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Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a foot ball match? Ans: equally likely because they are mutual
Determine or find out the direction cosines and direction angles for a = (2, 1, -4) Solution We will require the magnitude of the vector. ||a|| = √ (4+1+16) = √ (21)
If tanA+sinA=m and tanA-sinA=n, show that m 2 -n 2 = 4√mn Ans: TanA + SinA = m TanA - SinA = n. m 2 -n 2 =4√mn . m 2 -n 2 = (TanA + SinA) 2 -(TanA - SinA) 2
a
Q. There are 10 students on the school debating team. How many different ways can the team choose a president and a secretary? Ans. There are 10 choices for the president
(19 + 7 i)
Determine if the following sequences converge or diverge. If the sequence converges find out its limit. a. {3n 2 - 1 / 10n + 5n 2 } ∞ n =2 b. {e 2n / n} ∞ n =1 c
Show that 571 is a prime number. Ans: Let x=571⇒√x=√571 Now 571 lies between the perfect squares of (23)2 and (24)2 Prime numbers less than 24 are 2,3,5,7,11,13,17,1
Find out the greater of two consecutive positive odd integers whose product is 143. Let x = the lesser odd integer and let x + 2 = the greater odd integer. Because product is a
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