Find the maximum and minimum value of 8 cos A + 15 sin A + 15
Using Pythagorean triplets, we know that (8,15,17) is one ∴ The expression becomes: 17 (817 CosA +1517 SinA) Let there be a angle B for which sin B = 817, cos B = 1517 => 17( sin B cos A + cos B sin A) + 15 17(sin(A+B)) + 15 We know that sin(A+B)max = 1 sin(A+B)min = -1 ∴ Max value = 17 * 1 +15 = 32 Min value = 17 * -1 + 15 = -2
In a group of 100 persons, 72 people can speak English and 43 can speak French. How many can speak English only? How many can speak French only?
Let A be the set of people who speak English. B be the set of people who speak French. A - B be the set of people who speak English and not French. B - A be the set of people who speak French and not English. A ∩ B be the set of people who speak both French and English. Given, n(A) = 72 n(B) = 43 n(A ∪ B) = 100 Now, n(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 72 + 43 - 100 = 115 - 100 = 15 Therefore, Number of persons who speak both French and English = 15 n(A) = n(A - B) + n(A ∩ B) ⇒ n(A - B) = n(A) - n(A ∩ B) = 72 - 15 = 57 and n(B - A) = n(B) - n(A ∩ B) = 43 - 15 = 28 Therefore, Number of people speaking English only = 57 Number of people speaking French only = 28
Who is better among the two cricketers? Anand who makes runs 25, 100, 5. Shiv who makes 45,50,55. How to find?
Here to compare the result we should not calculate the mean of both the players but medians of scores is to be compared.