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# 4 answer should be    14x^6 +35/(x^8)      is the only issue I see....but I am not an expert.

Another method for 9: 

           (6x^3 +2) (5x-3) =          (multiply it out)

           30x^4 -18x^3 +10x -6    now d/dx =

f'(x) =  120 x^3 -54x^2 + 10

is 4/8 less than 3/8?

It is not a problem Max :)

Having Latex in the message section would be good but I don't see it as a major issue because maths should really be on the forum anyway.  What you have done is perfectly fine :)

An easy way to message latex is to start a new question, write your latex, copy the result with a screen capture, gyazo is a great program for this (although it does play up sometimes) and then just post the clip as a picture.  If all works properly it does not take much extra time.

Of course you would never finish posting the new message, it was just a tool.  :)

BUT

Putting it on the forum like this was the best idea.   :)

No problem or flak from me 'cookie'....I learn a lot from other people's answers !    Thanx     

1. Addison currently has an account balance of $1,737.83. She opened the account 11 years ago with a deposit of $1,334.62. If the interest compounds semiannually, what is the interest rate on the account?

We have

1737.83  =  1334.62( 1 + R/2)^(11 *2)

1737.83  =  1334.62( 1 + R/2)^(22)       divide both sides by   1334.62

[1737.83 / 1334.62]  = ( 1 + R/2)^(22)    take the 22nd root of both sides 

[1737.83 / 1334.62]^(1/22)  = 1 + R/2    subtract 1 from both sides

[1737.83 / 1334.62]^(1/22) −  1  = R/2      multiply both sides by 2

2 ( [1737.83 / 1334.62]^(1/22) −  1]  =  R ≈  0.0241437  ≈  2.41%

\(\infty \times \infty\\ = \dfrac{1}{0}\times \dfrac{1}{0}\\ =\dfrac{1\times 1}{0\times 0}\\ =\dfrac{1}{0}\\ =\infty\)

\(1.\\ f(x) = 5\pi^2\\ f'(x) = 0\text{ as it is a constant}\\ ......................................................\\ 2.\\ f(x) = 5\sqrt x\\ f'(x) = \dfrac{5}{2\sqrt x}\\......................................................\\ 3.\\ f(x) = \dfrac{1}{x^4}=x^{-4}\\ f'(x) = -4x^{-5}=-\dfrac{4}{x^5}\\......................................................\\ 4.\\ f(x) = 2x^7 - 5x^{-7}\\ f'(x) = 14x^6 +35x^{-6}=14x^6 + \dfrac{35}{x^6}\\......................................................\\ 5.\\ f(x) = \dfrac{2x-1}{x^3}=\left(x^{-3}\right)(2x-1)=2x^{-2}-x^{-3}\\ f'(x) = -4x^{-3} +3x^{-4}=-\dfrac{4}{x^3}+\dfrac{3}{x^4}\\ f'(1) = -\dfrac{4}{1^3}+\dfrac{3}{1^4}=-4 + 3 = -1 \\\text{P.S.: Need not use quotient rule nor product rule}\\ ......................................................\\ 6.\\ f(x) = 3x^4 \ln x\\ f'(x) = (12x^3)(\ln x)+(3x^4)(\dfrac{1}{x})=12x^3\ln x + 3x^3\\ f'(1) = 12(1^3)\ln 1 + 3(1^3)=12(0) + 3(1) = 3 \\......................................................\\ 7.\\ f(x)=8\sqrt x + 6x^{3/4}=8x^{1/2}+6x^{3/4}\\ f'(x) = \dfrac{4}{\sqrt x}+\dfrac{9}{2x^{1/4}}\\......................................................\\8.\\ y=\dfrac{5}{x^2}-\dfrac{3}{\sqrt x}+5x^4 = 5x^{-2} - 3x^{-1/2} + 5x^4\\ \dfrac{dy}{dx} = -10x^{-3} +\dfrac{3}{2x^{3/2}}+20x^3 = -\dfrac{10}{x^3}+\dfrac{3}{2x^{3/2}}+20x^3\\​......................................................\\ 9.\\ y = (6x^3 + 2)(5x - 3)\\ \dfrac{dy}{dx} = (18x^2)(5x - 3) + (6x^3 + 2)(5) = 120 x^3 -54x^2+10\\​......................................................\\ 10.\\ f(t) = \dfrac{(8t-3)(2t+5)}{t-7}= \dfrac{16t^2 +34t-15}{t-7} = 16t + 146 +\dfrac{1007}{t-7}\\ f'(t) = 16 - 1007(t-7)^{-2}=16-\dfrac{1007}{(t-7)^2}\\ f'(1) = 16 - \dfrac{1007}{(1-7)^2}=16 - 27\dfrac{35}{36} = -\dfrac{431}{36}\)

Hey :)

How ya doing?

~The smartest cookie in the world

x^2 + 16x  - 225 = 0           factor

(x + 25) (x  − 9 )  =  0

Set each factor to 0

x + 25  = 0  →  x  = − 25          or            x  −  9  = 0  →   x  = 9

Solve for x:
x^2 + 16 x - 225 = 0

The left hand side factors into a product with two terms:
(x - 9) (x + 25) = 0

Split into two equations:
x - 9 = 0 or x + 25 = 0

Add 9 to both sides:
x = 9 or x + 25 = 0

Subtract 25 from both sides:
Answer: |x = 9              or               x = -25

What good manners,       You are very welcome arshan :)

Half of D.

I don't choose any of these but I have an idea.

\(1,000,000,000 - 999,999,999,999\\ =-(999,999,999,999-1,000,000,000)\\ =-998,999,999,999\)

Step one is a way that I found in Primary 1, which is grade 1 in some countries, to do subtractions which answers are negative. So that's why I can already do negative addition, subtraction, and multiplication in Primary 1.

~The smartest cookie in the world

Hmmmm.... I cannot see any of them that work....are you sure about the fractions   3/4....or  3/8?    7/12 ..or 7/8???

Hi Melody,

Thank you very much for your help :)

Arnolde1234, do you realize how rude it sounds to say "Incorrect" just like that?

Guest one has attempted your question and you need to be polite.  

You should say something like

"Thanks guest, I don't think that is quite right because ......." you put something in for the dots.

Also, if you already know the answer and it is just an interest question then you should state this in your question.  

You know how you do a 12 by 12 grid for times tables?

well

do a 6 by 6 grid for your dice.  Maybe a red die 1 to 6 across the top and a blue die 1 to 6 down the side.

There are 36 possible outcomes when you throw your dice.

Just go through the grid and find all the outcomes that are favourable to what you want and the probabliliy of thowing that will be  that number over 36.

Density is mass per volume    or  mass/ volume

mass= x kg = 1000x g

volume = .002 m^3 = .002m^3 x 100 cm/m x 100 cm/m x 100 cm/m = 2000 cm^3

Density =    1000x g /2000 m^3  =  0.5x g/cm^3

  (-2ur^6t^4)^3 = -8 r^18 t^12 u^3

Congrats!!. You got both of them RIGHT!. That is what you should always do. Try and get the answer, and then submit the question with the answer that you got and will tell you if you are right or not. Because we have computers that can calculate these simple problem almost instantly and will give you the answers in a few minutes.

My answer I thought for 1 and 2 were 2.4% & $3,546,50

Guest

1) - You should try and do some of these financial problems yourself and show your work. Will tell you if you are right or not, and will explain to you where you went wrong. Just make an attempt!. Hint: Use PV, FV formulas

1) - You should try and do some of these financial problems yourself and show your work. Will tell you if you are right or not, and will explain to you where you went wrong. Just make an attempt!. Hint: Use PV, FV formulas.

Hi ElectricPavlov

This is how you could have displayed your LaTex :D

\displaystyle\sum_1^\infty(1+\frac{1}{n})^n

\(\displaystyle\sum_1^\infty(1+\frac{1}{n})^n\)

Maybe you already know this but if you right click on anyone's Latex you can get (and copy) their coding.  This is one very useful tool as you are learning. :)

Right click ...     Maths setting .... Show teX comments     (as shown)