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Solve the equation sec^2(A) = 3 - tan(A), for 0<= A <= 360 (degrees)

Using simple trig identities, we know tan^2(A) + 1 = sec^2(A).Substituting for sec^2(A) into our equation, we get: tan^2(A) + 1 = 3 - tan(A).Moving this over to one side, we get the quadratic in terms of tan...
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Answered by Lachlan F. • Maths tutor
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If the functions f and g are defined: f: x--> x/5 + 4 g : x--> 30x + 10. what is x, if fg(x) = x. ?? What would fgf(x) = x^2 be??

You should insert function g into function f. (30x + 10) / 5 + 4 = 0 6x + 2 + 4 = 0 6x + 6 = 0 x = -1 This is a more complex problem:You need to do a similar task but you should do it in steps.gf(x) = 30 (x/...
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Answered by Lottie M. • Maths tutor
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Differentiate y = ln (3x + 2)

The equation for the derivative of the natural log is dy/dx = f'(x)/f(x) where f(x) = the contents of the natural log, in this case 3x+2. So, to get dy/dx we first need f'(x), the derivative of f(x). This is...
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Answered by Will S. • Maths tutor
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Solve the simultaneous equations: y+4x+1=0 and y^2+5x^2+2x=0

y= -4x-1y 2 = (-4x-1) 2 = 16x 2 +8x +1y 2 +5x 2 +2x = 0lets substitute what we found y 2 equal to earlier, which gives us(16x 2 +8x +1) + 5x 2 +2x = 021x 2 + 10x +1 = 0after factorising this we get(7x+1)(3x+...
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Answered by Oleksandr U. • Maths tutor
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Solve int(ln(x)dx)

To solve this we must use integration by parts: int(udv) = uv - int(vdu) (1) Hence let u = ln(x), dv = dx =&gt; du=(1/x)dx, v=x, and now using (1) and substituting values we obtain int(ln(x)dx) = ln(x)x - in...
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Answered by George B. • Maths tutor
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