Question and Answers Forum

AllQuestion and Answers: Page 400

Question Number 178556 Answers: 0 Comments: 0

Question Number 178553 Answers: 2 Comments: 0

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

$${Solve}\:\mathrm{1}{st}:\:\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{11}>\:\mathrm{0} \\ $$$$\:\mathrm{2}{nd}:\:{x}^{\mathrm{4}} +\:\mathrm{4}{x}^{\mathrm{3}} −\:\mathrm{12}{x}^{\mathrm{2}} \leqslant\:\mathrm{0} \\ $$

Question Number 178550 Answers: 1 Comments: 0

Question Number 178543 Answers: 1 Comments: 0

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

$${Find}\:{n}\:,\:{P}_{{n}+\mathrm{2}} ^{\:\mathrm{4}} =\:\mathrm{14}{P}_{{n}} ^{\:\mathrm{3}} \\ $$

Question Number 178533 Answers: 0 Comments: 0

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

$${Find}\:{values}\:{of}\:{n}\:{for}\:{the}\:\left({x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}}\right)^{{n}} {can}\:{be}\:{contain} \\ $$$$\:{a}\:{constant}\:{term} \\ $$

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

$${Conclude}\:{the}\:{value}\:{of}\:{the}\:{sum}: \\ $$$${S}_{{n}} =\begin{pmatrix}{{n}}\\{\mathrm{0}}\end{pmatrix}\:+\:\mathrm{2}\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}+...+\:\mathrm{2}^{{n}} \begin{pmatrix}{{n}}\\{{n}}\end{pmatrix}\: \\ $$$$\:{with}\:{help}\:{of}\:\left(\mathrm{1}+\mathrm{2}{x}\right)^{{n}} \\ $$

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”

$$\mathrm{Check}\:\mathrm{if}\:\mathrm{the}\:\mathrm{following}\:\mathrm{argument}\:\mathrm{is}\:\mathrm{valid} \\ $$$$``\mathrm{If}\:\mathrm{am}\:\mathrm{clever}\:\mathrm{then}\:\:\mathrm{I}\:\mathrm{understand}\:\mathrm{physics}. \\ $$$$\mathrm{I}\:\mathrm{dont}\:\mathrm{understand}\:\mathrm{physics}\:.\mathrm{therefore} \\ $$$$\mathrm{I}\:\mathrm{am}\:\mathrm{not}\:\mathrm{clever}'' \\ $$

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”

$$\mathrm{Write}\:\mathrm{the}\:\mathrm{converse},\:\mathrm{contrapostive}\:\mathrm{and} \\ $$$$\mathrm{inverse}\:\mathrm{of}\:\mathrm{the}\:\mathrm{statement} \\ $$$$\left(\mathrm{a}\right)``\mathrm{If}\:\mathrm{two}\:\mathrm{angles}\:\mathrm{are}\:\mathrm{congruent},\mathrm{then} \\ $$$$\mathrm{they}\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{measure}'' \\ $$$$\left(\mathrm{b}\right)``\mathrm{If}\:\:\mathrm{a}\:\mathrm{person}\:\mathrm{is}\:\mathrm{18}\:\mathrm{years}\:\mathrm{old},\mathrm{then}\:\mathrm{he}\:\mathrm{is} \\ $$$$\mathrm{a}\:\mathrm{legal}\:\mathrm{adult}'' \\ $$

Question Number 178511 Answers: 1 Comments: 0

Simplify (p↓q)∧(∼q↓p)

$$\mathrm{Simplify}\: \\ $$$$\left(\mathrm{p}\downarrow\mathrm{q}\right)\wedge\left(\sim\mathrm{q}\downarrow\mathrm{p}\right) \\ $$

Question Number 178508 Answers: 3 Comments: 1

Question Number 178500 Answers: 1 Comments: 1

Question Number 178468 Answers: 0 Comments: 0

For the sequence {u_n } if u_1 =1, u_2 =2 and u_(n+2) ^2 =u_n ^2 +u_(n+1) ^2 −u_n u_(n+1) , for all natural number n. Find lim u_n ?

$${For}\:{the}\:{sequence}\:\left\{{u}_{{n}} \right\}\:{if}\:{u}_{\mathrm{1}} =\mathrm{1},\:{u}_{\mathrm{2}} =\mathrm{2}\:{and}\:{u}_{{n}+\mathrm{2}} ^{\mathrm{2}} ={u}_{{n}} ^{\mathrm{2}} +{u}_{{n}+\mathrm{1}} ^{\mathrm{2}} −{u}_{{n}} {u}_{{n}+\mathrm{1}} ,\:{for}\:{all}\:{natural}\:{number}\:{n}. \\ $$$${Find}\:{lim}\:{u}_{{n}} ? \\ $$

Question Number 178467 Answers: 1 Comments: 0

find n^(th ) terms of 2,3,5,7,11,13,15,17,.

$${find}\:{n}^{{th}\:} {terms}\:{of}\:\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{11},\mathrm{13},\mathrm{15},\mathrm{17},. \\ $$

Question Number 178452 Answers: 1 Comments: 0

show that ((p∧q)⇒r)⇒((p∧∼r)⇒∼q) is tautology

$$\:\:\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\:\:\:\left(\left(\mathrm{p}\wedge\mathrm{q}\right)\Rightarrow\mathrm{r}\right)\Rightarrow\left(\left(\mathrm{p}\wedge\sim\mathrm{r}\right)\Rightarrow\sim\mathrm{q}\right) \\ $$$$\:\:\:\mathrm{is}\:\mathrm{tautology}\: \\ $$

Question Number 178450 Answers: 1 Comments: 3

Question Number 178448 Answers: 1 Comments: 0

Using the algebra propositions simplify (p↔q)→(p→q)

$$\mathrm{Using}\:\mathrm{the}\:\mathrm{algebra}\:\mathrm{propositions} \\ $$$$\mathrm{simplify} \\ $$$$\left(\mathrm{p}\leftrightarrow\mathrm{q}\right)\rightarrow\left(\mathrm{p}\rightarrow\mathrm{q}\right) \\ $$

Question Number 178454 Answers: 2 Comments: 0

In a chess board number of unit squares with 1)one vertex common? 2)2 vertices common?? 3)2 sides common??

$${In}\:{a}\:{chess}\:{board}\:{number}\:{of}\:{unit}\:{squares} \\ $$$$\left.{with}\:\mathrm{1}\right){one}\:{vertex}\:{common}? \\ $$$$\left.\mathrm{2}\right)\mathrm{2}\:{vertices}\:{common}?? \\ $$$$\left.\mathrm{3}\right)\mathrm{2}\:{sides}\:{common}?? \\ $$

Question Number 178434 Answers: 3 Comments: 0

Simplify by using law of algebra (a) [p∨(p∧q)]→∼p (b)(p∧q)→q

$$\mathrm{Simplify}\:\mathrm{by}\:\mathrm{using}\:\mathrm{law}\:\mathrm{of}\:\mathrm{algebra} \\ $$$$\left(\mathrm{a}\right)\:\left[\mathrm{p}\vee\left(\mathrm{p}\wedge\mathrm{q}\right)\right]\rightarrow\sim\mathrm{p} \\ $$$$\left(\mathrm{b}\right)\left(\mathrm{p}\wedge\mathrm{q}\right)\rightarrow\mathrm{q} \\ $$

Question Number 178433 Answers: 1 Comments: 0

Determine whether the following proposition is true or not [(p→∼q)∧(q∨r)∧p]→r

$$\mathrm{Determine}\:\mathrm{whether}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{proposition}\:\mathrm{is}\:\mathrm{true}\:\mathrm{or}\:\mathrm{not} \\ $$$$\left[\left(\mathrm{p}\rightarrow\sim\mathrm{q}\right)\wedge\left(\mathrm{q}\vee\mathrm{r}\right)\wedge\mathrm{p}\right]\rightarrow\mathrm{r} \\ $$

Question Number 178423 Answers: 2 Comments: 0

(m/n) = (k/p) and (m/n) = (k/p) = 1,5 Find (m/n) + (k/p) = ?

$$\frac{\mathrm{m}}{\mathrm{n}}\:=\:\frac{\mathrm{k}}{\mathrm{p}}\:\:\:\mathrm{and}\:\:\:\frac{\mathrm{m}}{\mathrm{n}}\:=\:\frac{\mathrm{k}}{\mathrm{p}}\:=\:\mathrm{1},\mathrm{5} \\ $$$$\mathrm{Find}\:\:\:\frac{\mathrm{m}}{\mathrm{n}}\:+\:\frac{\mathrm{k}}{\mathrm{p}}\:=\:? \\ $$

Question Number 178415 Answers: 2 Comments: 0

If acosh x+bsinh x=c show that. x=ln [((c±(√(c^2 +b^2 −a^2 )))/(a+b))]

$$\mathrm{If}\:\mathrm{acosh}\:\mathrm{x}+\mathrm{bsinh}\:\mathrm{x}=\mathrm{c}\: \\ $$$$\mathrm{show}\:\mathrm{that}. \\ $$$$\mathrm{x}=\mathrm{ln}\:\left[\frac{\mathrm{c}\pm\sqrt{\mathrm{c}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} }}{\mathrm{a}+\mathrm{b}}\right] \\ $$

Question Number 178413 Answers: 1 Comments: 2

(2x^3 y+3xy−5x^2 y^2 +12)÷(2x−4) Divide it using compound division

$$\left(\mathrm{2}{x}^{\mathrm{3}} {y}+\mathrm{3}{xy}−\mathrm{5}{x}^{\mathrm{2}} {y}^{\mathrm{2}} +\mathrm{12}\right)\boldsymbol{\div}\left(\mathrm{2}{x}−\mathrm{4}\right) \\ $$$$ \\ $$Divide it using compound division

Question Number 178412 Answers: 1 Comments: 0

Express sinh^(−1) x−ln x in terms of natural logarithms.Hence find the limit as x→∞

$$\mathrm{Express}\:\mathrm{sinh}\:^{−\mathrm{1}} \mathrm{x}−\mathrm{ln}\:\mathrm{x}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of} \\ $$$$\mathrm{natural}\:\mathrm{logarithms}.\mathrm{Hence}\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{limit}\:\mathrm{as}\:\mathrm{x}\rightarrow\infty \\ $$

Question Number 178400 Answers: 1 Comments: 0

evaluate Σ_(k=1) ^n k e^(kx)

$$\:\:\mathrm{evaluate}\:\:\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{k}\:\mathrm{e}^{\mathrm{kx}} \\ $$

Pg 395 Pg 396 Pg 397 Pg 398 Pg 399 Pg 400 Pg 401 Pg 402 Pg 403 Pg 404

Contact: info@tinkutara.com