我知错了。:( I try to solve the Sadako Loi problem k? 不要再来找我了。

]]>**mathslover:** Marked your workings. Aiyooo so many careless mistakes! Think you're the first victim of Sadako Loi's Curse!

**a_x:** Sadly, respect for aunties was the outcome of the day, and the poor cashier really had no choice but to apologize to the *young & gracious* Miss Loi profusely.

**Stan:** Ooi don't be rude to aunties here! This is an aunty-friendly blog! *BEEP*!!!

2) F = kt^{−2}

When t is tripled,

New F = k(3t)^{−2}

New F = (1/9)kt^{−2}

New F = (1/9)F

Percentage change = change / original x 100%

= −(8/9)F / F x 100% = −0.889%

**Miss Loi:** This part is actually a test on your concept of Percentages - a very basic Sec 1 topic that sadly managed to caught many students out.

After correcting your careless mistake in Comment #2, you're right to list that:

- Original
F = k/t^2

So the change in `F` = New `F` − New `F` =

∴ % change

= (change in `F`/ original `F`) x 100%

= × 100%

≈ −88.9%

So when `t` is tripled, `F` will **decrease** by 88.9% → not 11.1%, or 800%, and most certainly NOT a Sadako Loi-induced 0.889%!!!!!!!!!!!!!!!

On hindsight it would've served a greater purpose if this part of the question had been changed to "Find the percentage change in `F` when `t` is *reduced* by 3 times" to emphasize the importance of the formula: **% change = change / original x 100%**.

So in such a case, what would the % increase of `F` be? 900%? 800%? 90%?????

Sigh.. not going to check le...

]]>"F inversely proportional to t squared means F = kt^{−2} means t cannot be 0." can be used to explain why all your graphs are wrong except IV already...

*really shouldn't have viewed Sadako Loi's video so late that night*

]]>Question hijacking time!

1) IV

- I and II definitely out, inversely proportional means as t goes up F goes down.

- V definitely out because inversely proportional to square of t means the F/t graph cannot be straight line.

- III is out because F inversely proportional to t squared means F = kt^{−2} means t cannot be 0.

Hence by elimination of impossible answers, the answer of IV is obtained. 😛

**Miss Loi:** Yes the question states that "`F` is ** inversely** proportional to the

Putting this English statement in mathematical context

⇒ `F`↑, `x`^{2}↓ ⇔ `F`↓, `x`^{2}↑ (⇒ Graphs I & II are out!)

⇒ `F` ∝ (by definition)

⇒ `F` =

If you're an upper sec student who's already familiar with the various sketches of important graphs, you should *straightaway* be able to identify the graph of , jump up from your seat and scream "*It's IV! It's IV! IT'S IV*" excitedly like a *siao cha/ta boh* (to the chagrin of those around you).

Else you may follow **mathslover**'s wisdom of elimination and/or her comment below to arrive at the same conclusion.

P.S. It's good to write out the `F` = expression coz it's easy to forget that we're dealing with a **square of x** here, as many of us may already have the image of

2) F = kt^{−2}

When t is tripled,

New F = k(3t)^{−2}

New F = 9kt^{−2}

→ Aiyooo! Tsk tsk! Luckily you managed to 悬崖勒马 below BUT ...

~~New F = 9F~~

~~Percentage change = change / original × 100%~~

~~= 8F / F × 100% = 800%~~

*Puts up WRONG WORKING tape* Move along now ... see corrected workings below!

3) When t = 70, F = 0.1.

By substituting,

0.1 = k (70^{−2})

0.1 x 4900 = k

k = 490

3i) F = 490t^{−2}

When F = 0.1/2 = 0.05, Miss Loi will start to challenge the law by drinking unpaid barley water.

F = 490t^{−2} = 0.05

490 = 0.05t^{2}

t^{2} = 490 / 0.05 = 9800

t = 98.995s = 99.0s (3.s.f)

3ii) t = 99.0s

Part 3 is one of the two typically standard kinds of proportion/variations questions (the other kind being something like this that you can expect to see in your O-Level E-Maths Paper 1.

As shown by **mathslover**'s workings above, one can see that it's important to read the statement in the question carefully (i.e. pick out the critical words like "inversely", "square of `x`", "`F` falls to half of this value" etc.) in order to obtain the expression () and subsequently the value of `k` correct from the start.

After which it's simply sub, sub, sub in the given values to find that Miss Loi has about half a minute to take corrective action to prevent irreversible damage to her skin!

Miss Loi ah, next time don't wait till last minute then buy water...

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