few words as possible but as many as needed for you to 'truly' (your words) get the idea.

Our universe is a funny place. Apparently there are some things which just are the way they are and nothing we could ever do will change that. Mathematics is basically the motherload of unchangable consistency in the universe. Everything you'll ever do will be limited by the boundries of the material representation of mathematical systems known as physics.

Pi is an extremely elegant and easy to understand example of that. Pi, of course, has something to do with circles. Now, circles don't exactly exist in the 'real' world and what i mean by that is that there isn't a physical representation of a one-dimensional point or a one-dimensional distance on a two-dimensional plane by which the circle is defined. So really when we say circle in mathematics what we mean by that is a two-dimensional structure which consists of a center represented by any one-dimensional point you can imagine and all the points that have a certain fixed distance from that center-point. What's funny about all that is that you can arbitrarily choose any point you want and any distance from that center-point to 'build' a circle and even tho you can do this as often as you want and with as many different values and positions there's one property which you have no influence over and that, my friend, is the ratio between the diameter (or twice the radius) and the circumference of a circle, which is what pi is. Pi is an unchangable ratio a so called 'constant'.

f(x) = y/2 or y = x/2

y axis is the amount of money in the unit you chose but apparently didn't disclose to us and x is the amount candy in the unit pounds.

The reciprocal of a number is the number '1' divided by the number you want the reciprocal of.

So if you want the reciprocal of '3' you have to take '1' and divide it by the number you started with which was '3'.

1/3

You broke one of the rules. You divided by the variable as long as you don't know what that variable is it might as well be 0 so you divided by 0 congrats. Just kidding. You're right in this case but you didn't try to use the formula you simply saw a relationship between 15 and 10 right away.

If the equation was 1/576c^2-17c=0 the problem would be of the same nature but you couldn't solve it that fast the way you did so i really suggest learning how to make use of this \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)if you wanna get a good grade with the coming maths exam.

Bro the reason no one is answering to your question is that you've posted your entire maths homework here. You're not asking for help to understand you're asking these people to literally do your homework so if you wanna learn how to do it yourself post only one of those problems and i will solve it with the work for each step and then you can apply the way I solved them in to the other problems (they're all quite similar).

That is horrible... I really hope having to do unnecessary work like this isn't going to k**l of your curiosity for the wonders and the flawless logic mathematics has to offer.

Mathematics doesn't have a lot to do with being able to solve that by hand or even in your head. There's calculators for that. This site is one of those fancy 'calculators'. If you're teacher is making you solve this by hand then i'm very sorry for you.

| + 24

-> -8z = 40 | *(-1)

-> 8z = -40 | :8

-> z = -5

The 'c' in your equation is the 'x' in this one, the weird +- sign means that you gotta calculate it once for + and once for - (there's usually 2 answers to quadratic equations that's why). The a,b and c in this formula are the factors in front of your variable so 'a' is the first one in front on the c^2, b is the one in front of just the c and 'c' in the formula would be the third one which would then be alone without a variable but you don't have that in your equation so just write '0' where there's a 'c' in this formula.

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

google 'quadratic formula' and do that yourself man

20 ft^2 / 1 ft = 20 ft

20 ft^2 / 5 ft = 4 ft

20 ft^2 / 10 ft = 2 ft

Sry I read x+y > 3.

The answer is 100% - my 12.5% = 87.5%

It's not.

And the mass of the sun is 1.989 * 10^30 kg. No relation tho.

Hope i could help

Greetings

MayD

a+(-b) means you're adding something negative to the number 'a'.

This is exactly the same as simply writing a-b. Think about it for a minute it should make sense.

Hope i could help

Greetings

MayD

12.5%

There's a simple answer to this and a fairly complicated one. I'll hint you the hard one in a short manner and give you the easy one. If you wanna understand the hard one answer to this post. It's quite tricky if you wanna do it by hand every time (involves writing the two points where the secant intersects with your function as (x/f(x)) and ((x+h)/f(x)) (h simply stands for a value that makes sure x and x+h are not the same). But there's an easier way. Unluckily this involves you believing me that what i tell you is true and kinda ruins the whole point of mathematics but whatever here it goes: There's a way of deriving a formula for any function so that what you get is actually the gradient in any point you choose on the original function. You do this by taking your function and lowering the exponent of every term in that function by '1' and putting the number it was in front of the term as a factor to the term. Maybe not the easiest thing to put in words so here's an example:

Modifying x^2 with this method you get 2*x^1 = 2x

3x^4 + x^2 + 7 becomes 4*3x^3 + 2*x (the 7 dissapears since it had exponent '1' and you're lowering that to '0')

The functions you get out of this are the gradients for the secants approaching lenght 0 you talked about in any point 'x' chosen by you.

Example: f(x) = x^2 , f'(x)=2*x

So the function x^2 has the gradient 2*x in point 'x' of the function x^2. This means that if you want to know the gradient in the point, say 4, you have to put '4' in the f'(x) function which is 2*4 = 8.

Hope i could help

Greetings

MayD

There's a way to easily tell whether something can be reduced any further or not.

The way it works is starting from the point that any number can be written as a product of only prime numbers.

16 = 2^4 = 2*2*2*2

45 = 3^2 * 5 = 3*3*5

Now as you can see there are no common prime numbers with this specific pair of numbers you have provided which

indicates that you can truly not simplify this fraction.

Let's add a *2 to the second number and see what happens.

2*3*3*5 = 90

Now this number has one '2' as a common factor with the number 16 which means that you can simplify it by dividing both by two. This works with any number by the way. The way you figure out how to write a number in prime notation is to start from the smallest prime number (2) and see if you can divide your number by that. If so, how often? If not, whats the next higher prime number? Think you get the idea...

Hope i could help

Greetings

MayD

Answer: 6/7

Explanation: There's a little trick to help you if you have to divide two fractions.

3/4 divided by 7/8 is the same as (3/4)/(7/8) and maybe you've already realised that multiplying by half is the same as dividing by two (easiest example for this). If you need a moment to think about why that is take that moment and continue reading when it makes sense to you. Continuing with that logic multiplying by 1/4 is the same as dividing by 4 and multiplying by 1/8, 1/9 or 1/10 is the same as dividing by 8,9 or 10. Actually multiplying by a certain number is always the same as dividing by its 'reciprocal'. The reciprocal of a number is defined as the number one divided by that number.

So the reciprocal of 8 is 1/8, the reciprocal of 5 is 1/5 and so on...

If you've understood why that is you're holding a new power in your hands because now you can derive from that that (3/4) / (7/8) is the same as (3/4) * (8/7) and if you now imagine this as being written as fractions with the numbers under and above a line you can simply multiply together 3*8 and 4*7 to get 24/28 which can be simplified to 6/7.

Hope this helped.

Greetings

MayD