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AllQuestion and Answers: Page 1898

Question Number 12962 Answers: 1 Comments: 0

Question Number 12919 Answers: 0 Comments: 0

The value of the integral ∫_( 0) ^1 e^x^2 dx lies in the interval

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral}\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{e}^{{x}^{\mathrm{2}} } {dx}\:\:\mathrm{lies} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$

Question Number 12909 Answers: 1 Comments: 0

Question Number 12908 Answers: 1 Comments: 0

Question Number 12905 Answers: 2 Comments: 0

sin (x)=3cos (x) ⇔tan (x)=3 True or false?

$$\mathrm{sin}\:\left({x}\right)=\mathrm{3cos}\:\left({x}\right)\:\Leftrightarrow\mathrm{tan}\:\left({x}\right)=\mathrm{3} \\ $$$${True}\:{or}\:{false}? \\ $$

Question Number 12903 Answers: 1 Comments: 0

Question Number 12902 Answers: 1 Comments: 0

Question Number 12895 Answers: 1 Comments: 2

Question Number 12894 Answers: 1 Comments: 2

Question Number 12889 Answers: 2 Comments: 1

f(x−1)=(2/3)+f(x) f(0)=36−f(21) ⇒f(0)=?

$${f}\left({x}−\mathrm{1}\right)=\frac{\mathrm{2}}{\mathrm{3}}+{f}\left({x}\right) \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{36}−{f}\left(\mathrm{21}\right) \\ $$$$\Rightarrow{f}\left(\mathrm{0}\right)=? \\ $$

Question Number 12885 Answers: 1 Comments: 0

f(f(x))=f^2 (x) What is a solution?

$${f}\left({f}\left({x}\right)\right)={f}^{\mathrm{2}} \left({x}\right) \\ $$$$\: \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}? \\ $$

Question Number 12883 Answers: 1 Comments: 0

for −128≤x≤127 and −127≤y≤128 where x,y∈Z Point P(x,y) is a point on the cartesian plane. From the origin, angle θ is made counter −clockwise with the positive x−axis. (1) How many unique angles θ exist if x,y∈P? (2) Furthermore, how many unique angles θ exist for the full range of x,y∈Z?

$$\mathrm{for}\:\:\:\:\:−\mathrm{128}\leqslant{x}\leqslant\mathrm{127} \\ $$$$\mathrm{and}\:\:\:−\mathrm{127}\leqslant{y}\leqslant\mathrm{128} \\ $$$$\mathrm{where}\:\:\:{x},{y}\in\mathbb{Z} \\ $$$$\: \\ $$$$\mathrm{Point}\:{P}\left({x},{y}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{cartesian}\:\mathrm{plane}. \\ $$$$\: \\ $$$$\mathrm{From}\:\mathrm{the}\:\mathrm{origin},\:\mathrm{angle}\:\theta\:\mathrm{is}\:\mathrm{made}\:\mathrm{counter} \\ $$$$−\mathrm{clockwise}\:\mathrm{with}\:\mathrm{the}\:\mathrm{positive}\:{x}−\mathrm{axis}. \\ $$$$\: \\ $$$$\left(\mathrm{1}\right)\:\mathrm{How}\:\mathrm{many}\:\mathrm{unique}\:\mathrm{angles}\:\theta\:\mathrm{exist} \\ $$$$\mathrm{if}\:{x},{y}\in\mathbb{P}? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Furthermore},\:\mathrm{how}\:\mathrm{many}\:\mathrm{unique} \\ $$$$\mathrm{angles}\:\theta\:\mathrm{exist}\:\mathrm{for}\:\mathrm{the}\:\mathrm{full}\:\mathrm{range}\:\mathrm{of}\:{x},{y}\in\mathbb{Z}? \\ $$

Question Number 12875 Answers: 0 Comments: 3

Question Number 12874 Answers: 1 Comments: 0

Question Number 12873 Answers: 0 Comments: 0

How many flouride ion are there in 1.46 mole of aluminium flouride Alf_3

$$\mathrm{How}\:\mathrm{many}\:\mathrm{flouride}\:\mathrm{ion}\:\mathrm{are}\:\mathrm{there}\:\mathrm{in}\:\mathrm{1}.\mathrm{46}\:\mathrm{mole}\:\mathrm{of}\:\mathrm{aluminium}\:\mathrm{flouride}\:\mathrm{Alf}_{\mathrm{3}} \\ $$

Question Number 12861 Answers: 2 Comments: 0

change0.356^− into p/q form

$${change}\mathrm{0}.\mathrm{35}\overset{−} {\mathrm{6}}\:{into}\:{p}/{q}\:{form} \\ $$$$ \\ $$

Question Number 12859 Answers: 0 Comments: 0

Question Number 12855 Answers: 1 Comments: 0

f(x)=[1−(x−3)^4 ]^(1/7) find f^(−1) (x).

$${f}\left({x}\right)=\left[\mathrm{1}−\left({x}−\mathrm{3}\right)^{\mathrm{4}} \right]^{\mathrm{1}/\mathrm{7}} \\ $$$${find}\:{f}^{−\mathrm{1}} \left({x}\right). \\ $$

Question Number 12846 Answers: 2 Comments: 1

Question Number 12843 Answers: 0 Comments: 0

Let R be a cummutative ring with 1. and a,b member of R. Suppose a is invertible and b is nilpotent. Show that a + b is invertible.

$$\mathrm{Let}\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{cummutative}\:\mathrm{ring}\:\mathrm{with}\:\mathrm{1}.\:\mathrm{and}\:\mathrm{a},\mathrm{b}\:\:\mathrm{member}\:\mathrm{of}\:\mathrm{R}.\:\mathrm{Suppose}\:\mathrm{a}\:\mathrm{is} \\ $$$$\mathrm{invertible}\:\mathrm{and}\:\mathrm{b}\:\mathrm{is}\:\mathrm{nilpotent}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{a}\:+\:\mathrm{b}\:\mathrm{is}\:\mathrm{invertible}. \\ $$

Question Number 12841 Answers: 2 Comments: 0

The number of terms in the expansion of (1+5 (√2) x)^9 + (1−5 (√2) x)^9 is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{1}+\mathrm{5}\:\sqrt{\mathrm{2}}\:{x}\right)^{\mathrm{9}} \:+\:\left(\mathrm{1}−\mathrm{5}\:\sqrt{\mathrm{2}}\:{x}\right)^{\mathrm{9}} \:\mathrm{is} \\ $$

Question Number 12881 Answers: 1 Comments: 0

((lim)/(x→0))((√(1−cos x))/x) is equals to.

$$\frac{{lim}}{{x}\rightarrow\mathrm{0}}\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:{x}}}{{x}} \\ $$$${is}\:{equals}\:{to}. \\ $$

Question Number 12830 Answers: 1 Comments: 0

the LCM and HCF of 30 and a certain number are 150 and 5 respectively. find the number please help

$$\mathrm{the}\:\mathrm{LCM}\:\mathrm{and}\:\mathrm{HCF}\:\mathrm{of}\:\mathrm{30}\:\mathrm{and}\:\mathrm{a}\: \\ $$$$\mathrm{certain}\:\mathrm{number}\:\mathrm{are}\:\mathrm{150}\:\mathrm{and}\:\mathrm{5}\: \\ $$$$\mathrm{respectively}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{number} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help} \\ $$

Question Number 12829 Answers: 2 Comments: 0

Question Number 12828 Answers: 1 Comments: 0

The value of the infinite product (√3) ∙ (9)^(1/4) ∙ ((27))^(1/8) ∙ ((81))^(1/(16)) ...to ∞ is equal to ____.

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{infinite}\:\mathrm{product} \\ $$$$\sqrt{\mathrm{3}}\:\centerdot\:\sqrt[{\mathrm{4}}]{\mathrm{9}}\:\centerdot\:\sqrt[{\mathrm{8}}]{\mathrm{27}}\:\centerdot\:\sqrt[{\mathrm{16}}]{\mathrm{81}}\:...\mathrm{to}\:\infty\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\_\_\_\_. \\ $$

Question Number 12827 Answers: 2 Comments: 0

Sum of three numbers in GP be 14. If one is added to first and second and 1 is subtracted from the third, the new numbers are in AP. The smallest of them is

$$\mathrm{Sum}\:\mathrm{of}\:\mathrm{three}\:\mathrm{numbers}\:\mathrm{in}\:\mathrm{GP}\:\mathrm{be}\:\mathrm{14}.\:\mathrm{If}\:\mathrm{one}\:\mathrm{is} \\ $$$$\mathrm{added}\:\mathrm{to}\:\mathrm{first}\:\mathrm{and}\:\mathrm{second}\:\mathrm{and}\:\mathrm{1}\:\mathrm{is}\:\mathrm{subtracted} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{third},\:\mathrm{the}\:\mathrm{new}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}. \\ $$$$\mathrm{The}\:\mathrm{smallest}\:\mathrm{of}\:\mathrm{them}\:\mathrm{is} \\ $$

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