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+118725

fred:
True or False Some cubic equations have no real roots and explain

Hi Fred,

All cubic equations have to have at least 1 real root. (unless you place restriction on the domain)

consider y=ax ³+bx ²+cx+d

As x approaches positive infinity the ax ³ term will have far more impact on the answer than any of the other terms. If a is positive, y will approach infinity.
As x approaches negative infinity the ax ³ term will have far more impact on the answer than any of the other terms. If a is positive, y will approach negative infinity.
(If a is negative it will be the other way around)

In order to get from y= -infinity to y= +infinity the curve must go through y=0 at least once. So there must be at least one real root.

do you understand what I am trying to say?

Here is a web page if you would like to take a look.

http://en.wikipedia.org/wiki/Cubic_function

MelodyDec 9, 2013

+118725

Helpme123:
What is the HCF of 120 and 42 and how do I find it out?

One good way is as follows.
Choose the smaller number which is 42
1*42=42 so 1 and 42 are factors and 42 is the biggest factor of 42. Does 42 go into 120? NO so we'll look for the next biggest factor of 42

2*21=42 so 2 and 21 are factors and 21 is the next biggest factor of 42. Does 21 go into 120? NO so we'll look for the next biggest factor of 42

3*14=42 so 3 and 14 are factors and 14 is the next biggest factor of 42. Does 14 go into 120? NO so we'll look for the next biggest factor of 42 (4 and 5 don't go into 42)

6*7=42 so 6 and 7 are factors and 7 is the next biggest factor of 42. Does 21 go into 120? NO so we'll look for the next biggest factor of 42

Since there is no numbers between 6 and 7 we have now found all the factors of 42 so the next biggest one must be 6
does 6 go into 120? YES
So 6 must be the Highest common factor.
---------------------------------------------------

It might have been easier just to write down all the factors of 42 then put them in order and then look which ones go into 120 and select the biggest one.
1,42,2,21,3,14,6,7
1,2,3,6,7,14,21,42
The biggest one that goes into 120 is 6
So 6 must be the Highest common factor.

MelodyDec 9, 2013

+118725

oman:
soppose a new breed of rabbits triples its population every month,if there are three rabbits after one month the population is after n months would be 3 to the power of n " please i need help.

I am not sure what your question is Oman but I will talk about the situation that you are describing

After 1 month, when n=1 Population=3=3 ¹
After 2 months when n=2 Population=3*3=3 ²
After 3 months when n=3 Population=3 ²*3 = 3 ³
can you see the pattern?
for any number of months 'n' the population will be 3 ⁿ

I hope that helps.

MelodyDec 9, 2013

+118725

1/5(a+3)=1/3(5-a)

Hi Sam
First I'm just going to talk about the left hand side LHS
it would be good if you realize that
1/5(a+3) = 1/5 * (a+3)/1
if you write this as an upright fraction you will be able to see that it isthe same as 1*(a+3) / (5*1) = (a+3)/5
so your equation would more usually be written as
(a+3) / 5 = (5-a) /3
Please write these fraction upright, it will make it much easier to see what is happening

3 and 5 are both denominators and they have no common factors and 3*5=15
If you multiply both sides by 15 then the denominators will cancel out and there won't be any fractions any more.
Then you just expand the brackets and solve like any other non-fraction equation.
Can you do the rest yourself?

MelodyDec 9, 2013

wait no -16

GuestDec 9, 2013

[math] yup

GuestDec 9, 2013

as fas as I understand the question
4x^3 x 3x^4

go 4x3 = 12
and the exponents add: 3+4=7

answer: 12x^7

GuestDec 9, 2013

f(x) = 5x
g(x) = x/2

f(g(12)
1) g(12) = x/2 .... 12/2 = 6
g(x) = 6
2) f(6) = 5*6 = 30

f(g(12) = 30

GuestDec 9, 2013

Dec 8, 2013

284.61538%

GuestDec 8, 2013

please buy lots of cats

GuestDec 8, 2013

as many times as you want to or can afford

GuestDec 8, 2013

+3146

Melody:
I did your question and got 41.07 hours

[input]70000*3^(x/4)=112000[/input]
x=1.7112629599857806 days = 41.07 hours

adminDec 8, 2013

+3146

NickOs:
Is there any other way of finding the answer for this except for doing the operation?
2^0+2^1+2^2+…+2^63

2^0= 1
2^0+2^1= 3
2^0+2^1+2^2= 7
2^0+2^1+2^2+2^3= 15
...

1=2^1-1
3=2^2-1
7=2^3-1
15=2^4-1
...
2^0+2^1+2^2+…+2^63= 2^64-1

adminDec 8, 2013

+118725

how to put a minute sign

Hi asdasd

If you want to write
35degrees, 14minutes and 12seconds

you could do it like this

35 ^o 14' 12"

On the calculator you have a button with ^o ' "
You use that button for angles and for time.

So one apostrophy is the symbol for minute.
does that answer your question?

MelodyDec 8, 2013

+118725

а где это знак а и б 2пиф
(translation for Russian)
and where is the sign of a and b 2pif

I am sorry amah,
I don't understand your question.
Maybe it you write it a different way, it might translate better.

Я сожалею, амаh,
Я не понимаю ваш вопрос.
Может быть это вы пишете это другому, он может перевести лучше.

MelodyDec 8, 2013

+118725

Hi Yolo,

There are lots of answers

The answerer gave you a good one.

How about

Q ³ - S ² = 36341

AND

S - Q = 88303

MelodyDec 8, 2013

+118725

hi Kgirl

what does a logistic graph look like?

f(x) = 1 / (1+e ^-x)
logistic sigmoid fuction.JPG
And here is an artical about it.
http://en.wikipedia.org/wiki/Logistic_function
-------------------------------------------------------------------------------------------------------------

This stuff under here is probably irrelevant but I did it before I realized so I'll just leave it there now.

Or did you meant what do logarithmic graphs look like?
Here are 2 examples.

log graphs examples.JPG
----------------------------------------

do you know what y = 10 ^x looks like?
and, do you know what y=x looks like?
If you reflect y=10 ^x across the line y=x then the new curve will be y=log x (that's y=log of x base 10)

I'll see if I can draw the graphs to show you.

log illustration.JPG

There you go, can you see how they are reflections of each other? Graphs that reflect across the line y=x are called inverse graphs.

I hope that I have answered your question.
Melody.

MelodyDec 8, 2013

+118725

Hi this guy,
This is a you tube clip that I found for you.
don't worry about part c, especially if you haven't done any calculus yet.
but part d is almost the same as your questions.
Go through it and try to understand.

I did your question and got 41.07 hours. I think that's about 41 hours and 4 minutes.
See if you can work it out and if you can't post again to get some more help.

https://www.khanacademy.org/math/trigonometry/exponential_and_logarithmic_func/exp_growth_decay/v/exponential-growth

Happy calculations
Melody.

MelodyDec 8, 2013

+118725

Hi Nicko,

Is there any other way of finding the answer for this except for doing the operation?
2^0+2^1+2^2+…+2^63

This is the sum of a geometric progression GP for short.
Each number in a number pattern can be called a term, So you have a 1st term, a second term etc.

These are examples of GPs
5,50,500,5000 because each term is 10* the term before it
120,60,30,15.7,5, because each term is 0.5 * the term before it
Any number pattern where the next number is found by multiply the one before by a specific number (r) is called a Geometric progression
r is that specific number it is called the common ratio
because
r = term3/term2 = term5/term4 = any term/the term before it.

What is r in your series ? That is, what is each term multiplied by to get the next term?
You also need n.
n is the number of terms that you want to add together, Be careful, the answer is not 63, can you see why not?
a, also called T ₁ is the first term.

The sum of a GP is given by the following formula

Sn = a(r ⁿ-1) / (r-1)

When you work out what a,r and n are then you can substitute them in and work out what the answer is.
It is a very big number so your calculator will probably give the answer in scientific notation
If you use the web2.0calc, it will give you the answer in normal notation

MelodyDec 8, 2013

+118725

5.52=a*-2

Hi Viktor,

Guest, you had the right idea but you got a bit muddled up.

5.52=a*-2

a*-2 divided by -2 = a
You can do that so long as you do it to the other side as well.

5.52 divided by -2 = a*-2 divided by -2

you can finish it I think.

MelodyDec 8, 2013

+118725

I think that this is your second cone problem.
This is the answer that Ialready gave you

What is volume of cone
a cone is a circular pyramid. (because the bottom of a cone is a circle and then it goes up to a point at the top.)
The volume of any pyramid is 1/3 * the area of the base * the perpendicular height
The base is a circle so it's Area is pi * r^2
so,
The volume of a cone must be 1/3 * pi * r^2 * h

Now lets look at your next problem.
What is a volume of cone which have 28mm height and 132mm circumference of base?
You have the height so that is good.
You have the circumference and you should know that the circumference of a circle is 2*pi*r
So you can set up an equation for the circumference and then solve it to find the value of r
Once you have r you can work out the volume of the cone.

MelodyDec 8, 2013

+118725

What is volume of cone

a cone is a circular pyramid. (because the bottom of a cone is a circle and then it goes up to a point at the top.)

The volume of any pyramid is 1/3 * the area of the base * the perpendicular height

The base is a circle so it's Area is pi * r^2
so,

The volume of a cone must be 1/3 * pi * r^2 * h

MelodyDec 8, 2013

+118725

1/1+x

Divide has to be done before plus and 1/1 = 1

so the answer is just 1+x

MelodyDec 8, 2013

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