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AllQuestion and Answers: Page 1555

Question Number 53755    Answers: 1   Comments: 9

Question Number 53720    Answers: 0   Comments: 1

Question Number 53709    Answers: 0   Comments: 1

A supermarket pays its sales personnel on a weekly basis. At the end of each week, each sales person receives a basic weekly wage plus bonus, which varies directly as the number of complete weeks that particular person has worked in the shop. At the end of her fourth week a sales girl received a pay packet containing $2060. Six weeks later her pay had jumped to $2150. Find the exact relation for determining how much the shop′s personnel are paid every week.

$$\mathrm{A}\:\mathrm{supermarket}\:\mathrm{pays}\:\mathrm{its}\:\mathrm{sales}\:\mathrm{personnel} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{weekly}\:\mathrm{basis}.\:\mathrm{At}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{each}\:\mathrm{week}, \\ $$$$\mathrm{each}\:\mathrm{sales}\:\mathrm{person}\:\mathrm{receives}\:\mathrm{a}\:\mathrm{basic}\: \\ $$$$\mathrm{weekly}\:\mathrm{wage}\:\mathrm{plus}\:\mathrm{bonus},\:\mathrm{which}\:\mathrm{varies} \\ $$$$\mathrm{directly}\:\mathrm{as}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{complete} \\ $$$$\mathrm{weeks}\:\mathrm{that}\:\mathrm{particular}\:\mathrm{person}\:\mathrm{has}\: \\ $$$$\mathrm{worked}\:\mathrm{in}\:\mathrm{the}\:\mathrm{shop}.\:\mathrm{At}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{her} \\ $$$$\mathrm{fourth}\:\mathrm{week}\:\mathrm{a}\:\mathrm{sales}\:\mathrm{girl}\:\mathrm{received}\:\mathrm{a}\:\mathrm{pay} \\ $$$$\mathrm{packet}\:\mathrm{containing}\:\$\mathrm{2060}.\:\mathrm{Six}\:\mathrm{weeks} \\ $$$$\mathrm{later}\:\mathrm{her}\:\mathrm{pay}\:\mathrm{had}\:\mathrm{jumped}\:\mathrm{to}\:\$\mathrm{2150}.\: \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{relation}\:\mathrm{for}\:\mathrm{determining} \\ $$$$\mathrm{how}\:\mathrm{much}\:\mathrm{the}\:\mathrm{shop}'\mathrm{s}\:\mathrm{personnel}\:\mathrm{are}\: \\ $$$$\mathrm{paid}\:\mathrm{every}\:\mathrm{week}. \\ $$

Question Number 53697    Answers: 0   Comments: 1

The solution of the equation ∫_(log 2) ^x (1/(√(e^x −1))) dx= (π/6) is given by

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\underset{\mathrm{log}\:\mathrm{2}} {\overset{{x}} {\int}}\:\:\frac{\mathrm{1}}{\sqrt{{e}^{{x}} −\mathrm{1}}}\:{dx}=\:\frac{\pi}{\mathrm{6}}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$

Question Number 53696    Answers: 2   Comments: 2

Let I_n =∫_( 0) ^(π/4) tan^n x dx, (n>1 and n∈N), then

$$\mathrm{Let}\:{I}_{{n}} =\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\mathrm{tan}^{{n}} {x}\:{dx},\:\left({n}>\mathrm{1}\:\mathrm{and}\:{n}\in{N}\right),\:\mathrm{then} \\ $$

Question Number 53695    Answers: 1   Comments: 1

If ∫_( 0) ^∞ e^(−x^2 ) dx = (√(π/2)) , then ∫_( 0) ^∞ e^(−ax^2 ) dx, a > 0 is

$$\mathrm{If}\:\underset{\:\mathrm{0}} {\overset{\infty} {\int}}\:{e}^{−{x}^{\mathrm{2}} } {dx}\:=\:\sqrt{\frac{\pi}{\mathrm{2}}}\:,\:\mathrm{then}\:\underset{\:\mathrm{0}} {\overset{\infty} {\int}}\:{e}^{−{ax}^{\mathrm{2}} } {dx}, \\ $$$${a}\:>\:\mathrm{0}\:\:\mathrm{is} \\ $$

Question Number 53694    Answers: 1   Comments: 0

∫_( 0) ^(r π) sin^(2n) x dx =

$$\:\underset{\:\mathrm{0}} {\overset{{r}\:\pi} {\int}}\:\:\mathrm{sin}^{\mathrm{2}{n}} {x}\:{dx}\:= \\ $$

Question Number 53693    Answers: 1   Comments: 1

∫_( 0) ^(π/2) ((x+sin x)/(1+cos x)) dx =

$$\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{{x}+\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}\:{x}}\:{dx}\:= \\ $$

Question Number 53689    Answers: 2   Comments: 1

Question Number 53688    Answers: 2   Comments: 1

i^(i ) ?? Whis is it,, plz explain it i=(√(−1))

$${i}^{{i}\:} \:?? \\ $$$${Whis}\:{is}\:{it},,\:{plz}\:{explain}\:{it} \\ $$$${i}=\sqrt{−\mathrm{1}} \\ $$

Question Number 53686    Answers: 0   Comments: 5

Question Number 53684    Answers: 1   Comments: 4

Question Number 53676    Answers: 0   Comments: 5

If (√(x^2 −1)) +(√(y^2 −1)) =(1/2)(x+y) show that (dy/dx)+(√((y^2 −1)/(x^2 −1))) =0

$${If}\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\:+\sqrt{{y}^{\mathrm{2}} −\mathrm{1}}\:=\frac{\mathrm{1}}{\mathrm{2}}\left({x}+{y}\right) \\ $$$${show}\:{that} \\ $$$$\frac{{dy}}{{dx}}+\sqrt{\frac{{y}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{1}}}\:=\mathrm{0} \\ $$$$ \\ $$

Question Number 53675    Answers: 2   Comments: 0

Given that 1+log_3 x =log_(27) y, express y in terms of x.

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{1}+\mathrm{log}_{\mathrm{3}} \mathrm{x}\:=\mathrm{log}_{\mathrm{27}} \mathrm{y},\:\mathrm{express}\:\mathrm{y} \\ $$$$\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{x}. \\ $$

Question Number 53727    Answers: 2   Comments: 0

Question Number 53664    Answers: 1   Comments: 1

Question Number 53647    Answers: 1   Comments: 2

lim_(𝛗→∞) (1 + (1/φ))^φ = e

$$\underset{\boldsymbol{\phi}\rightarrow\infty} {\mathrm{lim}}\:\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\phi}\right)^{\phi} \:\:=\:\:\mathrm{e} \\ $$

Question Number 53630    Answers: 1   Comments: 0

Question Number 53624    Answers: 0   Comments: 0

find ∫_(−∞) ^(+∞) e^(−x^2 ) (√(1+2x^2 ))dx

$${find}\:\int_{−\infty} ^{+\infty} \:{e}^{−{x}^{\mathrm{2}} } \sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 53623    Answers: 1   Comments: 3

1) study the function f(x)=ln(x+1−(√x)) 2) determine f^(−1) (x) 3) cslculate ∫ f(x)dx snd ∫ f^(−1) (x)dx 4) dtermine ∫ f^(−1) (x^2 +f(x))dx

$$\left.\mathrm{1}\right)\:{study}\:{the}\:{function} \\ $$$${f}\left({x}\right)={ln}\left({x}+\mathrm{1}−\sqrt{{x}}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{cslculate}\:\:\int\:{f}\left({x}\right){dx}\:{snd} \\ $$$$\int\:{f}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{dtermine}\:\int\:{f}^{−\mathrm{1}} \left({x}^{\mathrm{2}} \:+{f}\left({x}\right)\right){dx} \\ $$$$ \\ $$

Question Number 53621    Answers: 0   Comments: 0

How many group homomorphism exist from A_(4 ) to Z_2 ×Z_2 ?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{group}\:\mathrm{homomorphism}\:\mathrm{exist} \\ $$$$\mathrm{from}\:\mathrm{A}_{\mathrm{4}\:} \:\mathrm{to}\:\mathbb{Z}_{\mathrm{2}} ×\mathbb{Z}_{\mathrm{2}} \:\:? \\ $$

Question Number 53620    Answers: 1   Comments: 4

Σ_(n=0) ^∞ (((−1)^n )/(2n+1)) =? 1. (π/4) 2. (π^2 /(12)) 3. (π/8) 4. (π^2 /6)

$$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{2n}+\mathrm{1}}\:=? \\ $$$$ \\ $$$$\mathrm{1}.\:\frac{\pi}{\mathrm{4}}\:\:\:\:\:\:\:\:\mathrm{2}.\:\frac{\pi^{\mathrm{2}} }{\mathrm{12}}\:\:\:\:\:\mathrm{3}.\:\frac{\pi}{\mathrm{8}}\:\:\:\:\:\mathrm{4}.\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$

Question Number 53619    Answers: 0   Comments: 0

If Σ_(n=0) ^∞ ((cosnsin(na))/n) is converge then a is? 1. a∈Z 2. a∈{kπ:k∈Z} 3. a∈R−{((2k+1)/2)π:k∈Z} 4. a∈R

$$\mathrm{If}\:\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{cosnsin}\left(\mathrm{na}\right)}{\mathrm{n}}\:\mathrm{is}\:\mathrm{converge}\:\mathrm{then}\:\mathrm{a}\:\mathrm{is}? \\ $$$$\mathrm{1}.\:\mathrm{a}\in\mathbb{Z} \\ $$$$\mathrm{2}.\:\mathrm{a}\in\left\{\mathrm{k}\pi:\mathrm{k}\in\mathbb{Z}\right\} \\ $$$$\mathrm{3}.\:\mathrm{a}\in\mathbb{R}−\left\{\frac{\mathrm{2k}+\mathrm{1}}{\mathrm{2}}\pi:\mathrm{k}\in\mathbb{Z}\right\} \\ $$$$\mathrm{4}.\:\mathrm{a}\in\mathbb{R} \\ $$$$ \\ $$

Question Number 53601    Answers: 1   Comments: 0

calculate ∫_0 ^∞ ((e^(−x^2 ) −e^(−x) )/x) dx .

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−{x}^{\mathrm{2}} } −{e}^{−{x}} }{{x}}\:{dx}\:. \\ $$

Question Number 53600    Answers: 0   Comments: 1

calculate A_m =∫_0 ^∞ ((sin(mx))/(e^(2πx) −1)) dx with m>0

$${calculate}\:{A}_{{m}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{sin}\left({mx}\right)}{{e}^{\mathrm{2}\pi{x}} −\mathrm{1}}\:{dx}\:\:{with}\:{m}>\mathrm{0} \\ $$

Question Number 53599    Answers: 0   Comments: 1

1) calculate A_n =∫_0 ^∞ (x^(n−1) /(e^x +1)) dx with n integr natural (n≥2) 2) find the value of ∫_0 ^∞ (x/(e^x +1))dx

$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{{n}−\mathrm{1}} }{{e}^{{x}} \:+\mathrm{1}}\:{dx}\:\:\:{with}\:{n}\:{integr}\:{natural}\:\:\left({n}\geqslant\mathrm{2}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}}{{e}^{{x}} \:+\mathrm{1}}{dx} \\ $$

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