E-maths variation

lolaminx SG

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.

iamapebble SG

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