All Answers 358095 Answers

I'm guessing you want to simplify this.

3 (0.5x + 0.4y) + 15 (0.3x - 0.8y)

= 1.5x + 1.2y + 4.5x - 12y

= 6x -10.8y

Melody your end of day wrap is really helpful , though u don't check all the questions , bit still atleast u check half of them ao I can get an idea of what's goin on on the forum! Actually now a days I'm super busy so I don't get time to even open the website! And yesterday and today I was super busy with preparing for my practical computer test , making a geography poster doing other subjects homeworks and all ! And now I'm  so glad that the weekend has come i really needed it ! Anyways thanks for your wrap , I'd give u a thumbs up for that!

This is testing my memory 

12) Make a box- and- whisker plot for each set of values. 12 12 11 15 12 19 20 19 14 18 15 16

11 12 12 12 14 15 15 16 18 19 19 20    12 scores

Lowest = 11

Lower quartile = 12

Median=15

Upper quartile =19 

Highest=20

I think that this is it. 

$$y=x^2-3\\\\
\begin {tabular}{|c|c|c|c|c|c|c|c|}\hline
$x$&\;\;-1\;\;&\;\;0\;\;&\;\;1\;\;&\;\;2\;\;&\;\;3\;\;&\;\;4\;\;&\;\;5\;\;& \hline
$y$&(-1)^2-3=-2&0^2-3=-3&1^2-3=-2&2^2-3=1&3^2-3=6&4^2-3=13&5^2-3=22& \hline
\end{tabular}$$

Sat 23-8-14

* 1) Why is  $$-3^2=-9\;\; not\;\; +9?$$       (Great answer from Ninja)

@@ End of Day Wrap :     Fri 22/8/14          Sydney, Australia         Time 9:00pm        ♬  

Hello all,

Our great answers today were delivered by TakahiroMaeda, AzizHusain, CPhill, DragonSlayer554, Heureka, NinjaDevo and Admin.  Thank you all.  

I have definitely not looked at all the questions and answers today.  The forum is getting too popular for that to be possible on many days.  However, almost all questions have been ticked and this can only be done by moderators or the question asker.  So I am assuming most answers are satisfactory or better.  

Please if you see a great question, or answer or you write a wonderful answer yourself please let me know and I will reference it in the wrap and Ninja may reference it in one of his fabulous threads.  I want to know what is going on but I will be increasingly relying on other people to keep me informed.

Chris, you have ticked off many questions today.  I really thank you for steadily taking over this area of administration and responsibility.  

Here are some interesting posts for the day:

* 1) Bearings with Vectors (Trigonometry or vectors)

Do you mean this?  And, what is your question?

$$f(x)=7x^6-4x^4+2x-4$$

Is there a question here?

Anonymous appears to be correct except that there are 13 letters.  

(Unless I can't count which is always a possibility)

$$Number of Permutations is $\frac{13!}{2!2!2!}$$$

$${\frac{{\mathtt{13}}{!}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}\right)}} = {\mathtt{778\,377\,600}}$$

I am never overly confident about these so I used this site for reference.  

$$21 million times 100 million is \\
$=21\times 10^6\times 100\times 10^6\\
$=2.1\times 10^7\times 10^8\\
$=2.1\times 10^{15}\\
$=2,100,000,000,000,000\\$$

If I can make of what you are asking... You are asking how many ounces are in one pitch.

Okay... So Sally as seven or several... pitches. If I am right pitches is just a random measure of liquid for the sake of this question? So then you state some pitches can hold 64 ounces and some can hold 48 ounces?

Looking at the question, it looks like you are missing something in the second sentence. But nevertheless... I

l'll try to work around it.

So... $$(x*64)+(4*48)=y$$

$$x$$ being the around of bigger pitches

$$y$$ being the total amount of lemonade.

So... $$64x+192=y$$

Or.. $$64*(\frac{1}{64}y-3)=y$$

If you simplify that:

$$0.015625*64y-192=x$$

$$0.015625*64y=x$$

$$y=x...?$$

And then I get this... Which is... not mathematically correct....

That is as far as I can do it while trying to understand that question...

And I feel like a made a mistake...

You are very welcome.  Why don't you join up it is very easy and then we would get to know you. 

Find the most left and right tangent

$$\boxed{y=a*x^2\quad a=3.48}\\
\mbox{Point }(x_p,y_p) \text{ : } \left( x_p = -5.67 \mbox{ , }y_p =-44.75 \right)\\
\text{Find the tanget Point } (x_t, y_t) \\ \\
y_t = a*x_t^2\\
\text{Slop of } y=a*x^2 \text{ is } y'= 2a*x_t \\
\text{Slop of the line through Point p is } y' = \dfrac{y_t-y_p}{x_t-x_p}\\
\text{the slops must be equal: } y' = 2a*x_t = \dfrac{y_t-y_p}{x_t-x_p}\\\\
\Rightarrow 2a*x_t*(x_t-x_p)=y_t-y_p \quad | \quad y_t=a*x_t^2 \\
2a*x_t*(x_t-x_p)=a*x_t^2-y_p \\
2a*x_t^2 - 2a*x_t*x_p=a*x_t^2-y_p \\
2a*x_t^2 -a*x_t^2 - 2a*x_t*x_p + y_p = 0 \\
\boxed{a*x_t^2 - 2a*x_t*x_p + y_p = 0 }\\$$

$$\Rightarrow \boxed{ x_{t_{1,2}}=x_p\pm\sqrt{x_p^2-\dfrac{y_p}{a}}
\qquad y_{t_{1,2}}=a*x_{t_{1,2}}^2}$$

$$x_{t_1}=-5.67+\sqrt{(-5.67)^2-\left(\dfrac{-44.75}{3.48}\right) }\\
x_{t_1}=-5.67+6.70880730103 = 1.03880730103 \\
y_{t_1}=3.48*1.03880730103 ^2 = 3.75533971815$$right most tangent

$$x_{t_2}=-5.67-\sqrt{(-5.67)^2-\left(\dfrac{-44.75}{3.48}\right) }\\
x_{t_2}=-5.67-6.70880730103 = -12.3788073010\\
y_{t_2}=3.48*(-12.3788073010)^2 = 533.257348282$$ left most tangent 

Sorry I just posted and lost it all.  Not sure why. 

I used the the following identity

$$\\$cos^2\theta+sin^2\theta=1$\\\\
If you divide everything by $sin^2 \theta$ you end up with\\\\
$cot^2\theta+1=csc^2\theta$\\\\
$1=csc^2\theta-cot^2\theta$\\\\
this is an identity, it is true for all angles. In the case of this question the angle is 2a but it is still true.$$

Then when you get through the next bit the answer can be in the 1st or 3rd quadrant because that is where tan is positive.

think about it and if you still need more help ask again. 

Yes expand please. I am a little lost. Thank you so much!

csc(2a)-cot(2a)=tan(a)=1/Sn(2a)-cos(2a)/Sn(2a)=

It looks like this is just tentative working for the submitted question.  

anyway,  If you dont understand the answer in my last past please say so and I will expand my explanation. 

csc(2a)-cot(2a)=tan(a)

$$\begin{array}{rll}
csc(2a)-cot(2a)&=&tan(a)\\\\
\frac{1}{sin(2a)}-\frac{cos(2a)}{sin(2a)}&=&tan(a)\\\\
1&=&tan(a)\\\\
a&=&n\pi+\frac{\pi}{4}\qquad \mbox{Where }n \in Z
\end{array}$$

Yes sin I apologize. I have no idea I was asked for help on it. It doesn't make sense?

Yes. Just place all the like terms together. This will turn into 5a+2b=5a+2b

Is Sn meant to be sin?

Why is there a whole string of equal signs on the second one?

$${\frac{{\frac{{{\mathtt{306.3}}}^{{\mathtt{78}}}{\mathtt{\,\times\,}}\left({{\mathtt{891}}}^{-{\mathtt{22}}}\right)}{{\mathtt{90}}}}}{{\mathtt{230}}}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{698\,231}}{\mathtt{\,-\,}}{\mathtt{33\,214\,568}} = -{\mathtt{32\,516\,337}}$$

I am sorry, the wording on this question is really poorand I do not understand what you are asking. 

This one is a little tough!!

The slope of a tangent line to the given parabola at any point is just y' = 6.96x

Now, what we're looking for is at least one point on the parabola where the line through  (-5.67, - 44.75) is tangent to that point (or points).

Let's call the point(s) on the parabola (x, 3.48x^2). And the slope of the tangent line at that point is just 6.96x.

So, using this point on the parabola and the point (-5.67 , - 44.75), we have that, using the slope "formula,"

(3.48x^2 + 44.75) / (x + 5.67) = 6.96x

(3.48x^2 + 44.75)  /(x + 5.67) - 6.96x = 0

And solving this equation using the onsite calculator, we have....

$${\frac{\left({\mathtt{3.48}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{44.75}}\right)}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{5.67}}\right)}}{\mathtt{\,-\,}}{\mathtt{6.96}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{3\,406\,662\,741}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{49\,329}}\right)}{{\mathtt{8\,700}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{3\,406\,662\,741}}}}{\mathtt{\,-\,}}{\mathtt{49\,329}}\right)}{{\mathtt{8\,700}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{12.378\: \!807\: \!301\: \!025\: \!932}}\\
{\mathtt{x}} = {\mathtt{1.038\: \!807\: \!301\: \!025\: \!932}}\\
\end{array} \right\}$$

And the equation of the line that goes through (-5.67, -44.75) and touches the parabola at 1.038807301025932 is given by

y +44.75 = 6.96(1.038807301025932)(x + 5.67)

y = 7.23009881514048672x + 40.9946602818465597024 - 44.75

y = 7.23009881514048672x -3.7553397181534402976 ........ and rounding, we have

y = 7.23x - 3.755

And the equation of the line that touches the graph at - 12.378807301025932 is given by

y + 44.75 = 6.96( - 12.378807301025932)(x + 5.67)

y = -86.15649881514048672x -488.5073482818465597024 - 44.75 

y = -86.15649881514048672x - 533.2573482818465597024  .....and rounding, we have

y = -86.156x - 533.257

Your answers were all correct as well  (I think).

You are getting me a little confused Heureka.  Don't worry about it though.  I spend my whole life in a state of confusion. lol.

$$\\(9.09\times 10^8 )-(6.33\times 10^9\times 4.06\times 10^{-7}) =\\\\
(9.09\times 10^8 )-(6.33\times 4.06 \times 10^9\times 10^{-7}) =\\\\
(9.09\times 10^8 )-(25.6998 \times 10^{9-7}) =\\\\
(9.09\times 10^8 )-(25.6998 \times 10^{2}) =\\\\
(9.09\times 10^8 )-2569.98 =\\\\$$$$$$

$${\mathtt{9.09}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{8}}}{\mathtt{\,-\,}}{\mathtt{2\,569.98}} \approx {\frac{-{\mathtt{1\,794\,768\,755}}}{{\mathtt{50}}}} \approx {\mathtt{908\,997\,430.02}}$$

That minus sign in the calculator working should not be there.  It's a glitch in the calculator