prove that x^15+x^5+2=0, do not have positive roots?

Let's write x^5 = y

Then we get:

y^3 +y +2 = 0

y^3 +y = -2

y(1 +y^2) = -2 

y =-2 or y^2 +1 =-2

We solve y^2 +1 =-2

y^2 = -3

y doesn't have any solution among the real numbers R.

y = √-3 = √3 *i or -√3 *i

To sum it up: y = -2 or y = √3 *i or y = -√3 *i

x^5 = y

...

a tangent is a line that just touches the curve.

When I say that the slope and is decreasing with time I mean the gradient of the tangent of f(t) is decreasing.  It is becoming less steep as the time increases.

Lets look at these velocity verses time graphs.

For  A, C and E the velocities are increaing with time.

A is incresing uniformly so acceleration is a positive constant.

C is increasing at an increasing rate (the tangent to the curve is becoming steeper, the curve is concave up)

Hence, for C the acceleration is positive and increasing.

E is increasing at a decreasing rate ( the tangent to the curve is becoming less steep, the curve is concave down)

Hence, for E the acceleration is positive and decreasing, at the end of the curve the acceleration has become 0.

For D,and F the velocities are decreasing with time. (Although they are both traveling in a positive direction)

D is decreasing at a decreasing rate (the tangent to the curve is becoming less steep, the curve is concave up)

F is decreasing at an increasing rate (the tangent to the curve is becoming more steep.  The curve is concave down)

B is speeding up but in a negative direction.  The acceleration is constant and negative

G, H and I have zero acceleration.  G is stop so velocity is zero, H has positive velocity and I has negative velocity.

I think these are all okay but Alan, could you please check what I have said.   

The answer is 6

Yes!! And so can pigs!!!

What is 3 to the power of 5 +9 to the power of 2

I assume you mean 3^[(5+9)^2]

Start by adding the addends in the round paranthesis, 5+9=14:

3^(14^2)

Multiply 14 by itself: 14^2= 196

3^196 

Multiply 3 with itself 196 times. Since this is done by hand, you better have a few clean pages in your notebook:

3^196= 

3279185047850305794305942247355304034928808057449314765118209404186327048164224481412156778321 ≈ 3,3*10^93

@@ End of Day Wrap        Sun 28/9/14        Sydney, Australia      Time 11:45 pm      ♬  

Hello everyone,

Our great answers today were delivered by Alan, Geno3141, NinjaDevo, CPhill and Quinn. A very big thank you to each of you.    

Now for the interest posts:

1) A Circuit called Infinite Loop and a place called Useless Loop LOL

Thanks alot but can you tell me the best way to know the behaviour of the slope specially with concave functions ! not the straight line functions 

The last one is A.  The object is slowing down at a decreasing rate.

the velocity is pos at the begining and near zero at  the end so it must be slowing down.

The gradient of the curve is slowly decreasing so the rate is decreasing (the curve is concave up)   

The middle question I am not so sure about.  The question does not talk about the acceleration at all.  

 I don't think enough info is given.

Maybe Alan will come back and help us out here.  

The first one is C,  velocity is negative because the object is moving in a negative direction.

The acceleration is also negative because the object is covering more ground in each equal time period and it is speeding up in a negative direction.

We have confirmed it ......the answer is   2 !!!!!!!

We have

2log25 - 3log5 + log20

2log(5*5) - 3log 5 + log (4*5)

2log 5 + 2log 5 - 3log 5 + log4 + log 5      combine like terms

5log5 - 3log 5 + log4 =

2log5 + log 4 =

log5² + log 4 =

log 25 + log 4 =

log (25*4) =

log 100 =

2

Great work anon.    

I'm just going to look at it a slightly different way. 

$$\\2log25 - 3log5 + log20 \\
=2log5^2-3log5+log4+log5\\
=4log5-3log5+log2^2+log5\\
=2log5+2log2\\
=log25+log4\\
=log100\\
=log10^2\\
=2log10\\
=2*1\\
=2$$

You beat me Alan.   

You can take it just a little further Anonymous:

2log(5) + 2log(2) = log(5²) + log(2²) = log(25) + log(4) = log(25*4) = log(100) = 2 (assuming log to the base ten)

2log25 - 3log5 + log20 =

2 log (5*5) -3 log 5 + log (2*2*5)

We know that: log (a*b)= log a + log b:

2 (log 5 + log 5) -3 log 5 + log 2 + log 2 + log 5=

4 log 5 - 3 log 5 +log 5 + 2 log 2=

2 log 5 + 2 log 2

25/50

First, get the denominator to 100. This can be done by multiplying both the numerator (top) and denominator (bottom) by 2:

50/100

Divide 50 by 100:

0,5

Mon 29/9/14

1) do donkeys fly?  What a silly question.

This is the answer to that question.

$$2\sqrt3=\sqrt4*\sqrt3=\sqrt{12}$$

$$4\sqrt{27}=4\sqrt{9*3}=4*3*\sqrt3=12\sqrt3$$

That is sweet Rosala, you must have a day for EVERYTHING in India.   

Λυπάμαι, αλλά η μετάφραση δεν έχει νόημα.    

Thanks Chris.

The forum calc uses $$atan\;1.345$$  but a more common notation (meaning exactly the same thing) is    $$tan^{-1}1.345$$

Please note: the forum calc is on the home page.  

are you really that stupid?

This question doesn't make sense...we have more people "ticking" than are in the survey !!!!

Maybe we could figure this out with  "clock" arithmetic ?????