All Answers 358514 Answers

A good answer Sally, thank you

Just make sure the scores are sorted smallest to largest - or vice versa first.

$$y=ax^2+bx+c\qquad a\ne0$$     

this is a parabola.

If a>0 then it is concave up, If a<0 then it is concave down.

The y intercept is c

$$\mbox{The axis of symmetry is }\qquad x=\dfrac{-b}{2a}\\

\mbox{Substitute in this value of x to get the y co-ordinate of the vertex}$$

The roots, x intercepts are 

$$x=\dfrac{-b}{2a}\pm \dfrac{\sqrt{b^2-4ac}}{2a}$$

That is usually enough.  

1 135 263 408 000 000 000 metres per hour.

Use the calculator: 120[ly/h] in [m/h]

I think that is right too

In his case the probability of at least 1 bomb was 100% or 1 because he took it on board with him.

So the probability of two bombs, just in his case was 1* 9*10^{-7 =}9*10^-7 

Taking the extra bomb on board did not decrease his chances of another being on the plane.  

It just got him arrested  

(I think that is what you meant?)

Hmm, not really sure what I should simplify here,

$${\frac{{\mathtt{24}}}{{\mathtt{103}}}} = {\mathtt{0.233\: \!009\: \!708\: \!737\: \!864\: \!1}}$$

and 103 is a prime number so there's no simpler fraction I could make of this.

You're welcome.

You could've googled it though, it's a pretty well known math mistake to trick people. 

Aaah, thanks 

You're making the wrong addition here,

The money you need to put together to pay your parents back is

49+49-1 = 97, because you already have 1 dollar.

Because you keep 1 dollar to yourself and only give 2 dollars to your parents

the money you still need to pay back to your parents is $98 (of which you already have 1 dollar)

The t-shirt shop has 97 dollars, your mum has 1 dollar, your father has 1 dollar and you have 1 dollar which totals 100 dollars.

To summarize, there is no missing dollar. 

Reinout

oh now i think it may be 12 i guess , isnt it ! but mine is about to be 4 pm so as i said half of the day has passed ! 

Haha I agree to disagree,

it was 11:00 am over here when I posted that.

maybe or no idea !but its not starting of the day btw , half of it has already passed !lol!

I wasn't really asking,

Was just beeing a smart-a*s.

Thanks for the answer though 

$$100*v_1^n=200*(5v_1)^n\\\\
100*v_1^n=200*5^n*v_1^n\\\\
1=2*5^n\\\\
$ Take logs\\
$$\ln{1}=\ln{2}+n*\ln{5}\\\\

0=\ln{2}+n*\ln{5}\\\\
n=-\frac{\ln{2}}{\ln{5}}$$

$${\mathtt{n}} = {\mathtt{\,-\,}}{\frac{{ln}{\left({\mathtt{2}}\right)}}{{ln}{\left({\mathtt{5}}\right)}}} \Rightarrow {\mathtt{n}} = -{\mathtt{0.430\: \!676\: \!558\: \!073\: \!393\: \!1}}$$

$$\\P(-1, 1)\quad and \quad Q(5, 9)\\
\boxed{Center = \frac{1}{2}\left( P+Q\right)}
=\frac{1}{2}* \left[
\left(\begin {array} {c} -1 \\1 \end {array} \right)
+
\left(\begin {array} {c} 5 \\ 9 \end {array} \right)
\right]\\
=\frac{1}{2}* \left(\begin {array} {c} -1+5 \\1+9 \end {array} \right)\\
=\frac{1}{2}* \left(\begin {array} {c} 4 \\10 \end {array} \right)\\
=\left(\begin {array} {c} \frac{1}{2}* 4 \\\frac{1}{2}* 10 \end {array} \right)\\
\boxed{Center=\left(\begin {array} {c} 2 \\5 \end {array} \right) =(2, 5)
}$$

$$\\\boxed{\vec{radius}= \frac{1}{2}\left( P-Q\right)}
=\frac{1}{2}* \left[
\left(\begin {array} {c} -1 \\1 \end {array} \right)
-
\left(\begin {array} {c} 5 \\ 9 \end {array} \right)
\right]\\
=\frac{1}{2}* \left(\begin {array} {c} -1-5 \\1-9 \end {array} \right)\\
=\frac{1}{2}* \left(\begin {array} {c} -6 \\-8 \end {array} \right)\\
=\left(\begin {array} {c} \frac{1}{2}* -6 \\\frac{1}{2}* -8 \end {array} \right)\\
\vec{radius}= \left(\begin {array} {c} -3 \\-4 \end {array} \right)\\
radius=\|\vec{radius}\|=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\
\boxed{radius=5}$$

The equation for the circle is: $$(x-2)^2+(y-5)^2=25 \qquad | \quad(x-x_{center})^2+(y-y_{center})^2=r^2$$

A linear relationship means that you can write  C = m*d + k where m and k are constants to be found from the information you are given.

From May:  360 = m*500 + k  ...(1)

From June:  440 = m*900 + k ...(2)

Re-write (1) as k = 360 - m*500 and put this into (2)

440 = m*900 + 360 - m*500

Rearrange and simplify:

440 - 360 = m*400

80 = m*400

m = 80/400 = 0.2  ...(3)

Use (3) in (1)  (or (2) if you prefer)

360 = 0.2*500 + k

k = 360 - 0.2*500 = 360 - 100 = 260

So, in general

C = 0.2*d + 260

so when d = 1200 the cost is

C = 0.2*1200 + 260 = 500

Cost of driving 1200 miles is $500

Deleted deleted

No, the first one is (x - 2)² + (y - (-8))² = 9², or (x - 2)² + (y + 8)² = 9²

2⁷ = 128 so x = 7

Just divide both sides by  ... (v1 - v2)

So , we have ..... 1/√x =  x^(-1/2)

The antiderivative is just

F(x)  =  (2)x^(1/2) + C     or    2√x  + C

Prove this for yourself

F'(x) = x^(-1/2)  = 1/√x

Thanks Chris, the trig identity works fine - Here's another take on the problem.

ok sine is postitive for theta must be in the first or second quadrant.  This just means that Cosθ can be positive or negative.  To find the one in the first quad just draw a right angled triange.  Put your info on it and find the third side using Pythagoras' Theorems.

Like this.  So reading straight from the triangle        $$cos\theta=\pm \frac{2\sqrt6}{7}$$

Find an equation of the circle that satisfies the given conditions.

Did any one find out how a workound for this?