Melody

Are you multiplying adding or what?

Multiply both sides by 7

I'll start you off

write it as a fraction and then mult top and bottom by 100 the simplify.

Thanks Alan.

Use the compound interest formula

FV=P(1+r)^n

It is the 2nd button at the top  

Hi chilledz3non,

Well the exact instantaneous velocity is given by h'(t) = 2t    so when t=2  velocity=2*2=4 units per time.

Now perhaps you are meant to do it from first principles so lets think about that.

Average velocity between t=some value, I'll call it t₁ and t=2 would be     $$\frac{f(t_1)-f(2)}{t_1-2}$$

The instantaneous velocity would be given by this as t₁ tends to 2

That is 

$$\\\lim_{t_1\rightarrow2}\;\frac{f(t_1)-f(2)}{t_1-2}\\\\
f(t_1)=(t_1)^2-1\\
f(2)=2^2-1=3\\\\
$Instantaneous velocity at t=2 is $\lim_{t_1\rightarrow2}\;\frac{f(t_1)-f(2)}{t_1-2}\\\\
=\lim_{t_1\rightarrow2}\;\frac{(t_1)^2-1-3}{t_1-2}\\\\
=\lim_{t_1\rightarrow2}\;\frac{(t_1)^2-4}{t_1-2}\\\\
=\lim_{t_1\rightarrow2}\;\frac{((t_1)-2)((t_1)+2)}{t_1-2}\\\\
=\lim_{t_1\rightarrow2}\;\frac{(t_1-2)(t_1+2)}{t_1-2}\\\\
=\lim_{t_1\rightarrow2}\;(t_1+2)\\\\
=4$$

Maybe Alan or Heureka could tell me why my limits are not displaying properly.  

Alan would you fancy answering this one?

f(x)=x^2e^-x/2, [-1,8]

$$\\f(x)=x^2e^{-\frac{x}{2}}, [-1,8]\\\\
f'(x)=2xe^{-\frac{x}{2}}+\frac{-1}{2}e^{-\frac{x}{2}}x^2\\\\
f'(x)=2xe^{-\frac{x}{2}}-0.5x^2e^{-\frac{x}{2}}\\\\
f'(x)=xe^{-\frac{x}{2}}(2-0.5x)\\\\
$stationary points when $ f'(x)=0\\\\
x=0\;\;or\;\;2=0.5x\\
x=0\;\;or\;\;x=4\\$$

So you now need to find the y values for 

$$x=0,\;x=4,\;x=-1\;\; and\;\; x=8$$

Then you will have your minimum and your maximum values for the given region.

Ane even function is one where f(x)=f(-x)

When you graph is it will be symmetrical about the y axis.  

$$f(x)=x^2$$     is an example of an even function because  f(x)=f(-x)    eg f(3)=9     f(-3)=9

There is more than one graph that will fit this description.

but here is one of them.

Perhaps one of the other mathematicians can tell me what the equation of  a graph like this might be?

I really have no idea.