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**Hannibal lecter**- Replies: 1

Bob wrote:

Let's say you want to do 1 / 3 as a decimal.

Let's try 100 / 3 first.

100 - 3 = 97 97 - 3 = 94 Oh dear! This will take ages. Let's speed it up by taking 30 at a time.

100 - 30 = 70 70 - 30 = 40 40 - 30 = 10

Now I haven't got enough left to take another 30 so I'll switch to taking 3s.

10 - 3 = 7 7 - 3 = 4 4 - 3 = 1

Now I haven't got enough to take any more 3s so I'll switch to taking away 0.3 each time.

1 - 0.3 = 0.7 0.7 - 0.3 = 0.4 0.4 - 0.3 = 0.1

This is going to go on forever because I always get a bit left over.

If I was setting this out as a division the answer space would have this:33.333333

If I want to do 1 / 3, it's exactly the same except the decimal point shifts two places left.

1 / 3 = 0.33333333

Bob

I understand everything now completely but that last segment of your post it's a little not clear to me

because you take 100 - 3 until you reached 40 - 30 = 10 then stopped (first time)

then you take 10 - 3 = 7 until you reached 4 - 3 = 1 then stopped (second time)

finally you take 1 - 0.3 = 0.7 until you reached 0.4 - 0.3 = 0.1 then stopped (third time)

so the number would be 0.3? right? it's 3 times right?? how it's 33.333333 or 0.33333333 it should be 0.3 right

So we record that in the answer space as not 4 subtracts but 0.4 subtracts because we shifted the carriage one place.

I mean we made 15 become 1.5 the number is changed who gives the right to do such a thing is that legal in math and clearly understandable? is there explaintion for that ..

I mean we chose a different number it's 1.5

I can't imagine that is there interactive example like 6 apples iver 16 people

First you try 6 - 15. Cannot do that as you're trying to take away too much. So 'shift the carriage' and try to take away 1.5s. You can do that exactly 4 times; 6 - 1.5 - 1.5 - 1.5 - 1.5 = 0. So we record that in the answer space as not 4 subtracts but 0.4 subtracts because we shifted the carriage one place.

bob why we can't do repeated subtraction

like 8 ÷ 4

8 - 4 = 4 (1 time)

4 - 4 = 0 (1 time)

then the result is 2

why in 5 ÷ 16 you said (Cannot do that as you're trying to take away too much)

what you mean by that can you please explain further to me

and after that you said :-

, so 'shift the carriage' and do 1 - 0.6 = 0.4. You can do that once but then there's not enough left to do it again.

what you mean by "there is not enough left"

can you please explain that further for a beginner

Bob wrote:++++++++++++++++++++++++++++++++++++

I'm old enough to have used mechanical calculators to do arithmetic.can you please tell me or send me a photo of that mechanical calculators and where to do you have a similar links to buy it from amazon or ebay

And to do division you had to do repeated subtraction.

++++++++++++++++++++++++++++++++++++I couldn't understand how division is a repeated subtraction

++++++++++++

example. If the calculation was 48 divided by 6 you would set up 48 in the register, then set up 6 as the amount to subtract, and then wind the handle backwards so the display showed 42, then 36 then 30 and so on until zero was showing. A side register would show how many times you had turned the handle and it would be showing 8 in the case.

++++++++++++but 48 divided by 6 is 8 directly how could it displayed 42 at first from where did we get this number even in papers couldn't find it

++++++++++++

If the calculation was 1 divided by 8 the procedure was as follows:

Now you are subtracting 0.08 each time.1-

0.8

0.2-

0.08

0.012

++++++++++++

the number is 0.08?? is very ambiguous to me, from where we get that number even in papers I tried a lot I couldn't figure it

you said " subtracting 0.08 each time "and thanks you so much you understand what I want it's really my problem I can't understand division process

**Hannibal lecter**- Replies: 10

What is the concept of dividing small number over a larger one (ex: 1/6)

1/6=0.16666666666

is 1 divided into 6 pieces and become 0.16666666666

and these pieces called units of 1 or something like that?

so 0.16666666666 * 6 = 1

what is the concept of this division and why number one cut into pieces and become exactly 0.16666666666

how to measure that or represent it on Number line!

also when calculation 0.16666666666 * 6 it's 0.99999999996 not 1 !!!

and is there a resources and math books to illustrate this but not YouTube channel please it's only give the ways to calculate it not explantion.

and I have example of a second problem it's 6/15 as following in the picture ..

my question is who gives as the rights or standards to put zero down? (u will see what I mean from the picture)

and my second question is who gives as the right and standards to place a decimal point (you will see that also from the picture)

**Hannibal lecter**- Replies: 1

The university bookstore has a Kilobyte Day sale every October 24, giving an 8 percent

discount on all computer accessory purchases if the price is less than $128, and a 16 percent

discount if the price is at least $128. Write a program that asks the cashier for the original price

and then prints the discounted price

solution :

{

If original price < 128

discount rate = 0.92

Else // i't mean if the other condition true which is (if original price ≥ 128) but the problem not here!

discount rate = 0.84

discounted price = discount rate x original price

}

my problem is what is the meaning of 0.92?

and what is the meaning of 0.84?

in the exercise it said discount only 8% mentioned and 16%, from where did we get 0.92 and 0.84???

because I solve it like that :

discount price = original price - DiscountedValue

example : 110

discount price = 110-8.8 // because discountPrice will be (8/100 * 110 = 8.8)...

this way of mine is gives the same answer! why the book used something like that and how the book find that rate?

**Hannibal lecter**- Replies: 2

Hi,

which logic gate gives :

x y result

0 0 1

0 1 0

1 0 1

1 1 0

this is the question :

if (A = '1') and (B = '1') then tempY <= '0';

elsif (A = '0') and (B = '0') then tempY <= '0';

else tempY < = '1';

end if;

if (A = '0' and B = '0') then tempZ <= '1';

elsif(A = '0' and B = '1') then tempZ <= '0';

elsif(A = '1' and B = '1') then tempZ <= '0';

elsif(A = '1' and B = '0') then tempZ <= '1';

end if;

end process;

Y <= tempY;

Z <= tempZ;

Y is an xor gate

but what is z

my problem was I tried to start to solve it row by row not the column f first then column g so sorry

now I remamber and completely understand

**Hannibal lecter**- Replies: 2

If g(x) is an even function then f(g(x)) is even for every

function f(x).

solution :

True. We have g(−x) = g(x) since g is even, and therefore f(g(−x)) = f(g(x))

is that mean wherever I compose f(even function input) the output will be even?

**Hannibal lecter**- Replies: 2

Hi please see this question in the following pic :

I tried a lot to solve it and to complete the table values but it didn't work for me

I know composed function and studied it and know how to calculate functions like f(g(x)) or f(f(x)) .. etc but I stopped in this exercise

I don't know what is my weak point that made me stop from solving and understanding it, the silly thing that I got the solution and still don't understand it!

solution from solution book :

thanks, and how to think in reverse? for example :

the answer of 36. is f(x) = x^3 , g(x) = x + 1

and Answer of 39. is f(x) = e^x , g(x) = 2x

can you tell me what is the step of thinking to extract the inside function and outside function?

why not g(x) = x^3 , and f(x) = x+1 is that possibles. it's very difficult to determine them in just looking at them please tell me how to think to find them in any question

**Hannibal lecter**- Replies: 3

if

and

the book solution :-

why is that? it should be

which isbecause

is wherver I find x I should double it so when I found I should replace the x by x^2hence will be

am I right? If I'm not right why how should I look to the problem.

I saw it goes up a little so I thought it didn't moved to the left sorry now everything is clear I use a grapher not by hand

do you advice me to plot things on paper or keep using grapher computer?

**Hannibal lecter**- Replies: 3

In math whatever we plug number to x it shift it horizontally but if plug it like that f(x) +1 it shifted it vertically

But my problem in e^x it shifted on y-axis when I plug 1 for example. what is the secret behind that

Like e^(x+1)

It should shift the e^(x+1) to the left! But it’s didn’t happen why

Like x^2 when plug +1 which became (x+1)^2 it shifted it to left! Correct

**Hannibal lecter**- Replies: 1

Hi,

int number 123456;

int firstDigit;

int totalDigits = (int) Math.log10(number);

firstDigit = (int) (number/ (int) Math.pow(10,totalDigits));

System.out.println("First Digit is: " + firstDigit);

how could log10 of a number like 123456 is 5?

I type that in google and it's 5.09151220163 not 5, I know we used casting so it discard the fractional parts to get 5, but my question is not about the Java it's about log10 why log10 always get the total digits with fractional parts always!

like log10 of 532 is 2.7259116323 which is 2 digits that is working! but how mathematically is that

how can Math.log10(12345) calculate the number of digits which is 5 correct!?

only that first part of the code is really ambiguous

so you mean for example :

for (1,1)

(1 % 2) + (1 % 2) = 1 + 1 = 1 white, is this the way I apply by numbers? am I correct

and please why the book in the end used additional mod :

color = ( (row % 2) + (column % 2) ) % 2

look he used again %2!! he found sum of reminders than take mod 2 again? why? and where locations should I apply this formula only in the last row? because he said "fourth entries" is he mean the last row, isn't enough to use only (row%2) + (col%2)

**Hannibal lecter**- Replies: 3

Hi, I have this problem the solution it needs is not advanced not using "if and else statement" the book needs to see the answer with simple algebra.

I have the question and the solution but it's not understandable completely expect I know that we need mod 2 (ODD and even) in my solution.

A robot needs to tile a floor with alternating black and white tiles. Develop

an algorithm that yields the color (0 for black, 1 for white), given the row and

column number. Start with specific values for the row and column, and then

generalize

////// solution of the book start

Solution of the book :

Clearly, the answer depends only on whether

the row and column numbers are even or odd,

so let’s first take the remainder after dividing by 2. Then we can enumerate all expected

answers:

In the first three entries of the table, the color

is simply the sum of the remainders. In the

fourth entry, the sum would be 2, but we want

a zero. We can achieve that by taking another

remainder operation:

color = ( (row % 2) + (column % 2) ) % 2

////// solution of the book Ended

pls explain the book solution only I want to understand it step by step I didn't understand what he mean by dividing

note that the dividing here is integer division ex : 3/2 = 1 not 1.5 because it discard the fractional part

I didn't understand the solution from beginning like " first take the remainder after dividding by 2"

which reminder? and what number we are dividing it by 2 ?

the solution is confusing be and ambiguous

Mathegocart wrote:

Hello,

See:

https://i.postimg.cc/rs1py38L/mathclarificationopaque.png

thank you a lot

**Hannibal lecter**- Replies: 4

**Hannibal lecter**- Replies: 1

how cold write

to becomeis there simple another example by numbers only without variable to illustrate this because I'm so beginner in these algebra

**Hannibal lecter**- Replies: 1

what is microfabrication related to mathematics?

if anyone have ideas, comments, opinion, on that topic please talk here

Mathegocart wrote:

How so? As zetafunc mentions above, the function

is equivalent to the function you mentioned, and the equation is continuous.

can you please see this YouTube link it talked about it and it said there is differences :-

https://www.youtube.com/watch?v=VmxESGI4zdA&t=18s

also see this sheet pls :

Mathegocart wrote:

Yes, the equation does represent continuous growth. As noted, you can convert that equation into the form of the continuous standard equation

with the substitution mentioned above.

I think it's not right, because I found the answer today

the form model without e and k like this :

is called non-continuous exponential models functions

because in case of increasing (a>1) while in case of model contain e, and k, if k is positive it's increasing continuously rate (because any positive number is acceptable and in case of base a there is numbers less then 1 are positive but not included)

and in case of decreasing (0<a<1) while in case of e, and k, here k is has to be negative <0 so it's continuously decreasing rate

so now

its growth rate is not continuous,

am I right?

by the way I learned this today from a YouTube channel but I still don't understand why we can't called the base a a continuous if it's >1

I knew because it doesn't included the numbers that less than 1 and bigger than 0

but why? why this is a reasons that we can't call it continuously, what is meaning continuously in this case anyway? because every graph I draw in form of non-continuous exponential models I see them clearly in my naked eyes that they are continuous, I draw these random examples as in example I see them all goes beyond without end