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differentiate: y=[xcos(x^3)]/[(x^4 + 1)^3] with respect to x

This question is on the trickier side as it is heavily computational and requires a good knowledge of the differentiation rules however it is a good way to practise using multiple rules at once.First we will...
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Answered by Elizabeth W. • Maths tutor
3095 Views

Find the volume of a right angled triangular prism with an angle of 28 degrees, hypotenuse of length 10 cm, and projected length of 12.5 cm. Give your answer in cm^3, to three significant figures.

The area of a prism is found by multiplying the area of the end face by the projected length. The adjacent and opposite side lengths of the triangle can be found using SOHCAHTOA. sin(28)= opposite/10, theref...
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Answered by Lily M. • Maths tutor
3716 Views

Solve Simultaneous equations: 3x + 4y = 23 & 2x + 3y = 16

We need to cancel one of the variables (the x or y) out. Find the LCM of x or y.e.g. for x --> 6Multiply the WHOLE eqn to get 6x. So multiply the 1st eqn by 2 and the 2nd by 3[1] 6x + 8y = 46[2] 6x + 9y =...
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Answered by Eric E. • Maths tutor
3596 Views

The curve C has parametric equations x=cos(t)+1/2*sin(2t) and y =-(1+sin(t)) for 0<=t<=2π. Find a Cartesian equation for C. Find the volume of the solid of revolution of C about the y-axis.

Note the simplest relation to eliminate t is the fact cos 2 (t)+sin 2 (t)=1 for all t, so we need only find x and y in terms of cos(t) and sin(t).Note we have sin(t)=-(y+1) from the equation for y already.Fr...
LP
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How do vaccines prevent certain diseases?

Vaccines introduce a dead, inactive or altered form of a pathogen (a microbe that causes an infectious disease) into the body. These pathogens have antigens, which have a shape specific to that pathogen. The...
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Answered by Alice M. • Biology tutor
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