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(1)  P(t)   = 25t + 30

(2) At 4PM....this is 10 hours after 6AM.....so

P(10)  = 25(10) + 30  =    280 PPM

Let t be the time elapsed since it arrived at the nursery and let g be the height at any time, t.

Notice....at t = 0, h = 2 cm    = ( 0, 2)

And at t = 2, h = 5  = (2, 5)

So.....to get a linear equation, we first need to find the slope.....so we have

[ 5 - 2 ] / [ 2 - 0 ]   = 3/2      and using (0, 2)  we have

y - 2  = (3/2) (x - 0) 

y = (3/2)x + 2  and we can this  linear function  as :

g(t)  = (3/2)t + 2

(2)  3 months = 12 weeks....so we have

g(12) = (3/2) (12) + 2   =  18 + 2  = 20 cm

3,14 = PI 

Or write it in the form

 \(r_1e^{i\theta_1}/r_2e^{i\theta_2}\rightarrow r_1e^{i\theta_1}\times \frac{1}{r_2}e^{-i\theta_2}\rightarrow \frac{r_1}{r_2}e^{i(\theta_1-\theta_2)}\)

Edited to correct the magnitudes.

NO!!!!!.....this violates the triangle inequality which says that the sum of any two sides of a triangle is greater than the remaining side.

But  :

6 + 2  < 9.3

So....this triangle is impossible.....

Put the numbers in their polar forms, \(r(\cos\theta+\imath\sin\theta)\), multiply top and bottom by the conjugate of the denominator and then, having multiplied out the brackets,  use some standard trig identities to simplify.

I have to go out now, I'll get back to it later if it's still a problem.

@@ What is Happening?  [Wrap4]    Mon 2/11/15   Sydney, Australia Time 10:30pm   ♪ ♫

Hi all Web2.0calc  forumites,    

Our wonderful answerers today were  Geno3141, Saseflower, Okim2001, Cars_456, Alan, and Heureka.   

Interest Posts:

1) Fun with numbers

Silly me,  thank you :))

I  would like more explanation of the division please :)

I don't think this one really is answered yet !!

Most of those answers look a bit 'fudged' to me.       lol      

Mon 2/11/15

1) Fun with numbers

    http://web2.0calc.com/questions/using-1-2-3-4-only-once-operations-pemdas-and-factorials-allowed-how-do-you-get-100-and-12-75

2) Sir Phill La-TeX is still with us.    

    http://web2.0calc.com/questions/in-the-diagram-below-we-have-overline-mn-parallel-overline-pq-om-9-oq-6-and-pn-24-find-op-asy-pair-o-m-nn-p-q-m-0-4-0-5-nn#r10

3)  Physics / chemistry            Thanks Heureka  

     http://web2.0calc.com/questions/angle-of-twist

4) Solar cooker                      Not answered yet

    http://web2.0calc.com/questions/solar-cooker

5) When does a derivative exist?  Hence find co-efficient.   Melody

    http://web2.0calc.com/questions/lnx-x-gt-1

6) US Treasury Bonds            Melody

    http://web2.0calc.com/questions/us-treasury-bond

7) line equation.

   I think this would be a good one for other junior high/high school students to look at too.

    http://web2.0calc.com/questions/help_26366

8) Another interesting linear equation question.  Thanks Alan

   http://web2.0calc.com/questions/economy-cars-linear-function#r1

9) Complex number division.   Thanks Guest.  (I'd like more discussion please)

    http://web2.0calc.com/questions/having-troubles-0-72-5-36-1-38-17-90#r4

   http://web2.0calc.com/questions/having-troubles-0-72-5-36-1-38-17-90

The equation of a straight line can be written as f(x) = m*x + c where m and c are constants found from the given information as follows:

 f(-4) = 21  so  21 = -4*m + c    ...(1)

 f(4)  = -3  so   -3 = 4*m + c     ...(2)

Add (1) and (2) term by term to get  21 - 3 = -4m + 4m + c + c  or 18 = 2c so c = 9

Put this back into (2) to get  -3 = 4m + 9   so 4m = -12  so m = -3

Hence the straight line function is  f(x) = -3x + 9

Now simply replace x by 9 to work out what f(9) is.

Yes it is the equation of a concave up parabola.  

What about it?

Our guest has shown you haopw to solve the equation and get the solution.

Once you do that you should also be able to substitute the solution back into the original equation and check that it makes the equation true.

-(y+3)=2                     check that y=-5 makes this true.

-(-5+3)

=-(-2)

=2

=right hand side.

therefore  y=-5 really is the correct solution.    :))

For part (a) which rod should I take the Aluminum or the brass and why ? 

Shaft\(_{ \mathbf{\text{aluminum} }}\)   CB:

\(\begin{array}{lcl} c=\frac12 d = 0.006\ \text{m} \qquad L=0.300\ \text{m} \qquad G= 26\cdot 10^9\ \text{Pa} \qquad T=100\ \text{N}\cdot \text{m}\\\\ J=\frac{\pi}{2}c^4 = \frac{\pi}{2}\cdot (0.006^4)\ \text{m}^4 = 2.0357520\cdot 10^{-9}\ \text{m}^4 \\\\ \varphi_{_{\text{CB}}} = \frac{T\cdot L}{G\cdot J} = \frac{100\cdot 0.300\ \text{N}\cdot \text{m}^2} {26\cdot 10^9\cdot 2.0357520\cdot 10^{-9}\ \text{Pa}\cdot\text{m}^4} = \frac{30}{52.929553}\ \text{rad} =0.5667911079\ \text{rad} \end{array}\)

Shaft\(_{ \mathbf{ \text{brass}}}\)  BA:

\(\begin{array}{lcl} c=\frac12 d = 0.006\ \text{m} \qquad L=0.200\ \text{m} \qquad G= 39\cdot 10^9\ \text{Pa} \qquad T=100\ \text{N}\cdot \text{m}\\\\ J=\frac{\pi}{2}c^4 = \frac{\pi}{2}\cdot (0.006^4)\ \text{m}^4 = 2.0357520\cdot 10^{-9}\ \text{m}^4 \\\\ \varphi_{_{\text{BA}}} = \frac{T\cdot L}{G\cdot J} = \frac{100\cdot 0.200\ \text{N}\cdot \text{m}^2} {39\cdot 10^9\cdot 2.0357520\cdot 10^{-9}\ \text{Pa}\cdot\text{m}^4} = \frac{20}{79.3943295415}\ \text{rad} =0.2519071591\ \text{rad} \end{array}\)

\(\begin{array}{lrcl} \text{answers:}\\ (a) & \varphi_{_{\text{B}}}&=& \varphi_{_{\text{BA}}}\\ &&=& 0.2519071591\ \text{rad} \\ &&=& 14.4332170431^{\circ}\\\\ \hline (b)& \varphi_{_{\text{C}}} &=& \varphi_{_{\text{BA}}} + \varphi_{_{\text{CB}}}\\ &&=& 0.2519071591\ \text{rad}+0.5667911079\ \text{rad}\\ &&=&0.8186982670\ \text{rad}\\ &&=& 46.9079553913^{\circ} \end{array} \)

For part (a) which rod should I take the Aluminum or the brass and why ?

\( \varphi_{_{ \text{B}_{\text{brass}} }} < \varphi_{_{\text{B}_{\text{aluminum}} }} \)

because

\(G_{\text{brass}} > G_{\text{aluminum}} \)

A line passes through the points (p, a) and (p, –a) where p and a are real numbers and p ≠ 0. Describe each of the following. Explain your reasoning.

slope of the line

equation of the line

y-intercept

slope of a line perpendicular to the given line

Just make up any numbers for p and a and plot the two points and then draw a line between them.

What can you tell me about the line.

If you used different a and p values, what couls you tell me about the line still.

Try this and maybe you will be able to answer your own question. :))

They are complex numbers, or rather standard abbreviations for complex numbers.

0.72\(\angle (-5\pi/36)\) is a complex number with modulus 0.72 and argument \(-5\pi/36\).

The rule for division, (deduce it by writing the numbers in their cos + i.sin form), is divide the moduli and subtract the arguments.

So, for example \(12\angle(\pi/4)/2\angle(\pi/6)=6\angle(\pi/12).\)

how do you add fractions i am so confused plze help

If you mean on the calculator,

it is just 

1/2 + 3/4      etc.

If you mean by hand maybe this will help

https://www.mathsisfun.com/fractions_addition.html

I knew Sir La-TeX is a very generous philanthropist, He has agreeed to help us I believe.  If he is a gold bricker sometimes that is ok, Sir Lancelot should not come down on him to hard.  He is working for bananas after all!  I suppose when a chimp has the name like Sir Phil LaTeX it is very obvious that he would be a philatelist!     I have some old stamps he may be interested in seeing!  Give him a little space.  Let him study his stamps.  He may find some great code in there somewhere.

I think any Troll who is worth his salt would like sushi.  He probably would like it best when it has ben naturally putrified by the resident croc or gator.  Crocs and gators like to stow there dinner in underwater crevices and come back for it in a few weeks when it is soft and ripe for they have no teeth to chew it with.  I think any self respecting troll would like it that way too!  Steak can be prepared in this way too  

Hi Guest,    You used the 2 twice in both you answers.     

I can 'fudge' too.   LOL

using 1,2,3,4 only once {operations (PEMDAS) and factorials allowed} how do you get -100 and 12.75?

1)        (2+3)1 / 4   =   51  /  4   =   12.75       LOL    

Here is another 'fudge' one

2)         (12)+3/4      = 12  3/4

HERE IS A REAL ONE!!

3)      (3!+4)^2  =100      If I haver to use the 1 as well I can just multiply the whole lot by 1.   

  -[(1 X 2) -(3 X 4)]^2

  - [2 - 12]^2

  -[-10^2]=-100

12 + 3/4=12.75

[(3x4)-(1x2)]²

or just

(3x4-1x2)²

Thanks!!!

I started with 0.01 and the penalty doubled every day. What is the equation?

 .01 X(2^n - 1)=Penalty for n days. So, for 10 days, your penalty would be:

 .01 X(2^10 - 1)=$10.23. For 5 days: 1+2+4+8+16=31 X .01=.31 cents, or,

 .01 X(2^5 - 1)  =.31 cents.............etc.

Use Desmos graphing calc to graph it

I have started it for you

https://www.desmos.com/calculator/ta2h7syry8

THEN give us the link and we will help you with the next bit.

I started with 0.01 and the penalty doubled every day. What is the equation?

The penalty on day one is   0.01

The penalty on day two is   0.01 * 2

The penalty on day three is   0.01 * 2*2*2 = 0.01*2^2 = 0.01*2^(3-1)

etc

The penalty on day  "d "is   0.01 * 2^(d-1)

P = 0.01 * 2^(d-1)