All Answers 358110 Answers

Sun 28/9/14

1) A place called Useless Loop LOL

You don't have to.  No one can make you 'learn' anything.

You have posted 2 questions Quinn, both of them were really good ones that took quite a lot of time.

Both times you made a mistake in the question, hence we 'wasted' our time.  You must be more careful.  

We will lose interest if you continue to do this.

Your questions are great.  If  you can get them to us without error then you will be a very popular member of this forum.  

Melody.

thanks Heureka  

I am just going to look at the revised question.

$$a(1-x^2)+2bx+(1+x^2)c=0$$

with only one solution

I get to down to 

$$c^2=a^2+b^2$$     

ADDED: (This is the result based on the fact that the descriminant must equal zero)

Which means it is a right angled triangle where c is the hypotenuse.

$$3c=a+3b$$   

$$\\c=\frac{a+3b}{3}\\\\
c^2=\frac{a^2+9b^2+6ab}{9} \qquad (2)\\\\
$Sub (2) into (1)$\\\\
\frac{a^2+9b^2+6ab}{9} =a^2+b^2\\\\
a^2+9b^2+6ab =9a^2+9b^2\\\\
6ab =8a^2\\\\
3b =4a\\\\
b =\frac{4}{3}a\\\\
c=\sqrt{1+\frac{25}{9}}a=\frac{5}{3}a\\\\$$

multiplying all these by 3 and I find that the sides of this triangle are in the ratio 3:4:5

$$sinA+sinB = \dfrac{a+b}{c}=\frac{7}{5}=1.4$$

There are three forces acting on it.  The force of gravity (mass*g) is one.  The reaction of the road surface on the boulder is another. The static friction of the road surface is the other - this will be given by μ*mass*g*sin(13°), where μ is the coefficient of static friction between the boulder and the road.  The net force is zero, as the boulder isn't accelerating (unless one of the cars slams into it!).

2 3/4 x 3 1/2 = 9 5/8 

First you have to turn it into an improper fraction:

11/4 x 7/2

Now we times:

11 x 7 = 77

             __

4 x 2 =   8

Now we simplify

8 can go into 72 9 x

9 5/8

Iodine-131 decays according to the radioactive decay equation N/N₀ = e^-λx, or N/N₀ = e^-ln(2)x/τ, where N is amount, N₀ is initial amount, x is time, λ is the decay constant and τ is its half-life  (λ = ln(2)/τ).  For Iodine-131 the half-life is approximately 192.5 hours.  

So, if we replace N/N₀ by f(x), then b = 1 and a = e^-λ or a = e^-ln(2)/τ  (your choice!).  Plug the numbers into a calculator to find the numerical value of a.

98675630927

1238095238.0952380952380952380952380952380952380952380952380952380952380952

I don't know how you're doing to fit that in a maths book if you are of course!

9+10=19

Actually, now that i look at the actual graph it is really weird.

How can you go from +30m/s to -20m/s  in an instant.  Maybe it is in a different universe?   

what I said before still goes though.  

Thanks Chris.   

$${ceiling}{\left({\frac{{\mathtt{52\,000\,000}}}{{\mathtt{0.042}}}}\right)} = {\mathtt{1\,238\,095\,239}}$$             

This is to the nearest whole number

what would you want to know that for?

You put it over the number that you are dividing by

$$16\div3=5R1 =5\frac{1}{3}$$

Thanks Rosala,

These are great.

I like the B hair do the best.  But they are both really cool.

You know that hammock looks so much more comfortable than when they tied their victims to the rail tracks in the old movies.

I think that the slogan should be    "Going out in Style"

The Realm of Camelot is very honoured to have you as a subject.   

                                       ♫♪  ♪ ♫   Queen Guinevere.   ♫♪  ♪ ♫

It is a fraction; as a decimal it is approximately -0.088 235 294 12

Yes that makes sense I guess

On the left side you have a 4 in the numerator (as a multiplier) and a 4 in the denominator. 

I would cancel these two numbers.

Then you have: 2x - 5 = 11                       Add 5 to both sides.

     ----->   2x = 16                                  Divide by 2.

     ----->     x = 8

Check:    4( 2(8) - 5 ) / 4

              4( 16 - 5 ) / 4

              4( 11 ) / 4

                   44 / 4

                    11 

Let the distance travelled in the fist 5 seconds be x metres

We know u=0

When t=5, s=x

When t=10 s=x+150

I am going to use the formula     $${\mathtt{s}} = {\mathtt{ut}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{{\mathtt{at}}}^{{\mathtt{2}}}$$

since u=0,  the formula becomes  $${\mathtt{s}} = {\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{{\mathtt{at}}}^{{\mathtt{2}}}$$

Now we have 2 equations that can be solved simultaneously.

$$\\x=\frac{1}{2}a\times 5^2 \\\\\
x= \frac{1}{2}a\times 25 \qquad (1)\\\\
and\\\\
x+150=\frac{1}{2}a\times 10^2 \\\\
x+150=\frac{1}{2}a\times 100 \\\\
x+150=\frac{1}{2}a\times 25 \times 4 \\\\
\frac{x+150}{4}=\frac{1}{2}a\times 25 \qquad (2)\\\\
$putting these together I get\\\\
\begin{array}{rll}
x&=&\frac{x+150}{4}\\
4x&=&x+150\\
3x&=&150\\
x&=&50\\
\end{array}$$

So the ball rolls 50m in the first 5 seconds   

f(x) = 9

9 = 12.57 / (1 + 4.11 e^( -.026t) )

9(1 + 4.11e^(-.026t) )= 12.57                         Cross multiply

1 + 4.11e^(-.026t) = 12.57 / 9                 Divide by 9. Feel free to calculate and use decimals from here.

4.11e^(-.026t)  = 12.57 / 9  - 1                        Subtract 1.

e^(-.026t) = ( 12.57 / 9  - 1 ) / 4.11                  Divide by 4.11.

ln( e^(-.026t) ) = ln(  (12.57 / 9  - 1) / 4.11 )     Since the variable is in the exponent, find the ln of both                                                                             sides; also, use log instead, if you wish.

-.026t x ln( e ) = ln(  (12.57 / 9  - 1 ) / 4.11 )     The exponent comes out as a multiplier.

-.026t  = ln(  (12.57 / 9  - 1) / 4.11 )                  The ln(e) = 1; it will disappear in multiplication.       

t = ( ln(  ( 12.57 / 9  - 1 ) / 4.11 ) ) / -.026            Divide by -.026.

Add this answer to 1970.

Thank you! I needed to know that! 

Thanks for that explanation, Melody...I don't "do" Physics but I see what you are talking about.....!!!!

Usually you use a table 'backwards' for this.

Find the area in the body of the table and then see what z score it corresponds with.

I am assuming a normal distribution.

I think that you have given us only half the question.  

3,5 means 3+0,5.

0,5 is "a half". It is the same as 1/2. (one divided by two) 

Imagine that you and a friend of yours share a cake. If you cut the cake in two in such a way that both get an equal amount, then you get "a half" or 1/2 of the cake.