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AlgebraQuestion and Answers: Page 91

Question Number 178586 Answers: 0 Comments: 0

Question Number 178577 Answers: 1 Comments: 0

prove that (a)cosh^(−1) x=±ln (x+(√(x^2 −1))) (b)tanh^(−1) x=(1/2)ln (((x+1)/(x−1))),∣x∣<1

$prove that$ $(a) \cosh^{- 1} x = \pm \ln (x + \sqrt{x^{2} - 1})$ $(b) \tanh^{- 1} x = \frac{1}{2} \ln (\frac{x + 1}{x - 1}), ∣ x ∣< 1$

Question Number 178576 Answers: 0 Comments: 0

If a>b>0 prove that b<((ae^x +be^(−x) )/(e^x +e^(−x) ))<a

$If a > b > 0 prove that$ $b < \frac{{ae}^{x} + {be}^{- x}}{e^{x} + e^{- x}} < a$

Question Number 178575 Answers: 1 Comments: 0

Solve for x e^(sinh^(−1) x) =1+e^(cosh^(−1) x)

$Solve for x$ $e^{\sinh^{- 1} x} = 1 + e^{\cosh^{- 1} x}$

Question Number 178573 Answers: 2 Comments: 0

Use the law of algebra of preposition to verify the validity of the following argument If I study,then I will not fail the examination. If I do not play football,then I will study. But I fail the examination. Therefore,I played football

$Use the law of algebra of preposition$ $to verify the validity of the following argument$ $If I study, then I will not fail the examination .$ $If I do not play football, then I will study .$ $But I fail the examination .$ $Therefore, I played football$

Question Number 178572 Answers: 0 Comments: 0

Show that ∼[p∨(∼p∧q)] and [∼p∧∼q] are logically equivalent

$Show that$ $\sim [p \lor (\sim p \land q)] and [\sim p \land \sim q] are$ $logically equivalent$

Question Number 178568 Answers: 1 Comments: 0

Given the preposition [(p→q)∧(q→r)]→(p→r) Write down (a)Converse (b)Inverse (c)Contrapositive

$Given the preposition$ $[(p \to q) \land (q \to r)] \to (p \to r)$ $Write down$ $(a) Converse$ $(b) Inverse$ $(c) Contrapositive$

Question Number 178553 Answers: 2 Comments: 0

Solve 1st: 3x^2 −2x−11> 0 2nd: x^4 + 4x^3 − 12x^2 ≤ 0

$S o l v e 1 s t : 3 x^{2} - 2 x - 11 > 0$ $2 n d : x^{4} + 4 x^{3} - 12 x^{2} ⩽ 0$

Question Number 178543 Answers: 1 Comments: 0

Find n , P_(n+2) ^( 4) = 14P_n ^( 3)

$F i n d n, P_{n + 2}^{4} = 14 P_{n}^{3}$

Question Number 178533 Answers: 0 Comments: 0

Find values of n for the (x^2 +(1/x))^n can be contain a constant term

$F i n d v a l u e s o f n f o r t h e {(x^{2} + \frac{1}{x})}^{n} c a n b e c o n t a i n$ $a c o n s t a n t t e r m$

Question Number 178530 Answers: 1 Comments: 0

Conclude the value of the sum: S_n = ((n),(0) ) + 2 ((n),(1) )+...+ 2^n ((n),(n) ) with help of (1+2x)^n

$C o n c l u d e t h e v a l u e o f t h e s u m :$ $S_{n} = (\begin{matrix} n \\ 0 \end{matrix}) + 2 (\begin{matrix} n \\ 1 \end{matrix}) + . . . + 2^{n} (\begin{matrix} n \\ n \end{matrix})$ $w i t h h e l p o f {(1 + 2 x)}^{n}$

Question Number 178525 Answers: 0 Comments: 0

Question Number 178522 Answers: 1 Comments: 0

Question Number 178513 Answers: 0 Comments: 0

Check if the following argument is valid “If am clever then I understand physics. I dont understand physics .therefore I am not clever”

$Check if the following argument is valid$ $‘ ‘ If am clever then I understand physics .$ $I dont understand physics . therefore$ $I am not {clever}^{″}$

Question Number 178512 Answers: 2 Comments: 0

Write the converse, contrapostive and inverse of the statement (a)“If two angles are congruent,then they have the same measure” (b)“If a person is 18 years old,then he is a legal adult”

$Write the converse, contrapostive and$ $inverse of the statement$ $(a) ‘ ‘ If two angles are congruent, then$ $they have the same {measure}^{″}$ $(b) ‘ ‘ If a person is 18 years old, then he is$ $a legal {adult}^{″}$