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Find the equation of the normal line at the point H, where θ= π/6, on the curve with equations x=3sinθ and y=5cosθ

Step 1: We begin solving this problem by finding the gradient of the tangent line at H, which is equal to dy/dx. In this case, our curve has equations x = 3sinθ and y= 5cosθ. Now, we differentiate x and y wi...
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Answered by Pantelis K. • Maths tutor
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Express (3x^2 - 3x - 2)/(x-1)(x-2) in partial fractions

Step 1: When asked to exrpess something in partial fractions, we first compare the power of the numerator to the power of the denominator. In our case we have that the power of quadratic equation in the nume...
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Answered by Pantelis K. • Maths tutor
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What is natural selection?

Within a population of a species there is great geetic variation giving rise to variation in their phentoypes. Some phenotypes enable an organism to be better adapted to its environment than other members of...
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Answered by Sabrina A. • Biology tutor
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How does covalent bonding work?

Covalent bonding relies on the fact that all atoms are desperately trying to get a full outer shell of electrons. By full outer shell we mean 2 electrons in the first shell, 8 in the 2nd shell, 8 in the 3rd ...
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Answered by Sabrina A. • Chemistry tutor
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Find the roots of the quadratic equation, x^2 - 8x + 24 = 0, by completing the square.

Step 1: The fisrt step is to use the following formula when asked to complete the square, ( x + (b/2) ) 2 - (b/2) 2 + c = 0 Step 2 In our case, b=8,c=24 Hence our equation, x 2 - 8x + 24= 0 becomes (x + (-8/...
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Answered by Pantelis K. • Maths tutor
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