MaxWong

Does a 'penny' means 0.01 dollar and a 'quarter' means 0.25 dollar?

Just a guess......

Let x be the number of quarter he has.

\(0.25x+0.01(1+90\%)x = 8.07\\ 0.25 x + 0.019 x = 8.07\\ 0.269 x = 8.07\\ 269x = 8070\\ x = 30\)

He has 30 quarters.

Looks like I have guessed correctly of the coins' value!! Yay :D

What do you mean? What is that? Post it here and we may be able to help you! :D

When t ranges from 1 to 54,

P ranges from 314889e^(0.00644) to 314889e^(0.34776).

:D

OK. :D

A student get 1 coin, B student get 5 coins

A student get 2 coins, B student get 4 coins

A student get 3 coins, B student get 3 coins

A student get 4 coins, B student get 2 coins

A student get 5 coins, B student get 1 coin.

Total 5 ways!! :D

No combination required!!
And if you really need combination for your homework:

6P2 - 6C2 = 5

And I am not sure if this thing above is correct. Sorry for the unsureness(I have made this word up :) hope you understand).

Also, tips!! 

Tips: Please do NOT solve it as a normal trig equation!! It can actually be solved like a quadratic!!

First we find the equation for tangent line;

\(f'(x)=-4x+7\\ \text{Gradient of tangent line}=f'(6)=7-24 = -17\)

When x = 6, f(x)=42 - 2(36)= -30

\(y-(-30)=-17(x-6)\\ y=-17x+72\)

There we go!!

Then we find the gradient for normal.

Negative reciprocal of -17 is 1/17:
Gradient of normal is 1/17

Equation for the normal:

 \(y-(-30)=\dfrac{x-6}{17}\\ y=\dfrac{x-516}{17}\)

Did I make a mistake? This is the first time I know what is normal line. :D

\(\dfrac{2}{3}x-8=0\\ \dfrac{2}{3}x=8\\ x = 8\times \dfrac{3}{2} = 12\)

OR 

If you mean 2/3x - 8 = 0 instead of 2/3 x - 8 = 0...... ('A dot can make extreme difference.' a Chinese idiom translated by me.)

\(\dfrac{2}{3x}-8=0\\ \dfrac{2}{3x}=8\\ \dfrac{1}{x}=8\times \dfrac{3}{2} \\ \dfrac{1}{x}=12\\ x=\dfrac{1}{12}\text{ OR }0.08\bar{3}\text{ <-- the bar is for repeating notation.}\)

\(2x\times 1/5\\ = 2x/5\)

There is no such thing called 'climate math form'.