All Answers 358514 Answers

You can just type in 'pi' too!  It's pretty cluey.

Remember GoldenLeaf, this is an approximation and you should state that but I've given you thumbs up.

sqrt(522) is an irrational number!

Using the distance formula, SQRT[(x₂- x₁)^2 + (y₂- y₁)^2], we have

((8-3)^2 + (12-4)^2))^(.5) =

(5^2 + 8^2)^(.5) = (25 + 64)^(.5) = (89)^(.5) =

$${\left({\mathtt{89}}\right)}^{\left({\mathtt{0.5}}\right)} = {\mathtt{9.433\: \!981\: \!132\: \!056\: \!603\: \!8}}$$

I really do not know what you mean.

do you mean the quadratic formula?

Here it is.

If      $$ax^2+bx+c=0$$

Look at the clip - remember that there should be an' $$x=$$' out the front.

It appears that you've asked two questions....

-12-6 = -18

-12-8 = -20

1728, Ramanujan's number.

The probability, (if that's what's being asked), of being born in this nation is 1/1400, the odds are 1399-1 against.

Yes but Heureka, these are one number -NOT one digit!

Thank you!

There are 20 options in total, 5 with holly, 4 with dragon scale.  However, there is one with both holly and dragon scale, so, to avoid double-counting that one, we have 5 + 4 - 1 = 8 possibilities.  So the overall probability is 8/20 = 2/5 = 0.4.

As a Potterhead, this Peeves me. The only cores are the heartstrings of a dragon, the feather of a phoenix, and the hair of a unnicorn.

Holly wood is 5/20, or 1/4

Dragon scale is 4/20, or 1/5

Add the two together.

5/20 + 4/20 = 9/20

However, do consider that there is one chance of those 'nine' that it can be both, and since the problem asks for 'or', take that out.

9/20 - 1/20 = 8/20 = 2/5

P(A or B) = 9/20

I'm going to assume this is a cube die?

1) 1/1 , 1/6 , 1/6 = 1/1*6*6 = 1/36

2) 5/6 . 5/6 , 5/6 = 5*5*5/6*6*6 = 125/216

3) 1/2 , 1/3 , 1/6 (considering that 2 , 4 , and 6 are your even numbers) = 1/2*3*6 = 1/36

1. p = 1*(1/6)*(1/6) = 1/36

2. p = (5/6)*(5/6)*(5/6) = 125/216

3. p = (1/2)*(1/3)*(1/6) = 1/36

$$\begin{array}{rll}
A&=&\pi r^2\\\\
15.89625&=&\pi r^2\\\\
\frac{15.89625}{\pi}&=&r^2\\\\
\sqrt{\frac{15.89625}{\pi}}&=&r\\\\
\end{array}\\\\
d=2r=2\sqrt{\frac{15.89625}{\pi}}\quad units$$

$${\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\frac{{\mathtt{15.896\: \!25}}}{{\mathtt{\pi}}}}}} = {\mathtt{4.498\: \!859\: \!201\: \!286\: \!069}}$$

diameter is approx 4.5 units

This is the sum of a converging infinite geometric series, so it can be written as a/(1-r) where a = 6 (the first term)  and r = -1/2 (the common ratio).  So the sum is 6/(3/2) = 4. 

The ratios for angle A are irrelevant. (there is no relationship mentioned between A and B)

SinB=3/4 (since it is positive, B must be in the 1st or second quadrant)

draw a right angled triangle.

Mark one of the accute angles B  Let the opposite side be 3 unit and the hypotenuse be 4 units.

using pythagoras' theorum

adj side = sqrt(16-9)=sqrt(7) 

CosB=sqrt(7)/4  (if B is in fist quad)

general answer 

$$Cos(B)= \dfrac{\pm \sqrt7}{4}$$

Is some of this question missing?

I am going to use the cosine rule.

$$\begin{array}{rll}
\overline{AC}^2&=&(2x)^2+x^2-(2*2x*x*Cos( \overline{AC}^2&=&4x^2+x^2-(4x^2Cos( \overline{AC}^2&=&5x^2-(4x^2Cos( \overline{AC}^2&=&x^2(5-4Cos( \overline{AC}&=&x\sqrt{5-4Cos( \overline{AC}&=&\overline{AB}\sqrt{5-4Cos( \end{array}$$

That should be okay if i didn't make any stupid mistakes.

tan(55)=height/9

$${\mathtt{height}} = {\mathtt{9}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{55}}^\circ\right)} \Rightarrow {\mathtt{height}} = {\mathtt{12.853\: \!332\: \!060\: \!678}}$$

A very good answer mjohnson.  Thank you.

-------------------------------------------------------------

Now I'll look at your answer GoldenLeaf.

$${\mathtt{\,-\,}}\left({\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{y}}\right) = {\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}$$

The next line that you wrote is not correct!

$${\mathtt{y}} = {\frac{{\mathtt{3}}}{{\mathtt{4}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{4}}}}$$          XXXXX     You don't subtract a quarter: you divide by -4!

Like this!

$$\begin{array}{rll}
-(4\times y)&=&-3x+1\\\\
-4y&=&-3x+1\\\\
\dfrac{-4y}{-4}&=&\dfrac{-3x+1}{-4}\\\\
y&=&\dfrac{-3x+1}{-4}\\\\
y&=&\dfrac{3x-1}{4}\\\\
\end{array}$$

Ok.  If I have f = (a*x+b)^c and want to differentiate say  with respect to x, I can first set z = a*x+b and I have f = z^c.  I can differentiate this with respect to z to get df/dz = c*z^c-1.  But I want it differentiated with respect to x not z, so I must use the chain rule, which says that df/dx = df/dz*dz/dx.

Now, we have found df/dz, so we need dz/dx.  Since z = a*x+b then dz/dx = a.  Hence overall we have df/dx = df/dz*dz/dx = c*z^c-1*a = c*(a*x+b)^c-1*a, where I've replaced z by its definition in terms of x.

In your case we have a = 5;  b = -4; and c = 1/2, so in your case df/dx = (1/2)*(5*x-4)^-1/2*5.

I did this all in one step. I'm so used to doing this I don't need to break it down into separate steps, but clearly I should have done here!

If this still isn't clear, let me know.

Zn+2HCl= H₂+ZnCl_{2  (you don't need to heat)}

I'm confused, are there 2 triangles here?

$${\frac{{\mathtt{1\,000\,000\,000}}}{{\mathtt{50\,000}}}} = {\mathtt{20\,000}}$$

Thanks so much! However for the first derrivative why are you "*5" I do not understand. Where are you getting it from?

I'm pretty sure it is just

$$\sqrt[3]{\frac{432}{250}}=1.2$$

so assuming that they are similar figures then the dimenstions of the big one are 1.2 times the little one

This is a ratio of 6:5