reinout-g

I did the second one 

For the second question

$$y = x^4 + 4x^3 + 2x^2 - 20x + 3$$

has as derivative

$$\frac{dy}{dx} = 4x^3+12x^2+4x-20 = 4(x^3+3x^2+x-5)$$

I just found

$$x^3 + 3x^2 + x - 5 = (x-1)(x^2+4x+5)$$

Which is $$0$$ only for $$x = 1$$

This is therefore the only stationairy point

$$y=x^4+4x^3+ 2x^2-20x+3 = 1^4+4*1^3+2*1^2-20*1+3 = 1 + 4 + 2 - 20 + 3 = -10$$

So the stationairy point is $$(x,y) = (1,-10)$$

Reinout 

p.s. Thanks Bertie

Okay, so we know (x-1) is a factor of $$x^3+3x^2+x-5$$.

Let's say we want to find the c in $$x^3+3x^2+x-5 = (x-1)c$$

We want $$x^3$$ so we know some part of c is $$x^2$$

Let's write $$x^3 + 3x^2 + x -5 = (x-1)(x^2+....)$$

We now have $$x^3$$ but we also have $$-x^2$$ because $$(x-1)(x^2+...) = x^3 - x^2+...$$

We want $$3x^2$$ so let's add $$4x$$ which multiplies to $$4x^2$$ and $$4x^2-x^2 = 3x^2$$

Now we have $$(x-1)(x^2+4x + ..) = x^3+3x^2-4x+..$$

we want $$x$$ instead of $$-4x$$ so we add $$5$$ which multiplies to $$5x$$

Now we have $$(x-1)(x^2+4x+5) = x^3 -x^2 + 4x^2-4x + 5x - 5 = x^3 +3x^2+x-5$$

Which was what we were looking for.

$$x^2+4x+5$$ can't be further factorized so $$(x-1)(x^2+4x+5)$$ is the final answer

Reinout 

Couldn't agree more...

Okay so we have $$\frac{5\frac{2}{3}}{\frac{1}{6}}$$

Let's first rewrite $$5\frac{2}{3}$$ into one fraction.

$$5\frac{2}{3} = \frac{17}{3}$$

Then we make it 6'th instead of 3'rds

$$\frac{17}{3} = \frac{34}{6}$$

Okay, so now we have $$\frac{\frac{34}{6}}{\frac{1}{6}}$$ Since they are both 6'th I can rewrite this to

$$\frac{34}{1} = 34$$

If you find this difficult to see you can also do this; rewrite $$5\frac{2}{3}$$ to $$\frac{17}{3}$$

Then $$\frac{\frac{17}{3}}{\frac{1}{6}} = \frac{17}{3}*\frac{1}{\frac{1}{6}}= \frac{17}{3}*6 = 17*\frac{1}{3}*6 = 17*\frac{6}{3} = 17*2 = 34$$

Reinout 

I can interpret this in multiple ways but all have an invalid answer.

I'm going to interpret it as

  $$y = ^4log(1.5*1.3*0.5*0.75-1)$$

which is the log {base4} of (1.5*1.3*0.5*0.75-1) 

(and y is your answer)

We can rewrite this to $$4^y = 1.5*1.3*0.5*0.75-1$$

Now since $$1.5*1.3*0.5*0.75-1 \leq 0$$ and $$4^y \geq 0$$ for any y

There exist no y for which this equality holds.

Therefore you equation has no answer.

Instead of base 4 I can interpret it as base 10 or a natural logarithm but it still won't give me an answer.

Perhaps you want to check whether you wrote down the question correctly 

Reinout

Give me an example, I'll explain while I work it out for you 

Depends on what volume you're calculating.

The most basic form is the box which has the formula volume = base*width*height

But there are several other too such as;

Cube - side^3

Sphere - (4/3)*pi*radius^3

Cylinder - pi*radius^2*height

etc.

Well done anonymous!

I think something messed up your table a little but your answer is still correct.

Do you have a registered account, so I can see who's the genius behind the answer?

If you don't please do... It takes little time and makes us able to identify you on the forum. 

Reinout