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solve the equation 4cos^2(x) -15sin(x) = 13

We first want to get every term in terms of the same variable, namely sin(x). to do so, we will use the identity sin^2(x) +cos^2(x) = 1 to get: 4(1-sin^2(x)) -15sin(x) -13 = 0. which we can then rewrite as: ...
MG
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What adaptions can a neurone have in order impulses to be transmitted faster?

A neurones role is to transmit electrical impulses rapidly around the organisms body so that the organism can respond to changes in both their external and internal environments. Their structure consists of ...
BB
Answered by Brogan B. • Biology tutor
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The function f is defined for x > 0 by f (x) = x^1n x. Obtain an expression for f ′ (x).

By taking the natural log on both sides we can see that: ln(f(x)) = ln(x)^2 This is a more familiar expression that we know how to differentiate LHS: f '(x)/f(x), RHS: 2*ln(x)/x By rearranging this we can se...
SE
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Given that y = 8x + 2x^-1, find the 2 values for x for which dy/dx = 0

First differentiate y with respect to x, which gives you dy/dx = 8 - 2x^-2. This needs to equal zero so equate to zero. 8-2x^-2 = 0. You can then bring the 2x^-2 to the other side giving 2x^-2=8. Dividing bo...
RB
Answered by Rosemary B. • Maths tutor
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Differentiate y = 4exp(6x) + cos(x) + 6x

dy/dx = 24e 6x - sin(x) + 6
BC
Answered by Benn C. • Maths tutor
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