reinout-g

Hi there!

I'm not sure where you're having trouble finding the answer to this question so let me help you.

f(8) means you have a function f(x) where you want to enter x = 8.

In this case your function is $$f(x) = \frac{1}{4}x^4+9x^2-3$$

So if we enter x = 8 into this function we have

$$f(8) = \frac{1}{4} \times 8^4+9 \times 8^2-3$$

Now you probably know the rules of operations in math, so first you would need to calculate

$$8^4 = 4096$$ and $$8^2 = 64$$

This would give us

$$f(8) = \frac{1}{4} \times 4096 + 9 \times 64 - 3$$

second we would need to do the multiplications so

$$\frac{1}{4} \times 4096 = \frac{4096}{4} = 1024$$ and $$9 \times 64 = 576$$

Now we have

$$f(8) = 1024 + 576 - 3$$

This gives

$$f(8) = 1597$$

Reinout-g 

'A so called 'woodchuck' (correctly speaking, a groundhog) would chuck - that is, throw - as much as the woodchuck in question was physically able to chuck (ibid.) if woodchucks in general had the capability (and, presumably, the motivation) to chuck wood' - siri

All right, I got very close to the answer, but was stuck with the condition that their positions were unknown. Was too impatient and googled it (shame on me). If you think you have the answer, pm me :). If you want to discuss the riddle, use this thread.

@Cphill, yeah that one! totally knew that! 

aah never mind, it was the norton toolbar blocking it!

Not sure if there's a specific name for it, but it is simply multiplication out of the brackets.

It is a showcase of the rule that

a(b-c) = ab-ac

Not sure what else I can say about it 

By now you probably get that it's been the total perimeter divided by 4, so if the perimeter is 16m all sides should be of the length 4.

Your welcome :)

Reinout

Similarly if the perimeter is 400 instead of 38 we have

$$A(x) = 200x-x^2\\
A'(x) = 200-2x\\
A'(x) = 0\\
200-2x = 0\\
x = 100\\$$

The third part is very similar to the first problem.

All the four sides together are 38m.

Since it is a rectangle the opposing sides have equal length.

Let's call one of these sides x.

Then the opposing side also had length x

and the other two sides together have a length of 38-2x.

Therefore one side has length 19-x

To calculate the area of the rectangle we multiply the two sides giving.

$$\mbox{Area } = \mbox{one side } \times \mbox{ the other side } = x \times (19-x) = 19x-x^2$$

To get the maximum, we again differentiate and equate the function to zero. Therefore;

$$A(x) = 19x-x^2 \\
A'(x) = 19-2x\\
A'(x) = 0\\
19-2x = 0 \Rightarrow 19 = 2x \Rightarrow x = 9.5$$

and the other side is

$$19-x = 19-9.5 = 9.5$$

Therefore all sides of the rectangle are 9.5m