last one, promise! before i start to wrap up my revision for maths -_-'
question 1:
y varies indirectly as the square root of x.
describe the change in y when the value of x is increased by 8 times.
so my steps are:
y = 1/x^2
y= k/x^2...
y= k/(8x)^2
y= k/64x^2...
k/x^2 divide by k/64x^2 = 64
so i wrote the answer in a sentence as: value of y increases to 64 when x is increased by 8 times.
but it's incorrect because the answer is actually "value of y now is one third of the original value of y"
question 2:
the force of attraction between two magnets is F newtons. This force is inversely proportional to the square of distance, d centimetres, between the magnets. When the two magnets are at a certain distance apart, the force is 10 Newtons. What is the force when this distance is doubled?
my steps:
10 = 1/d^2
10 = k/d^2
when distance is doubled --> F = k/(2d)^2
F = k/4d^2
so i took 10/F = (k/d^2) / (k/4d^2)
10/F = (k/d^2) X (4d^2/k)
10F = 4F
2.5 = F
are my steps + answer correct? the answer key is not with me right now, so it wld be great if someone can assist! thank you so much.
1] y varies indirectly as the square root of x.
We have:
y = k/sqrt x -- (1)
when x is increased by 8 times, it means it is now 8x.
k/sqrt 8x = k/[(sqrt 8).(sqrt x)]
= (1/sqrt 8)(k/sqrt x)
By comparing with (1):
y = k/sqrt x
(1/sqrt 8)y = (1/sqrt 8)(k/sqrt x)
Well, it's not one third exactly, I don't know if I've made any mistakes or the question just wants an approximate value because 1/sqrt 8 rounded off is around 1/3. But one thing for sure is square root is different from square, just like cube root is different from cube. (:
2]
Your answer is correct but I'm not too sure if your steps from here is appropriate:
10/F = (k/d^2) / (k/4d^2)
10/F = (k/d^2) X (4d^2/k)
10F = 4F
2.5 = F
Nevertheless, these are my steps which I think would make it clearer:
F = k/d^2
Let d be the distance when F = 10N,
10 = k/d^2 -- (1)
When d is doubled,
F = k/(2d)^2
F = k/(4d^2) -- (2)
From (2):
k/(4d^2) = (1/4)(k/d^2)
Therefore by comparing (1) & (2):
k/d^2 = 10
(1/4)(k/d^2) = (1/4)(10)
= 2.5N