All Answers 358136 Answers

Have you written them down correctly?  These two functions are clearly not equivalent.  For example:

Lengths scale as the square root of areas.  So, as heureka has calculated,

$${\mathtt{radiusofRhea}} = {\sqrt{{\frac{{\mathtt{34}}}{{\mathtt{3}}}}}}{\mathtt{\,\times\,}}{\mathtt{1\,530}} \Rightarrow {\mathtt{radiusofRhea}} = {\mathtt{5\,150.747\: \!518\: \!564\: \!660\: \!29}}$$

Note that this is 5150km to the nearest ten kilometres.

One to one means that if 'a' goes to 'b' then 'b' goes back to 'a'.  So f^-1(12) = 5

Looks like his maximum profit is $425 a day

You don't say what x is!  I've assumed it's the height of the vertical parts.

$$\begin{array}{rll}
-5(2x-1)&=&3(x+4)\\
-10x+5&=&3x+12\\
-13x&=&7\\
x&=&\frac{7}{-13}\\\\
x&=&\frac{-7}{13}
\end{array}$$

If you do not understand any of the steps I will go over them for you.

 $$x^{
(\frac{7}{3})
}=x^{2.\bar{3}}$$

I interpreted it differently from you Kitty but when I read the question again your interpretation is the correct one.

You found the intersection I was going to find the union. 

 $$\boxed{\mbox{Surface area of a sphere: } \quad S=\pi d^2}$$

$$S_{Titan}=\pi d_{Titan}^2$$

$$S_{Rhea}=\pi d_{Rhea}^2$$

$$\dfrac{S_{Titan}}
{S_{Rhea}}
=
\dfrac{\not{\pi} d_{Titan}^2}
{\not{\pi} d_{Rhea}^2}
=\dfrac{34}{3}$$

$$\dfrac{d_{Titan}^2}
{d_{Rhea}^2}
=\dfrac{34}{3}$$

$$d_{Titan}^2=d_{Rhea}^2*\left(\frac{34}{3} \right)$$

$$d_{Titan}=d_{Rhea}*\sqrt{\left(\frac{34}{3} \right)} \quad | \quad d_{Rhea}=1530\;km$$

$$\textstyle{d_{Titan}=1530\;km*\sqrt{\left(\frac{34}{3} \right)} =1530\;km*3.36650164612 = 5150.75\;km\approx5151\;km}$$

Diameter of Titan is 5151 km

Between 1 and 2009, how many numbers are multiples of 5 and 7?

Since the numbers must be multiples of 5 AND 7, it would be easier to just find multiples of 7 that end in 5 or 0. For example, 7*5 = 35, 7*10 = 70, 7*15 = 105, . . 140, 175, 210, 245, 280, 315, 350, 385, 420. . .  

Notice the pattern: 7 is simply being multiplied by multiples of 5. So a faster way to find the number of multiples of 5 and 7 from 1 - 2009 would be to divide 2009 by 7, = 287. The closest multiple of 5 under 287 is 285.

Then, divide 285 by 5, = 57. So there are 57 multiples of both 5 and 7 between 1 and 2009.

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Actually, there is a much simpler way (oops):

The least common multiple of 5 and 7 is 35. Divide 2009 by 35, = 57.4

Rounded down, that is 57.

So this way also results in 57 multiples of 5 and 7 between 1 and 2009.

$$h=\dfrac{\sin{(41\ensuremath{^\circ} )}*\sin{(48\ensuremath{^\circ})}}{\sin{(41\ensuremath{^\circ}+48\ensuremath{^\circ})}}*140\;m = 68.27\;m$$

Why don't you try it and tell us.  You could start with your favouite item.  We'd love to know how it goes.

What was the total length of wire used for the cuboid ?

length = 4a+4b+4c = 4 * 15cm + 4 * 11cm + 4 * 30cm = 4 * (15cm + 11cm + 30cm) = 4*56cm = 224cm

$$\underbrace{5}_{a=5}x^2\underbrace{-3}_{b=-3}x\underbrace{+1}_{c=1}=0 \quad ?$$

$$discriminant = b^2-4ac =(-3)^2-4*5*1=9-20=-11$$

$$\textcolor[rgb]{1,0,0}{discriminant < 0\qquad \mbox{no real solution}}$$

Hi Jedithious, it is great to see you again.

I can answer in full if you want but I am in a bit of a hurry right now so I will start with a condensed version.

You have an upside down triangle.  The top is the bridge, it is 140m long.  The apex at the bottom touches the water.

The perpendicular from the apex to the bridge is the height of the bridge.  Let that be h

The 2 angles at the top are 41 and 48 degrees.  I am assuming that the height of the bridge is the same on both sides.  this is important fo my solution.

So the perpendicular height cuts the bridge into 2 peices.  Let one peice be x metres and the other be 140-x metres.

Now you have tan 48=h/(140-x)  and tan 41=h/x

Make x the subject - put the 2 together and solve.

I haven't actually done this yet.  I don't know how difficult it is.  Have a play and get back to me.  I want to help you more if it is of any benefit to you.  This is a really good question.

♬ ♬ MELODY ♬ ♬

$1 as profit per day

Lots of great answers here

On Heureks' vein how about

$$-9=-(13-4)=-(\sqrt{13}-2)(\sqrt{13}+2)=(2-\sqrt{13})(\sqrt{13}+2)$$

It is good that you have posted here.  (Catalina has come across from the Spanish site)

Do you understand CPhill's answer?  If you do not it is important that you say so.  

If you do then it would be nice if you say gracias and give him a thumbs up. 

Es bueno que los que has publicado aquí. (Catalina ha llegado a través de la página española) ¿Entiende usted la respuesta de CPhill? Si no lo hace, es importante que usted lo dice. Si lo hace, entonces sería agradable si usted dice gracias y le dan un pulgar hacia arriba.

$$what\ is\ 3/14 \as\ a\ decimal?$$

3/14 is saying 3 divided by 14. To figure out the decimal form of 3/14, you simply divide 3 by 14!

$${\frac{{\mathtt{3}}}{{\mathtt{14}}}} = {\mathtt{0.214\: \!285\: \!714\: \!285\: \!714\: \!3}}$$

Your professor’s comment notwithstanding, in the set of real numbers, the solution is never infinity. There may be infinite solutions, and any one of them shares validity with all the others, this is why it is undefined. However, infinity is not a solution to division by zero. This also applies to zero divided by zero.

The above is a basic rewording of what CPhill described (He knows a lot about zero’s --especially Roman zeros).

The professor’s “b**w-up” comment may be a metaphor referring to the concept basis that is depicted in the equation below.

$$\.. \hspace{75pt} \ \lim\limits_{x \to 0}{\frac{c}{x}} = \infty\ where\ c = const$$

Here X is an asymptote. It never actually reaches zero.

I believe the answer is just 15450%

The 10^-9s cancel leaving

3.09 ÷ .02

another way you could look at this is

3.09*50 

154.5 

write as a percent

15450%

I hope this helps...

4x=16

We can simplify this by dividing both sides by 4.

x = 4

There you go!

Closing in 5 days.

Random number generated:

6,9,24,67,128 to make 1,353