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We know sin(x)^2+cos(x)^2=1Dividing by cos(x)^2: tan(x)^2+1=sec(x)^2Substitute into the Equation and Rearrange to get: tan(x)^2-2*tan(x)-3=0Let y = tan(x): y^2-2y-3=0Factorising: (y-3)(y+1)=0so y = 3 and ...

If y is inversely proportional to x. We know that y=k/x for some constant k. We need to find this constant before continuing. Looking at the information given to us in the question we know for one example...

Step 1) Rearrange the first equation to make y the subject: 8x + 2y = 48 , 2y = 48 - 8x , y = 24 - 4x. step 2) Sub y = 23 - 4x into the second equation: 14x + 6(24 -4x) = 94 , 14x + 144 - 24x = 94 Step 3)...

Formula for a Geometric series for term n = arⁿ , where a = the first term and r = common ratio.Therefore, with the information given we can write that ar² = 100 and ar⁴ =...

Equation of curve is: y = y =3x² - x³To find area need to integrate between 0 and 3So integrating each term gives x³ - x⁴/4 + ...