Question and Answers Forum

AllQuestion and Answers: Page 658

Question Number 143993 Answers: 1 Comments: 0

Question Number 143987 Answers: 1 Comments: 0

If f(x^2 −6x+6)+f(x^2 −4x+4)=2x ∀x∈R then f(−3)+f(9)−5f(1)=?

$${If}\:{f}\left({x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{6}\right)+{f}\left({x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{4}\right)=\mathrm{2}{x} \\ $$$$\forall{x}\in{R}\:{th}\mathrm{e}{n}\:{f}\left(−\mathrm{3}\right)+{f}\left(\mathrm{9}\right)−\mathrm{5}{f}\left(\mathrm{1}\right)=? \\ $$

Question Number 143980 Answers: 1 Comments: 0

Question Number 143979 Answers: 1 Comments: 0

Question Number 143970 Answers: 1 Comments: 0

Given that ω is a complex number, ω^7 =1, ω≠1, find the value of ω^1 +ω^2 +ω^3 +ω^4 +ω^5 +ω^6 .

$$\mathrm{Given}\:\mathrm{that}\:\omega\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}, \\ $$$$\omega^{\mathrm{7}} =\mathrm{1},\:\omega\neq\mathrm{1},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\omega^{\mathrm{1}} +\omega^{\mathrm{2}} +\omega^{\mathrm{3}} +\omega^{\mathrm{4}} +\omega^{\mathrm{5}} +\omega^{\mathrm{6}} . \\ $$

Question Number 143965 Answers: 1 Comments: 1

Question Number 143964 Answers: 1 Comments: 2

x_1 and x_2 are solutions of equality : cos (((πx+π)/6)) − sin (((πx−π)/6)) = (1/2) (√3) , 0 ≤ x ≤ 12 Find the value of x_1 + x_2 .

$${x}_{\mathrm{1}} \:{and}\:\:{x}_{\mathrm{2}} \:\:{are}\:\:{solutions}\:\:{of}\:\:{equality}\:: \\ $$$$\:\:\mathrm{cos}\:\left(\frac{\pi{x}+\pi}{\mathrm{6}}\right)\:−\:\mathrm{sin}\:\left(\frac{\pi{x}−\pi}{\mathrm{6}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\sqrt{\mathrm{3}}\:\:\:,\:\:\:\mathrm{0}\:\leqslant\:{x}\:\leqslant\:\mathrm{12} \\ $$$${Find}\:\:{the}\:\:{value}\:\:{of}\:\:{x}_{\mathrm{1}} +\:{x}_{\mathrm{2}} \:. \\ $$

Question Number 143963 Answers: 1 Comments: 0

A=x^(ln(y/x)) .y^(ln(z/x)) .z^(ln(x/y)) =??

$$\mathrm{A}=\mathrm{x}^{\mathrm{ln}\frac{\mathrm{y}}{\mathrm{x}}} .\mathrm{y}^{\mathrm{ln}\frac{\mathrm{z}}{\mathrm{x}}} .\mathrm{z}^{\mathrm{ln}\frac{\mathrm{x}}{\mathrm{y}}} =?? \\ $$

Question Number 143962 Answers: 2 Comments: 0

∫_0 ^(π/2) ((2xsin^2 t)/(cos^2 t+x^2 sin^2 t))dt=.....???

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{2}{xsin}^{\mathrm{2}} {t}}{{cos}^{\mathrm{2}} {t}+{x}^{\mathrm{2}} {sin}^{\mathrm{2}} {t}}{dt}=.....??? \\ $$

Question Number 143961 Answers: 1 Comments: 0

I=∫_(π/6) ^(π/3) ((cos^6 x)/(1−3sin^2 xcos^2 x))dx=?

$$\mathrm{I}=\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{3}}} \frac{\mathrm{cos}^{\mathrm{6}} \mathrm{x}}{\mathrm{1}−\mathrm{3sin}^{\mathrm{2}} \mathrm{xcos}^{\mathrm{2}} \mathrm{x}}\mathrm{dx}=? \\ $$

Question Number 143960 Answers: 2 Comments: 0

The value of lim_(x→0) ((√(1−cos x^2 ))/(1−cos x)) =?

$$\:\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:\mathrm{x}^{\mathrm{2}} }}{\mathrm{1}−\mathrm{cos}\:\mathrm{x}}\:=? \\ $$

Question Number 143959 Answers: 1 Comments: 0

If g(x)=(4cos^4 x−2cos 2x−(1/2)cos 4x−x^7 )^(1/7) then tbe value of g(g(100)) is equal to ...

$$\:\:\mathrm{If}\:\mathrm{g}\left(\mathrm{x}\right)=\left(\mathrm{4cos}\:^{\mathrm{4}} \mathrm{x}−\mathrm{2cos}\:\mathrm{2x}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{4x}−\mathrm{x}^{\mathrm{7}} \right)^{\frac{\mathrm{1}}{\mathrm{7}}} \\ $$$$\mathrm{then}\:\mathrm{tbe}\:\mathrm{value}\:\mathrm{of}\:\mathrm{g}\left(\mathrm{g}\left(\mathrm{100}\right)\right)\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to}\:... \\ $$

Question Number 143958 Answers: 1 Comments: 0

Question Number 143951 Answers: 0 Comments: 0

∫_0 ^(π/2) ((2xsin^2 t)/(cos^2 t+x^2 sin^2 t))dt=.....????

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{2}{xsin}^{\mathrm{2}} {t}}{{cos}^{\mathrm{2}} {t}+{x}^{\mathrm{2}} {sin}^{\mathrm{2}} {t}}{dt}=.....???? \\ $$

Question Number 143952 Answers: 3 Comments: 0

Question Number 143920 Answers: 2 Comments: 0

Question Number 143913 Answers: 1 Comments: 0

If ((cos α)/(cos β)) = m and ((cos α)/(sin β)) = n then prove that (m^2 +n^2 )cos^2 β = n^2

$$\mathrm{If}\:\:\frac{\mathrm{cos}\:\alpha}{{cos}\:\beta}\:=\:\mathrm{m}\:\mathrm{and}\:\frac{\mathrm{cos}\:\alpha}{\mathrm{sin}\:\beta}\:=\:\mathrm{n}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\left(\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} \right)\mathrm{cos}^{\mathrm{2}} \beta\:=\:{n}^{\mathrm{2}} \\ $$

Question Number 143932 Answers: 4 Comments: 0

Question Number 143923 Answers: 0 Comments: 1

What is the value of [sin^(−1) (sin(((2π)/3)))]?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left[\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)\right)\right]? \\ $$

Question Number 143904 Answers: 1 Comments: 0

Question Number 143906 Answers: 1 Comments: 0

Question Number 143909 Answers: 2 Comments: 3

Question Number 143899 Answers: 3 Comments: 0

Question Number 143898 Answers: 0 Comments: 0

Question Number 143892 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((cos^4 (2x))/((x^4 −x^2 +1)^2 ))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{cos}^{\mathrm{4}} \left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{4}} \:−\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 143890 Answers: 2 Comments: 0

if a+b+c=π tanA+tanB+tanC =tanA.tanB.tanC FAILED TO CALCULATE

$${if}\:{a}+{b}+{c}=\pi\:\:\: \\ $$$$\:{tanA}+{tanB}+{tanC}\:={tanA}.{tanB}.{tanC} \\ $$$$\mathrm{FAILED}\:\mathrm{TO}\:\mathrm{CALCULATE} \\ $$

Pg 653 Pg 654 Pg 655 Pg 656 Pg 657 Pg 658 Pg 659 Pg 660 Pg 661 Pg 662

Contact: info@tinkutara.com