smc-1119-50-Proportional

Algebra, STD1 A2 2020 HSC 20

The weight of a bundle of A4 paper (`W` kg) varies directly with the number of sheets (`N`) of A4 paper that the bundle contains.

This relationship is modelled by the formula `W = kN`, where `k` is a constant.

The weight of a bundle containing 500 sheets of A4 paper is 2.5 kilograms.

Show that the value of `k` is 0.005. (1 mark)

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A bundle of A4 paper has a weight of 1.2 kilograms. Calculate the number of sheets of A4 paper in the bundle. (2 marks)

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a. `W = 2.5\ text{kg when} \ N = 500:`

b. `text{Find}\ \ N \ \ text{when} \ \ W = 1.2\ text{kg:}`

♦ Mean mark 50%.

The weight of a steel beam, `w`, varies directly with its length, `ℓ`.

A 1200 mm steel beam weighs 144 kg.

Calculate the weight of a 750 mm steel beam. (2 marks)

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`90\ text(kg)`

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`w propto ℓ`

`w = kℓ`

`text(When)\ \ w = 144\ text(kg),\ \ ℓ = 1200\ text(mm)`

`text(When)\ \ ℓ = 750\ text(mm),`

`w`	`= 3/25 xx 750`
	`= 90\ text(kg)`

The weight of an object on the moon varies directly with its weight on Earth. An astronaut who weighs 84 kg on Earth weighs only 14 kg on the moon.

A lunar landing craft weighs 2449 kg when on the moon. Calculate the weight of this landing craft when on Earth. (2 marks)

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`14\ 694\ text(kg)`

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`W_text(moon) prop W_text(earth)`

`=> W_text(m) = k xx W_text(e)`

`text(Find)\ k\ text{given}\ W_text(e) = 84\ text{when}\ W_text(m) = 14`

`14`	`= k xx 84`
`k`	`= 14/84 = 1/6`

`text(If)\ W_text(m) = 2449\ text(kg),\ text(find)\ W_text(e):`

`2449`	`= 1/6 xx W_text(e)`
`W_text(e)`	`= 14\ 694\ text(kg)`

`:.\ text(Landing craft weighs)\ 14\ 694\ text(kg on earth)`