All Answers 358099 Answers

(4+2xyz)

*   (x+3)

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    12 + 6xyz

+  4x + 2x²zy

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(2x²yz + 6xyz + 4x + 12)

9 factorial = 9!

9! = 9*8*7*6*5*4*3*2*1

= 362,880

Yes maybe - I'm not sure.

I knew that is what the question was implying but I'd still like to know what other mathematicians think.

It is a lot better now that you have changed the word equation to function.  You are probably right.

Thanks Chris,

Silly me, you did not need to multiply both sides by r you just needed to simplify the right side and solve.

It is simple.  Shame on me!

Yes the number of terms is 9      r=0,1,2,......9  The middle on is the 5th one which is r=4

((3/x)+x²)⁸

$$\mbox{The middle term is }\quad 8C4\times \left(\dfrac{3}{x}\right)^4\times(x^2)^4$$

You can simplify this yourself.

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$$\mbox{The general term is }\quad 8Cr\times \left(\dfrac{3}{x}\right)^r\times(x^2)^{8-r}$$     

Where: $$0\le r\le 8\qquad \mox{ and }\qquad r \in Z$$

$$\mbox{This simplifies down to }\quad 8Cr\times 3^r\times x^{16-2r-r}=8Cr\times 3^r\times x^{16-3r}$$

Now if there is a constant term it will be when 16-3r=0 but the solution to this gives r as a non-integer.

So there must not be any constant term!

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=0.6363636363636364 or 0.64 if rounded.

4/5(x + 5) = -1/5x + 6     distribute 4/5 on the left

4/5x + 4 = -1/5x + 6       add 1/5x to both sides

x + 4  = 6                        so its clear that x = 2

Just put it into the on-site calculator and watch magic happen !!!

Let's go from  Melody's last step...

4.543 = R (1 + .7049/R)      ....distribute R through on the right

4.543 = R + .7049             .......subtract .7049 from both sides and that will give you "R'

$$4.543=R\left(1-\frac{cos(28.65*200.53)}{R}\right)\\\\
4.543= R\left(1-\frac{cos(5745.1845)}{R}\right)\\\\
4.543\approx R\left(1-\frac{-0.7049}{R}\right)\\\\
4.543\approx R\left(1+\frac{0.7049}{R}\right)\\\\$$

Now multiply both sides by R, take it all to one side and put =0, solve it as a quadratic equation.

I have not done this so I don't know what the answer will be.

You do it - if you have problems then post again. 

Come on Sportslover, you can at least start this.  What number can you not divide by?

What can the denominator NOT equal.

Okay sportslover, I did one like this for you yesterday.

First you need to determine a general term for the bernoulli expansion.

I don't want to do this - please find yesterday's answer and give it a go yourself.

I will help you walk through it. But i would like more from you first!

So....from my reading, the answer to "a" would be in this set-up??

pi *∫ (h/2)² - y²) dy  =  pi * ∫ (12/2)² - y²) dy =   pi * ∫ (6)² - y²) dy ..... where the limits on the integral are -6 and 6 ......???

2nd atan

arc tan is the same as inverse tan.

I don't get it.

Certainly I agree with what Alan has said.  The question tells you to work it out like as if there is no hole.  That is fine. BUT 

Isn't this bead just a sphere with a hole in it?  If you put a hole through the middle of the bead then the volume if the bead has to decrease.  Certainly if the diameter of the hole is 0 then there really is no hole and the volume is as it was to start with.  But if the diamer of the whole is equal to the diameter of the bead then there is no bead left and the volume of the bead is 0.  I obviously do not understand the wording of this problem.   

I think the penny just fell!  The volume is the constant, the radius is the variable, now I've got it!!

The answer was obvious from the wording, but I haven't even thought about why that would be so yet.  - But finally I think I understand the problem!  

I do not know what level you are studying at nosomathpro but the answer is given in the question.  You do not even have to understand the question to get the answer (I did not).  Is this question just trying to teach you to pull out the relevant details and ignore the rest?  Not a difficult problem, just a word exercise??

WOW - I am going to be thinking about this for days.  Thanks for sharing it with me notsomathpro and thank you Bertie for drawing my attention to this question.  Otherwise i probably would not have even thought about it at all.   

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Everything i have written is real but I have also demonstrated how a question asker can  'discussed' their question.

Your set-up to "a" is slightly incorrect...it should be

A = 5000(1+.05/12)^12*6  =  $6745.09

For "b', the amount invested doesn't really matter....let's see why......

3A = A (1 + .05/12)^12t      divide through by A....

3 = (1 + .05/12)^12t       (see why "A" doesn't matter??) .......take the log of both sides

log3 = log (1 + .05/12)^12t         and by a property of logs, we can write

log3 = (12t)*log(1 + .05/12)       divide both sides by 12*log(1 + .05/12)

[log3] / (12*log(1 + .05/12)) = t = about 22.018 years

Thursday  and Friday 5&6 june2014

This one is interesting and important.  Please take note of what Bertie and I have said.  It is important that you are interactive with your learning.  Answerers do not want to feel like they are just doing someone's homework and that the only thing that the asker cares about is the answer!  We want to help people learn!  I also find the question itself very thought provoking.

Sorry...I meant to type "function" rather than "equation".....I'll stand by the rest...

3.8*10⁸/1.2*10¹⁵ = (3.8/1.2)*10⁸*10^-15 = (3.8/1.2)*10^8-15 = (3.8/1.2)*10^-7

$$\left({\frac{{\mathtt{3.8}}}{{\mathtt{1.2}}}}\right){\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left(-{\mathtt{7}}\right)} = {\mathtt{0.000\: \!000\: \!316\: \!666\: \!666\: \!7}}$$

or $$3\frac{1}{6}*10^{-7}$$

The obtuse angle in any triangle will be opposite the longest side. We can use the Law of Cosines to find this.   So we have

11^2  = 9^2 + 5^2 - 2(9)(5)cosx     where x is the angle we're looking for

121 = 81 + 25 - 90cosx          rearranging, we have

90cosx = 81 + 25 - 121          simplify on the right

90cosx = -15        divide both sides by 90

cosx = -15/90   =  -1/6       use the acos function to find x

acos(-1/6) = x ≈ 99.59°

32 is 2⁵ and 243 is 3⁵ so 32/243 is (2/3)⁵.  Is this what you are looking for?

Oh, I see how you did that Alan.

Forget my old answer.