Search over 10,000 free study notes

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...

Ben: 5 apples and 3 pears costing £3.70, therefore: 5a + 3p = 3.7. Jenny: 6 apples and 6 pears costing £5.40, therefore: 6a + 6p = 5.4. (1) 5a + 3p = 3.7, (2) 6a + 6p = 5.4. Multiply equation (1) by 2: 10...