VCE Methods Question Thread!

[Einstein]

i see where you coming from, so i could just divide the first 2 terms by 2 and still get the same answer when completing the square?

would i get a different answer is i did 2(.....19/2) and completed the square?

[Champ101]

i see where you coming from, so i could just divide the first 2 terms by 2 and still get the same answer when completing the square?

would i get a different answer is i did 2(.....19/2) and completed the square?

yes, it would still work, however, you would then be working with fractions and it becomes easier to make mistakes.

[Einstein]

how do you solve for y in

1/y = 1/a - 1/b

Thanks

[b^3]

1. Combine the right side into a single fraction.
2. Multiply the denominator up for both sides.
3. Rearrange for .

Spoiler

[Einstein]

did you times the right hand side by ab? if so why the the left hand side?

thanks

[Einstein]

also, if you are aware do you know of any rearrange  function on the casio classpad?

thanks

[b^3]

did you times the right hand side by ab? if so why the the left hand side?

thanks

We need to get the right hand side to be over the same denominator. So what do the two have in common? If we multiply by we don't change the expression as , but we can get it over , similarly multiplying by .

Now we can multiply both sides by and both sides by to bring them out of the denominators.

Then dividing both sides by allows us to get on it's own.

[Mieow]

Can someone please help me solve this question?

The radius of a circular puddle is increasing at a rate of 10 cm/h. Find the rate at which the
area is increasing when the radius is 1.5 metres

[Zealous]

The radius of a circular puddle is increasing at a rate of 10 cm/h. Find the rate at which the
area is increasing when the radius is 1.5 metres

"radius of a circular puddle is increase at a rate of 10cm/h"


"Find the rate at which the area is increasing when the radius is 1.5m"

(careful of the units! 1.5m=150cm)

Set up chain rule equation - we want to find dA/dt, we are given dr/dt:



We need to find dA/dr - we know that the puddle is a circle and hence:



Sub this back into our chain rule equation:



Sub in r=150:



Hence when the radius is 1.5 metres, the rate at which the area is increasing is .

[Anchy]

The cost of production, C ($), of producing n pairs of shoes is given by C= (1/6)n^2 + 200. If each pair of shoes is sold for $88, how many pairs of shoes should be produced for maximum profit and what is the profit?

Thanks

[kinslayer]

The cost of production, C ($), of producing n pairs of shoes is given by C= (1/6)n^2 + 200. If each pair of shoes is sold for $88, how many pairs of shoes should be produced for maximum profit and what is the profit?

Thanks

The profit would be the revenue minus the cost. So

To maximise the profit, find the derivative and set it equal to zero.




.
So n = 3 * 88 = 264 pairs to maximise profit. The amount of profit is P(264) =  $11,416.

[Einstein]

How is this done, i have also attached answers - use of the sine rule

Thanks

[soNasty]

"Find the side length of the largest cube that can fit inside a sphere of diameter 24cm"
Help please (these max/min questions are annoying)

[lzxnl]

Try and fit the largest square inside a circle. You'll find that the diagonal of the square must be a diameter, meaning each side of the cube is 1/sqrt2 times the diameter.

[Zealous]

"Find the side length of the largest cube that can fit inside a sphere of diameter 24cm"
Help please (these max/min questions are annoying)

This might help: