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Express 3 cos θ + 4 sin θ in the form R cos(θ – α), where R and α are constants, R > 0 and 0 < α < 90°.

To find the value of R, use Pythagoras's Theorem using the coeffecients of cos θ and sin θ. The correct answer should be R=5. Expand the expression R cos(θ – α). Equate the expanded expression with 3 cos θ +...
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Answered by Anahita G. • Maths tutor
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The cost of 5 calculators is £35. Work out the cost of 8 of these calculators.

If the cost of 5 calculators is equal to £35, then we can use division to figure out how much one calculator costs. If we divide 35 by 5 we get the number 7. This means that one of the calculators is going t...
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Answered by Danielle S. • Maths tutor
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Define the term Humanism and identify (artist, title, date/location if appropriate) one work which has been affected by this idea.

Humanism in the Renaissance meant the revival of secular art forms and ideologies that exalted the Classical period as the height of intellectual thought and art forms. It was an ideology that was held by Re...
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What are surds and how does multiplying them work?

A surd is an irrational number which cannot be expressed as a fraction or a recurring number. E.g. root 2 = 1.4142135…. and it continues (but it does NOT repeat like a recurring fraction though) . E.g. pi wo...
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Answered by Febi S. • Maths tutor
9498 Views

You added 75cm^3 of 0.5moldm^-3 HCl to impure MgCO2, and some was left unreacted. The unreacted HCl reacted completely with 21.6cm^m of 0.5moldm^-3 NaOH. So what is the percentage purity of the MgCO3 sample?

MgCO 3 +2HCl --&gt; MgCl 2 + H 2 O +CO 2 For this kind of question, I would always try to convert what I can into moles because that is the link between the solid (the grams of the MgCO 3 ) and the liquid (t...
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Answered by Febi S. • Chemistry tutor
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