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Saturday, September 23 2017 @ 11:27 AM CDT
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By: soonteck_01 (offline)  Saturday, January 18 2014 @ 01:32 AM CST (Read 1243 times)  
soonteck_01

Q1. y is proportional to x^n
Write down the value of n when
(i) y cm^2 is the area of the circle of radium x cm
(ii) y hours is the time taken to travel a distance x km at a constant speed

Q2. y is directly proportional to x^2.
It is known that y=10 for a particular value of x.
Find the value of y when this value of x is halved

Please help Thanks

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By: echeewh (offline)  Sunday, January 19 2014 @ 11:34 PM CST  
echeewh

Hey <soonteck_01>,

Your questions do not look like primary questions to me. Are these from GEP class??

Appreciate that you also provide the <Answerkey> where possible, for verifying purpose. Thanks.

Anyway , My worked solution is as follows:

Q1.

Given y is proportional to x^n ( read as x to the power of n )

(i)
Area of circle = pi × radius × radius
y = pi × x^2

Since pi is constant, y is proportional to x^2

so n = 2

(ii)
distance = speed × time
x = speed × y

Since speed is constant, x is proportional to y.

so n = 1

========

Q2.

Given y is directly proportional to x^2,

y = kx^2 , where k = constant

When y = 10,

k = (10 / x^2)

when x is halved [i.e. x -> (x / 2)], we have ...

y = (10 / x^2) × (x / 2) × (x / 2)
= (10 / x^2) × (x^2 / 4)
= (10 / 4)
= (5 / 2)
= 2 1/2 (or 2.5)

=========

Trust this helps.

Do let me know again if this is different from your <Answerkey> or if there's further clarification.

Cheers,
Edward


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By: jo sarah (offline)  Wednesday, January 22 2014 @ 09:56 PM CST  
jo sarah

Q1. y is proportional to x^n
Write down the value of n when
(i) y cm^2 is the area of the circle of radium x cm
(ii) y hours is the time taken to travel a distance x km at a constant speed

Answer:
It means y = kx^n
(i) y = area of circle, and x = radius
Since area of circle = (pi) x radius^2; k = (pi)
n = 2

(ii) y = hours taken to travel, distance of x km at constant speed (say, h km/h)
Since time = distance / speed; then k = 1/h
so that, y = (1/h)(x^1)
n = 1

Q2. y is directly proportional to x^2.
It is known that y=10 for a particular value of x.
Find the value of y when this value of x is halved

Answer:
y = kx^2
In this case, there is no need to find the value of k if you don't want to.
And you will find that this is true: (y2) / (y1) = (x2)^2 / (x1)^2.............[since the constant k will cancel out]
where (x1) is some "particular value of x"; and (y1) = 10; with (x2) = (x1)/2, because halved.
And you are to find (y2), the new value of y, the required answer.
So,
(y2) / 10 = [(x1)/2]^2 / (x1)^2 = 1/4
giving you the value of y when x is halved = (y2) = 10/4 = 2.5

Trust this makes things clear Big Grin

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