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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
24445 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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How does a deletion of a base in the DNA base sequence lead to a mutated protein?

It is important to note that bases on the DNA (and mRNA) are read in separate sets of 3s along a DNA/(mRNA) stand (this is called a triplet code in DNA, or the codon in mRNA). So, if a base is deleted, the w...
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Answered by Febi S. • Biology tutor
17963 Views

How do I use the product rule for differentiation?

The product rule is a rule for differentiating products of expressions, i.e. 2 expressions multiplied together. The rule is: if y=A B, then dy/dx=A dB/dx +B*dA/dx. This can be remembered as &quot;Write down ...
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Answered by Thomas E. • Maths tutor
9907 Views

How do I approach an essay question?

The layout of your essay is crucial. Make sure your ideas are clear and explicit - your teacher shouldn't have to decode what you mean! Use correct grammar and make your vocabulary interesting, using words s...
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Answered by Caitlin B. • History tutor
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