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The main difference is that order of objects matters for permutations. Both involve choosing k objects from a group of size n. Permutations are used to ...

tan(x)+tan(45)/1-tan(x)tan(45) = 8tan(x)

8tan²(x)-7tan(x)+1=0

tan(x)=0.6952 or 0.1798

x = arctan(0.6952) = 34.8070 deg and arctan(0.1798) = 10.1932 deg

Using the substitution u = x³+1 the answer can be found 

(x³+1)⁷/7 + C

A quadratic equation has two equal roots when its discriminant is equal to 0. Calculating the discriminant of the given equation: D = k² - 4(k-1)(2k-3) = k² - 8k²+20k-12...

a) Substituting the coordinate (1,1) into the left hand side of the equation for C we obtain: (1³) + 3*1 - 4(1³)(1³) = 1 + 3 - 4 = 0 = The right hand side of the equation,...