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Question Number 144502 Answers: 0 Comments: 2

it is known that after injecting the 1^(st) dosage of a drug in exactly hours p(t)= { ((Ae^(−(t/(24))) , 0≤t≤8)),(((A+Ae^(−(1/3)) )e^(−(((t−8)/(24)))) , 8 ≤ t≤24)) :} A is the initial dosage at t= 0hours a) show that towards the application of the n^(th) dosage , the dosage remained in blood is (((1−e^(−(1/n)) )/(1−e^(−(1/3)) )))×A

$${it}\:{is}\:{known}\:{that}\:{after}\:{injecting}\:{the}\:\mathrm{1}^{{st}} \\ $$$${dosage}\:{of}\:{a}\:{drug}\:{in}\:{exactly}\:{hours} \\ $$$${p}\left({t}\right)=\begin{cases}{{Ae}^{−\frac{{t}}{\mathrm{24}}} ,\:\mathrm{0}\leqslant{t}\leqslant\mathrm{8}}\\{\left({A}+{Ae}^{−\frac{\mathrm{1}}{\mathrm{3}}} \right){e}^{−\left(\frac{{t}−\mathrm{8}}{\mathrm{24}}\right)} ,\:\mathrm{8}\:\leqslant\:{t}\leqslant\mathrm{24}}\end{cases} \\ $$$${A}\:{is}\:{the}\:{initial}\:{dosage}\:{at}\:{t}=\:\mathrm{0}{hours} \\ $$$$\left.{a}\right)\:{show}\:{that}\:{towards}\:{the}\:{application}\:{of} \\ $$$${the}\:{n}^{{th}} \:{dosage}\:,\:{the}\:{dosage}\:{remained}\:{in}\:{blood}\:{is} \\ $$$$\left(\frac{\mathrm{1}−{e}^{−\frac{\mathrm{1}}{{n}}} }{\mathrm{1}−{e}^{−\frac{\mathrm{1}}{\mathrm{3}}} }\right)×{A} \\ $$

Question Number 144500 Answers: 2 Comments: 0

calculate Σ_(n=0) ^∞ (1/(n^2 +4))

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} \:+\mathrm{4}} \\ $$

Question Number 144499 Answers: 1 Comments: 0

find ∫_0 ^∞ ((arctan(x^n ))/x^n )dx (n≥2) natural

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{x}^{\mathrm{n}} \right)}{\mathrm{x}^{\mathrm{n}} }\mathrm{dx}\:\:\:\left(\mathrm{n}\geqslant\mathrm{2}\right)\:\mathrm{natural} \\ $$

Question Number 144496 Answers: 2 Comments: 1

Question Number 144504 Answers: 0 Comments: 0

for what values of b is ln(a−b)ln(a+b)≤ln^2 a Note: 0≤b<a

$${for}\:{what}\:{values}\:{of}\:{b}\:{is} \\ $$$${ln}\left({a}−{b}\right){ln}\left({a}+{b}\right)\leqslant{ln}^{\mathrm{2}} {a} \\ $$$${Note}:\:\mathrm{0}\leqslant{b}<{a} \\ $$

Question Number 144484 Answers: 1 Comments: 0

Question Number 144482 Answers: 1 Comments: 0

show that ∀n∈Z E(((n−1)/2))+E(((n+2)/4))+E(((n+4)/4))=n

$${show}\:{that}\:\forall{n}\in\mathbb{Z}\: \\ $$$${E}\left(\frac{{n}−\mathrm{1}}{\mathrm{2}}\right)+{E}\left(\frac{{n}+\mathrm{2}}{\mathrm{4}}\right)+{E}\left(\frac{{n}+\mathrm{4}}{\mathrm{4}}\right)={n} \\ $$

Question Number 144474 Answers: 1 Comments: 0

A=(√(1+(√(7+(√(1+(√(7+(√(1+(√(7+...........))))))))))))

$$\mathrm{A}=\sqrt{\mathrm{1}+\sqrt{\mathrm{7}+\sqrt{\mathrm{1}+\sqrt{\mathrm{7}+\sqrt{\mathrm{1}+\sqrt{\mathrm{7}+...........}}}}}} \\ $$

Question Number 144483 Answers: 1 Comments: 0

(p_n )=(1+(1/n^2 ))(1+(2/n^2 ))...(1+(n/n^2 )) Σ_(k=1) ^n k^2 =(1/6)n(2n+1)(n+1) show that (1/2)(1+(1/n))−(1/(12n^2 ))(2n+1)(n+1)<ln(p_n )<(1/2)(1+(1/n)) hence find lim_(n→∞) (p_n ) 2) show that t−(t^2 /2) ≤ln(1+t) ≤t, ∀t>0 please help

$$\left({p}_{{n}} \right)=\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)\left(\mathrm{1}+\frac{\mathrm{2}}{{n}^{\mathrm{2}} }\right)...\left(\mathrm{1}+\frac{{n}}{{n}^{\mathrm{2}} }\right) \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{6}}{n}\left(\mathrm{2}{n}+\mathrm{1}\right)\left({n}+\mathrm{1}\right) \\ $$$${show}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)−\frac{\mathrm{1}}{\mathrm{12}{n}^{\mathrm{2}} }\left(\mathrm{2}{n}+\mathrm{1}\right)\left({n}+\mathrm{1}\right)<{ln}\left({p}_{{n}} \right)<\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right) \\ $$$${hence}\:{find}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left({p}_{{n}} \right) \\ $$$$\left.\mathrm{2}\right)\:{show}\:{that}\: \\ $$$${t}−\frac{{t}^{\mathrm{2}} }{\mathrm{2}}\:\leqslant{ln}\left(\mathrm{1}+{t}\right)\:\leqslant{t},\:\forall{t}>\mathrm{0} \\ $$$${please}\:{help} \\ $$$$ \\ $$

Question Number 144473 Answers: 2 Comments: 0

L=lim_(x→(π/3)) ((8cos^2 5x+2cosx−3)/(4cos^2 5x+8cosx−5)) =?

$$\mathrm{L}=\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {\mathrm{lim}}\frac{\mathrm{8cos}^{\mathrm{2}} \mathrm{5x}+\mathrm{2cosx}−\mathrm{3}}{\mathrm{4cos}^{\mathrm{2}} \mathrm{5x}+\mathrm{8cosx}−\mathrm{5}}\:\:=? \\ $$

Question Number 144471 Answers: 0 Comments: 0

Question Number 144470 Answers: 0 Comments: 0

Solve for real positive numbers the equation: z^(log(3)) + z^(log(4)) + z^(log(5)) = z^(log(6))

$${Solve}\:{for}\:{real}\:{positive}\:{numbers}\:{the} \\ $$$${equation}: \\ $$$$\boldsymbol{{z}}^{\boldsymbol{{log}}\left(\mathrm{3}\right)} \:+\:\boldsymbol{{z}}^{\boldsymbol{{log}}\left(\mathrm{4}\right)} \:+\:\boldsymbol{{z}}^{\boldsymbol{{log}}\left(\mathrm{5}\right)} \:=\:\boldsymbol{{z}}^{\boldsymbol{{log}}\left(\mathrm{6}\right)} \\ $$

Question Number 144468 Answers: 0 Comments: 1

Question Number 144525 Answers: 2 Comments: 0

If y=cosh (x^2 −3x+1) (d^2 y/dx^2 ) =?

$$\:\mathrm{If}\:\mathrm{y}=\mathrm{cosh}\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{1}\right) \\ $$$$\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:=? \\ $$

Question Number 144464 Answers: 1 Comments: 0

f(x)=(2/((1+sinx)^2 )) developp f at fourier serie

$$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\left(\mathrm{1}+\mathrm{sinx}\right)^{\mathrm{2}} } \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 144463 Answers: 1 Comments: 0

Determiner l′original de laplace F(p)=(1/((p^2 +p+1)^2 ))

$${Determiner}\:{l}'{original}\:{de}\:{laplace} \\ $$$${F}\left({p}\right)=\frac{\mathrm{1}}{\left({p}^{\mathrm{2}} +{p}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 144460 Answers: 1 Comments: 0

If C=226k find the least integal value of k that will make C a perfect square

$$ \\ $$$$\mathrm{If}\:\mathrm{C}=\mathrm{226}{k}\:\mathrm{find}\:\mathrm{the}\:\mathrm{least} \\ $$$$\mathrm{integal}\:\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{that}\:\mathrm{will} \\ $$$$\mathrm{make}\:\mathrm{C}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square} \\ $$

Question Number 144479 Answers: 0 Comments: 0

Consider the followinge statments P: All students with measles stay in the sick bay. T: All students in the sick bay do not do homework. Which of the following is/are valid deductions from the two statements a) Kofi does not have measles so Kofi does his homework. b)George has done his homework therefore he does not stay in the sick bay c) Jane does not have measles so she does not stay in the sick bay

$$ \\ $$$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{followinge} \\ $$$$\mathrm{statments} \\ $$$$\mathrm{P}:\:\mathrm{All}\:\mathrm{students}\:\mathrm{with}\:\mathrm{measles} \\ $$$$\:\mathrm{stay}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sick}\:\mathrm{bay}. \\ $$$$\mathrm{T}:\:\mathrm{All}\:\mathrm{students}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sick} \\ $$$$\:\mathrm{bay}\:\mathrm{do}\:\mathrm{not}\:\mathrm{do}\:\mathrm{homework}. \\ $$$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\:\mathrm{is}/\mathrm{are}\:\mathrm{valid}\:\mathrm{deductions} \\ $$$$\:\mathrm{from}\:\mathrm{the}\:\mathrm{two}\:\mathrm{statements} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Kofi}\:\mathrm{does}\:\mathrm{not}\:\mathrm{have}\: \\ $$$$\mathrm{measles}\:\mathrm{so}\:\mathrm{Kofi}\:\mathrm{does}\:\mathrm{his} \\ $$$$\:\mathrm{homework}. \\ $$$$\left.\mathrm{b}\right)\mathrm{George}\:\mathrm{has}\:\mathrm{done}\:\mathrm{his}\: \\ $$$$\mathrm{homework}\:\mathrm{therefore}\:\mathrm{he} \\ $$$$\mathrm{does}\:\mathrm{not}\:\mathrm{stay}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sick}\:\mathrm{bay} \\ $$$$\left.\:\mathrm{c}\right)\:\mathrm{Jane}\:\mathrm{does}\:\mathrm{not}\:\mathrm{have} \\ $$$$\mathrm{measles}\:\mathrm{so}\:\mathrm{she}\:\mathrm{does}\:\mathrm{not}\: \\ $$$$\mathrm{stay}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sick}\:\mathrm{bay} \\ $$

Question Number 144452 Answers: 2 Comments: 0

Find minimum value of f(x)=sin (x+3)−sin (x+1)−2cos (x+2) where xεR

$$\:\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{sin}\:\left(\mathrm{x}+\mathrm{3}\right)−\mathrm{sin}\:\left(\mathrm{x}+\mathrm{1}\right)−\mathrm{2cos}\:\left(\mathrm{x}+\mathrm{2}\right) \\ $$$$\mathrm{where}\:\mathrm{x}\epsilon\mathrm{R} \\ $$

Question Number 144450 Answers: 3 Comments: 0

.........Calculus(I)......... Lim_( x → 0) ((1 −cos(xcos((x/2)).cos((x/4))cos((x/8))))/x^( 2) )=?

$$ \\ $$$$\:\:\:\:\:\:\:\:.........\mathrm{C}{alculus}\left(\mathrm{I}\right)......... \\ $$$$\:\:\mathrm{Lim}_{\:\:{x}\:\rightarrow\:\mathrm{0}} \frac{\mathrm{1}\:−{cos}\left({xcos}\left(\frac{{x}}{\mathrm{2}}\right).{cos}\left(\frac{{x}}{\mathrm{4}}\right){cos}\left(\frac{{x}}{\mathrm{8}}\right)\right)}{{x}^{\:\mathrm{2}} }=? \\ $$

Question Number 144447 Answers: 1 Comments: 1