Melody

$$\frac{4x}{5}+\frac{x}{3}-x\\\\
=\frac{12x}{15}+\frac{5x}{15}-\frac{15x}{15}\\\\
=\frac{2x}{15}$$

If the daily balance of my account is $100 and the monthly interest is 90%, then what will my account balance be at in 10 years, starting at $7500

Okay, now I am looking properly.

I don't understand.  Is there $100 in the account at the beginning of $7500 ?

Could you please explain what those 2 amounts are?

Thank you.

90% interest per month WOW I want my money in THAT account.  

Then again,  you know what they say; If it seems to good to be true than it probably is too good to be true.

My money is staying under the bed.  And, in 10 years, if my house hasn't burnt down and I have not been robbed I will have $100.

(don't worry I will look at giving you a proper answer.)

$$slope=gradient=15\%=\frac{rise}{run}=\frac{15}{100}=\frac{3}{20}$$

Now the driveway is 12m long and we need to find the rise SO

$$\frac{3}{\sqrt{409}}=\frac{rise}{12}\\\\
\frac{36}{\sqrt{409}}=rise\\\\
rise\approx 1.780085m\\\\
rise\approx 1.8m\qquad \mbox{to the nearest 10th of a metre}$$

I think it is just coincidence that the 2 answers are the same.

Would another mathematician arbitrate please.

No Cphill,

I think that there are 2 acute adjacent complementary angles in that cute little bundle.

Maybe that is why there are 4 arms,  althought there really should only be three, isn't that correct? 

Umm

A=cos^-1(2/7)

which is the same as 

A=acos(2/7)

Now you can do it on the web2.0calculator (on the home page)  

Press 2nd to bring up acos

Edited: Thank you Alan for letting me know my error.  

(It's fixed now)

what pretty crayons NinjaDevo.  

Hi Sally,

This is an introductory lesson in Calculus.

By taking the limit as h tends to 0 Alan has found the differential of f(a).  That is f '(a)

f(a)=a²+8

f'(a)=2a

The differential is an equation that gives the value of the gradient of the tangent to the curve for any fixed a value.

It is really neat!

Yes, rearrange would have been a better choice of word.

Thanks Alan.

$$3(ab-a)-2(b-a)-4ab\\
= 3ab-3a-2b--2a-4ab\\
= 3ab-3a-2b+2a-4ab\\
= -1ab-a-2b\\
= -ab-a-2b$$