All Answers 358087 Answers

No of course they are not always good at maths

$$\sqrt[3]{216} = 216^{(1/3)}$$

216^(1/3)

$${{\mathtt{216}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)} = {\mathtt{5.999\: \!999\: \!999\: \!999\: \!999}}$$

That is rounding error - The answer is 6

if x+1<0

then 

x<-1

There are NO positive integers that will make this true!

Want to fly to the moon with me Melody? :)

https://www.youtube.com/watch?v=eQPiV_cauyI

WOW!    WOW!    WOW!

Only 42 folds.

That is incredible.   

Maybe the moon is closer than I thought   LOL

Thanks Alan     

$$2a+4b-8c=2(a+2b-4c)$$

if f(x)=3x find (i)f(1) (ii) f(3) (iii) f(4) (iv) f(6)

$$\mathbf{~ f(x) = 3\cdot x ~}$$

(i) f(1) 

Set x = 1

$$\small{\text{$
f(1) = 3\cdot 1 = 3
$}}$$

(ii) f(3)

Set x = 3

$$\small{\text{$
f(3) = 3\cdot 3 = 9
$}}$$

(iii) f(4)

Set x = 4

$$\small{\text{$
f(4) = 3\cdot 4 = 12
$}}$$

(iv) f(6)

Set x = 6

$$\small{\text{$
f(6) = 3\cdot 6 = 18
$}}$$

I don't get this question.   

Thanks SoulReaper, that is a good answer   

Anon, If you are serious about understanding, this post might help.

you can try answering the questions too if you want to.   After you finish I can give you the answers.

http://web2.0calc.com/questions/positive-and-negative-numbers-directed-numbers

1) Now -3+8 Start at -3 and go 8 in the positive direction and what do you get? 
2) Now 4 - 9 start at 4 and go 9 in the negative direction and what do you get? 
3) Now -2- 8 start at -2 and go 8 in the negative direction and what do you get? 
4) 0-8= 
5) -2-+6= 
6) 1-4+(-7)= 
7) -9++4 = 
8) 13+(-5)= 
9) -4 x 6 = 
10) 3 x -6 = 
11) -5 x -3= 
12) 20 / -4= 
13) -8 / 2= 
14) -15 / -5= 
15) +4 x +7=

2¹⁰ is 2¹*2⁹ so I just combined the 2⁹ with the 7⁹ to get 14⁹

I couldn't see any other combination giving a lower result (the original expression results in a sum of 28), though I guess I haven't actually proved that 26 is the smallest possible value.

.

Try the Texas Instruments TI-Nspire or the Casio FX-CP400, for example.  More generally, do a search on CAS calculators   (CAS stands for Computer Algebra System).

.

Thanks Alan and Heureka,

Anon, are you happy with these 2 great answers or were you needing a calculus answer?

2a+|a|/a

If a > 0 them

2a+a/a = 2a+1

if a<0  then   |a|=-a        for instance     |-6|=6     and   6= -(-6)

2a+-a/a = 2a-1

1487.7  = 6.5x - 12.3*e^-1.5x

Must have x>0 as the RHS is negative for x<0.

As x gets larger than zero the exponential term gets smaller and smaller, so an initial estimate for x might be to assume the exponential term is so small it's negligible. This will result in an initial guess for x as

x0 = 1487.7/6.5

$${\mathtt{x0}} = {\frac{{\mathtt{1\,487.7}}}{{\mathtt{6.5}}}} \Rightarrow {\mathtt{x0}} = {\mathtt{228.876\: \!923\: \!076\: \!923\: \!076\: \!9}}$$ 

With this value for x, how big is the exponential term?

$${\mathtt{12.3}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{{\mathtt{\,-\,}}\left({\mathtt{1.5}}{\mathtt{\,\times\,}}{\mathtt{228.866\: \!823\: \!076\: \!923\: \!076\: \!9}}\right)} = {\mathtt{0}}$$

It's not really 0, it's actually about 2*10^-14, but it is small enough to ignore for most purposes!

.

inverse cos is the same as arc cos

use   acos

Congratulations MG     

It certainly is, but I need one to be used at school. 

How did you do this Alan?

This is the best online calculator!!!!!!!!!

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NO      $$0^0$$      is undefined !!

Thanks anon  

And I already answered it.

Please follow the rules for reposting     - we do not have time to answer the same question twice !

Side X side.

Chris and I have both answered some of your questons Awesomeee   ;)

What does aops stand for :/