Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 478

Question Number 171440 Answers: 0 Comments: 0

Question Number 171431 Answers: 0 Comments: 0

Question Number 171426 Answers: 0 Comments: 0

Question Number 171425 Answers: 0 Comments: 0

Question Number 171423 Answers: 0 Comments: 0

Question Number 171421 Answers: 0 Comments: 0

Prove that arg(e^z )= Im(z) + 2kπ ,k=0,±1,±2,...(√)

$${Prove}\:{that}\:{arg}\left({e}^{{z}} \right)=\:{Im}\left({z}\right)\:+\:\mathrm{2}{k}\pi\:,{k}=\mathrm{0},\pm\mathrm{1},\pm\mathrm{2},...\sqrt{} \\ $$

Question Number 171406 Answers: 1 Comments: 1

1=(√1)=(√((−1)(−1)))=(√((−1)))×(√((−1)))=i.i=i^2 =−1 where is the mistake?

$$\mathrm{1}=\sqrt{\mathrm{1}}=\sqrt{\left(−\mathrm{1}\right)\left(−\mathrm{1}\right)}=\sqrt{\left(−\mathrm{1}\right)}×\sqrt{\left(−\mathrm{1}\right)}=\mathrm{i}.\mathrm{i}=\mathrm{i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$\mathrm{where}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mistake}? \\ $$

Question Number 171403 Answers: 1 Comments: 0

a , b , c ∈R and a≠b≠c and (a/(b+c)) , (b/(a+c)) , (c/(a+b)) are three consecutive terms of AP (Arithmetic progression ) find −: ((b^( 2) −a^( 2) )/(c^( 2) −b^( 2) ))

$$\:\:{a}\:,\:{b}\:,\:{c}\:\in\mathbb{R}\:\:{and}\:\:{a}\neq{b}\neq{c} \\ $$$$\:\:{and}\:\:\:\frac{{a}}{{b}+{c}}\:,\:\frac{{b}}{{a}+{c}}\:,\:\frac{{c}}{{a}+{b}}\:\:\:{are}\:{three}\:{consecutive}\:{terms}\:{of}\:{AP} \\ $$$$\:\:\left({Arithmetic}\:{progression}\:\right) \\ $$$$\:\:{find}\:−:\:\:\:\frac{{b}^{\:\mathrm{2}} −{a}^{\:\mathrm{2}} }{{c}^{\:\mathrm{2}} −{b}^{\:\mathrm{2}} } \\ $$

Question Number 171402 Answers: 2 Comments: 0

solve... ⌊x^( 2) ⌋+⌊x⌋^( 2) = x^( 2) +x +1 x=?

$$\:\:{solve}... \\ $$$$\:\:\:\lfloor{x}^{\:\mathrm{2}} \rfloor+\lfloor{x}\rfloor^{\:\mathrm{2}} =\:{x}^{\:\mathrm{2}} +{x}\:+\mathrm{1} \\ $$$$\:\:\:\:\:\:{x}=? \\ $$

Question Number 171397 Answers: 0 Comments: 3

ax+by+cz=(2/3) x+y+z=18 (1/a)+(1/b)+(1/c)=?

$${ax}+{by}+{cz}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${x}+{y}+{z}=\mathrm{18} \\ $$$$\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}=? \\ $$

Question Number 171395 Answers: 1 Comments: 2

∫_(−∞) ^(+∞) (x^2 /(1+x^4 ))dx

$$\int_{−\infty} ^{+\infty} \frac{\boldsymbol{{x}}^{\mathrm{2}} }{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{4}} }\boldsymbol{{dx}} \\ $$

Question Number 171392 Answers: 0 Comments: 1

∫_0 ^(π/2) ((cos x)/((1+(√(sin 2x)) )^3 )) dx =?

$$\:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{cos}\:{x}}{\left(\mathrm{1}+\sqrt{\mathrm{sin}\:\mathrm{2}{x}}\:\right)^{\mathrm{3}} }\:{dx}\:=? \\ $$

Question Number 171389 Answers: 0 Comments: 1

tan^2 ((π/7))+tan^2 (((3π)/7))+tan^2 (((5π)/7))=?

$$\:\:\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\pi}{\mathrm{7}}\right)+\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)+\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{5}\pi}{\mathrm{7}}\right)=? \\ $$

Question Number 171388 Answers: 1 Comments: 0

a,b, and c are positive real numbers such that a^2 +ab+(b^2 /3) = 25 , (b^2 /3) + c^2 =9 and c^2 +ca+a^2 = 16 find the value of ab+2bc+3ac

$${a},{b},\:{and}\:{c}\:{are}\:{positive}\:{real}\:{numbers} \\ $$$${such}\:{that} \\ $$$${a}^{\mathrm{2}} +{ab}+\frac{{b}^{\mathrm{2}} }{\mathrm{3}}\:=\:\mathrm{25}\:\:,\:\:\:\:\frac{{b}^{\mathrm{2}} }{\mathrm{3}}\:+\:{c}^{\mathrm{2}} \:=\mathrm{9} \\ $$$${and}\:{c}^{\mathrm{2}} +{ca}+{a}^{\mathrm{2}} \:=\:\mathrm{16} \\ $$$${find}\:\:{the}\:\:{value}\:{of}\:\:{ab}+\mathrm{2}{bc}+\mathrm{3}{ac} \\ $$

Question Number 171386 Answers: 0 Comments: 0

A fair coin is flipped 3 times and a random variable X is defined to be 3 times the number of heads minus 2 times the number of tails. Find the probability mass function of X. (Write it in table format).

$$ \\ $$A fair coin is flipped 3 times and a random variable X is defined to be 3 times the number of heads minus 2 times the number of tails. Find the probability mass function of X. (Write it in table format).

Question Number 171385 Answers: 3 Comments: 0

lim_(x→∞) ((rx^5 −4x^3 +3)/(sx^5 −2x+1)) = (1/4) 2r+3s=?

$$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{rx}^{\mathrm{5}} −\mathrm{4}{x}^{\mathrm{3}} +\mathrm{3}}{{sx}^{\mathrm{5}} −\mathrm{2}{x}+\mathrm{1}}\:=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\:\:\mathrm{2}{r}+\mathrm{3}{s}=? \\ $$

Question Number 171377 Answers: 0 Comments: 0

Question Number 171376 Answers: 0 Comments: 4

lim_(x→x^(tanx) ) tanx((x/e^(tanx) ))^(tanx) =?

$$\underset{{x}\rightarrow{x}^{{tanx}} } {\mathrm{lim}}\:{tanx}\left(\frac{{x}}{{e}^{{tanx}} }\right)^{{tanx}} =? \\ $$

Question Number 171371 Answers: 3 Comments: 0

∫_(−∞) ^(+∞) (dx/(1+x^4 ))=?

$$\int_{−\infty} ^{+\infty} \frac{\boldsymbol{{dx}}}{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{4}} }=? \\ $$

Question Number 171370 Answers: 0 Comments: 0

∫_0 ^(𝛑/2) x^3 (√(cos(x)))dx

$$\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \boldsymbol{\mathrm{x}}^{\mathrm{3}} \sqrt{\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}\right)}\boldsymbol{\mathrm{dx}} \\ $$

Question Number 171367 Answers: 0 Comments: 0

Question Number 171366 Answers: 0 Comments: 0

Question Number 171362 Answers: 1 Comments: 0

A rectangle is divided into 40 equal parts. How many of these parts should be shadded in other to cover three-five of the rectangle

$$ \\ $$$$\mathrm{A}\:\mathrm{rectangle}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{40}\:\mathrm{equal}\: \\ $$$$\:\mathrm{parts}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{these}\:\mathrm{parts}\: \\ $$$$\mathrm{should}\:\mathrm{be}\:\mathrm{shadded}\:\mathrm{in}\:\mathrm{other}\:\mathrm{to}\:\mathrm{cover}\: \\ $$$$\:\mathrm{three}-\mathrm{five}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle} \\ $$$$\: \\ $$

Question Number 171379 Answers: 0 Comments: 1

f(x)= { ((2x+3 ;x>0)),((3x−5 ;x≤0)) :} ((df(x))/dx)=?

$${f}\left({x}\right)=\begin{cases}{\mathrm{2}{x}+\mathrm{3}\:\:\:;{x}>\mathrm{0}}\\{\mathrm{3}{x}−\mathrm{5}\:\:;{x}\leqslant\mathrm{0}}\end{cases} \\ $$$$\frac{{df}\left({x}\right)}{{dx}}=? \\ $$

Question Number 171360 Answers: 1 Comments: 0

Solve for real numbers: log_9 x ∙ log_2 (7 − x) = 1

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{log}_{\mathrm{9}} \:\mathrm{x}\:\:\centerdot\:\:\mathrm{log}_{\mathrm{2}} \:\left(\mathrm{7}\:−\:\mathrm{x}\right)\:=\:\mathrm{1} \\ $$

Question Number 171359 Answers: 1 Comments: 0

A heavenly body has mass one third of the earth and its radius is half as that of the earth. if a stone weights 200N on the earth′s surface, find its weight on that heavenly body.

$$\mathrm{A}\:\mathrm{heavenly}\:\mathrm{body}\:\mathrm{has}\:\mathrm{mass}\:\mathrm{one}\:\mathrm{third}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{and}\:\mathrm{its} \\ $$$$\:\mathrm{radius}\:\mathrm{is}\:\mathrm{half}\:\mathrm{as}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}.\:\mathrm{if}\:\mathrm{a}\:\mathrm{stone}\:\mathrm{weights}\:\mathrm{200N}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{earth}'\mathrm{s}\:\mathrm{surface},\:\mathrm{find}\:\mathrm{its}\:\mathrm{weight}\:\mathrm{on}\:\mathrm{that}\:\mathrm{heavenly}\:\mathrm{body}. \\ $$

Pg 473 Pg 474 Pg 475 Pg 476 Pg 477 Pg 478 Pg 479 Pg 480 Pg 481 Pg 482

Contact: info@tinkutara.com