FWIW, I got the same answer as fiora.

☼☼☼

if I'm not mistaken you could be trying to find the volume of a sphere.

$${\frac{{\mathtt{4}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{{\mathtt{3}}}$$

$${\frac{{\mathtt{4}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{27}}$$  Now put this into your calculator to get . . .

113.0973 (4 d.c.p.) cubed units

In short, dividing by 1/3 = multiplying by 3.

Look at this example. . . 

$${\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{2}} = {\mathtt{8}}$$

$${\frac{{\mathtt{4}}}{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}} = {\mathtt{8}}$$  

$${\frac{{\mathtt{4}}}{{\mathtt{0.5}}}} = {\mathtt{8}}$$

See how there are 8 0.5's in 4?

Look at this also . . .

$$\frac{1}{2}\times{\frac{4}{5}=\frac{4}{10}=\frac{2}{5}$$

$${\frac{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}{\left({\frac{{\mathtt{5}}}{{\mathtt{4}}}}\right)}}$$=$$\frac{1}{2}\times{\frac{4}{5}=\frac{4}{10}=\frac{2}{5}$$

Instead of dividing by a fraction we flip the denomonator and numerator and then multiply by the fraction. Notice how 3 can be written as 3/1, which when it is flipped is 1/3.

Also when you are dividing by a third, you are seeing how many thirds go into a number, so it makes sense that there are 3 times more thirds in a number than 1's, because 1/3 goes into 1 3 times. 1/1 can be written as 3/3.

I may have overcomplicated this/been confusing but I hope I helped :) 

Actually go on Instagram or Facebook..? Or something.

You can chat at stuff on this website but most people do it rarely or even don't . but mainly on special occasion

This is for maths.

I thought you were going to do like a post. 

Here's (14)

.002 = e^(-.00012* t)      take the ln of both sides

ln .002 = ln e^(-.0002 * t)    and we can write

ln.002  = (-.00012 * t) ln e      and ln e = 1, so we can ignore this......so we have

ln .002  = -.00012 * t       divide both sides by -.00012

t = ln .002 / -.00012  = about 51,788 years old

$$3y+5x=18$$

$$3y=18-5x$$

$$y=6-\frac{5x}{3}$$   or  $$y=\frac{18-5x}{3}$$

$$3y+5x=18$$

$$5x=18-3y$$

$$x=\frac{18-3y}{5}$$

Hello :)))

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{96}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{10}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\mathtt{2\,314}}}}{\mathtt{\,-\,}}{\mathtt{48}}\\
{\mathtt{x}} = {\sqrt{{\mathtt{2\,314}}}}{\mathtt{\,-\,}}{\mathtt{48}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{96.104\: \!053\: \!883\: \!222\: \!773\: \!6}}\\
{\mathtt{x}} = {\mathtt{0.104\: \!053\: \!883\: \!222\: \!773\: \!6}}\\
\end{array} \right\}$$ 

Determine x such that  10^x = 2.278768 x 10⁴²

So, taking log_x of both sides, we have

x·log₁₀(10) = log₁₀(2.278768) + 42•log₁₀(10)

x = 0.3577001 + 42

   = 42.3577001   (Answer)

It's difficult to check this on a calculator, so to verify the approach repeat it but using an example you can realistically evaluate on a calculator, e.g.,

Determine x such that  10^x = 2.278768 x 10⁴

and if after you determine the value of x you check that the right side equals the left here, you may conclude that your answer in the first part should be right, too.

🚬   🚬   🚬   🚬

Here's  (15)

199200  = 80000(1 + r)⁵     divide both sides by 80000

2.49  = (1 + r)⁵       take the log of both sides

log 2.49  = log (1 + r)⁵    and we can write

log 2.49 = 5 log ( 1 + r)    divide both sides by 5

log2.49/5 =  log (1 + r)     

.079 = log(1 + r)   and in exponential form ,we have

10^.079 = 1 + r

r = 10^.079 - 1   = .20  = about 20% per year

Hi Fiora,  welcome to the forum.  

Did I talk to you before and suggest that you join and that you take that icon?

It looks great :))

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   Edited: this was wrong 

I am going to sleep.See you everybody

Men, I had been working on this several days,recently figured this out.... 

i stand for sqrt -1 ......and i might not be here aftet a minute....

Suppose you were required to add:

7 + 6 + 24 + 12 + 1

You could regroup as:

(7 + 12 + 1) + (6 + 24)

This is now easy to add in your head:

(20) + (30)

= 50  (Answer)

 ♞ ♞ ♞

972 pi  = (4/3) * pi * (r^3)     divide both sides by pi

972  = (4/3) * r^3      multiply both sides by 3/4

729 = r^3      take the cube root of both sides

9 = r    and the diameter is twice this  = 18

e^-x = 9/2    this is equivalent to :

e^x = 2/9       take the ln of both sides

ln e^x = ln (2/ 9)    and we can write

x ( ln e ) = ln (2/ 9)       and  ln e = 1   ....  so  .....

x = ln (2/9)  ≈ -1.504

6N + 8 = 32      subtract 8 from both sides

6N = 24             divide both sides by 6

N = 4      and that's the number.....!!!!

Great pic anon,

If you joined up a square out of there would make a great icon for you :)

Let's see.......

2 quarters  1 nickel

1 quarter  3 dimes

1 quarter 2 dimes  2 nickels

1 quarter  1 dime 4 nickels

1 quarter 6 nickels

5 dimes 1 nickel

4 dimes 3 nickels

3 dimes 5 nickels

2 dimes 7 nickels

1 dime 9 nickels

11 nickels

I think that's it......did I leave anything  out ???

This is a line so you only need to know two points.

when x=0   y=40+40*0 = 40+0=40     so that is  (0,40)

when x=1   y= 40+40*1=40+40=80   so  (1,80)  is another point

NOW just plot these 2 pointsand rule a line between them :)

-3y=-12x+24   →  y = 4x + 8

-y=-x+40     →      y = x - 40

b) one solution......these are lines with different slopes......such lines will always intersect at one point.

10 to the power of 12 would simply be 1 with 12 zeroes so basically, 1,000,000,000,000 so one trillion i guess

Thank you Geno! My own answer was way off the grid.

sin of any angle must be between -1 and +1` so this question has no answer. :)