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Question Number 116998 Answers: 2 Comments: 2

∫_((−π)/2) ^(π/2) ((sin^2 x)/(1+2^x ))dx

$$\int_{\frac{−\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{sin}^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{2}^{{x}} }{dx} \\ $$

Question Number 116997 Answers: 1 Comments: 0

Question Number 116996 Answers: 2 Comments: 0

Question Number 116987 Answers: 1 Comments: 0

Find the largest integer smaller than (7+4(√3))^3 .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{integer}\:\mathrm{smaller}\:\mathrm{than} \\ $$$$\left(\mathrm{7}+\mathrm{4}\sqrt{\mathrm{3}}\right)^{\mathrm{3}} . \\ $$

Question Number 116983 Answers: 1 Comments: 5

Luigi, an Italian cook, drops a spaghetti which breaks into three pieces. What is the probability of making a triangle with the three pieces ?

$$\mathrm{Luigi},\:\mathrm{an}\:\mathrm{Italian}\:\mathrm{cook},\:\mathrm{drops}\:\mathrm{a}\:\mathrm{spaghetti} \\ $$$$\mathrm{which}\:\mathrm{breaks}\:\mathrm{into}\:\mathrm{three}\:\mathrm{pieces}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{making}\:\mathrm{a} \\ $$$$\mathrm{triangle}\:\mathrm{with}\:\mathrm{the}\:\mathrm{three}\:\mathrm{pieces}\:? \\ $$

Question Number 116976 Answers: 2 Comments: 0

use the formula P=Ie^(kt) ,where P is resulting population ,I is the initial population and t is measured in hours. A bacterial culture has an initial population of 10,000. If its declines to 5000 in 6 hours , what will it be at the end of 8 hours? (a) 1985 (b) 3969 (c) 2500 (d) 4353

$$\mathrm{use}\:\mathrm{the}\:\mathrm{formula}\:\mathrm{P}=\mathrm{Ie}^{\mathrm{kt}} \:,\mathrm{where}\:\mathrm{P}\:\mathrm{is}\:\mathrm{resulting} \\ $$$$\mathrm{population}\:,\mathrm{I}\:\mathrm{is}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{population}\:\mathrm{and}\:\mathrm{t}\:\mathrm{is} \\ $$$$\mathrm{measured}\:\mathrm{in}\:\mathrm{hours}.\:\mathrm{A}\:\mathrm{bacterial}\:\mathrm{culture} \\ $$$$\mathrm{has}\:\mathrm{an}\:\mathrm{initial}\:\mathrm{population}\:\mathrm{of}\:\mathrm{10},\mathrm{000}.\:\mathrm{If} \\ $$$$\mathrm{its}\:\mathrm{declines}\:\mathrm{to}\:\mathrm{5000}\:\mathrm{in}\:\mathrm{6}\:\mathrm{hours}\:,\:\mathrm{what}\: \\ $$$$\mathrm{will}\:\mathrm{it}\:\mathrm{be}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{8}\:\mathrm{hours}? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{1985}\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{3969}\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{2500}\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{4353} \\ $$

Question Number 116975 Answers: 0 Comments: 1

Prove ((cos(A−B))/(sin(A+B)))=((1+tan Atan B)/(tan Atan B))

$$\mathrm{Prove}\:\frac{\mathrm{cos}\left({A}−{B}\right)}{\mathrm{sin}\left({A}+{B}\right)}=\frac{\mathrm{1}+\mathrm{tan}\:{A}\mathrm{tan}\:{B}}{\mathrm{tan}\:{A}\mathrm{tan}\:{B}} \\ $$

Question Number 116970 Answers: 1 Comments: 0

Question Number 116966 Answers: 2 Comments: 0

4 tan^(−1) ((1/5))−tan^(−1) ((1/(239))) = ?

$$\mathrm{4}\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{5}}\right)−\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{239}}\right)\:=\:? \\ $$

Question Number 116964 Answers: 1 Comments: 0

Question Number 116965 Answers: 1 Comments: 0

Σ_(k=1) ^∞ (−1)^(k+1) ((sin(kθ))/(kθ))

$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} \:\frac{{sin}\left({k}\theta\right)}{{k}\theta} \\ $$

Question Number 116961 Answers: 1 Comments: 4

Question Number 116990 Answers: 0 Comments: 0

let A = (((1 −1)),((2 3)) ) 1) calculate A^n 2) determine cosA and chA 3)determine sinA and shA

$${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:−\mathrm{1}}\\{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{cosA}\:{and}\:{chA} \\ $$$$\left.\mathrm{3}\right){determine}\:{sinA}\:{and}\:{shA} \\ $$

Question Number 116939 Answers: 2 Comments: 0

prof if the limitf(x)=L and limit f(x)=M,then L=M

$${prof}\:\:{if}\:\:{the}\:{limitf}\left({x}\right)={L}\:{and}\: \\ $$$${limit}\:{f}\left({x}\right)={M},{then}\:{L}={M} \\ $$

Question Number 116930 Answers: 2 Comments: 1

Given f(x)=5^(√x) find f ′(x) by using limit (first principal derivative)

$$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{5}^{\sqrt{\mathrm{x}}} \:\mathrm{find}\:\mathrm{f}\:'\left(\mathrm{x}\right)\:\mathrm{by}\:\mathrm{using}\:\mathrm{limit} \\ $$$$\left(\mathrm{first}\:\mathrm{principal}\:\mathrm{derivative}\right) \\ $$

Question Number 116941 Answers: 0 Comments: 8

prove that 7×8=7+8=78

$${prove}\:{that}\:\mathrm{7}×\mathrm{8}=\mathrm{7}+\mathrm{8}=\mathrm{78} \\ $$

Question Number 116921 Answers: 1 Comments: 0

Question Number 116917 Answers: 1 Comments: 0

Find the greatest coefficient and greatest term in (3x − 2)^(− 7) . Sir is it: (− 1)^(− 7) .(2 − 3x)^(− 7) = − (2 − 3x)^(− 7) = − ((8008 × 2^(10) )/3^(17) )

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{and}\:\mathrm{greatest}\:\mathrm{term}\:\mathrm{in} \\ $$$$\left(\mathrm{3x}\:\:−\:\:\mathrm{2}\right)^{−\:\mathrm{7}} . \\ $$$$ \\ $$$$\mathrm{Sir}\:\mathrm{is}\:\mathrm{it}:\:\:\:\:\:\left(−\:\mathrm{1}\right)^{−\:\mathrm{7}} .\left(\mathrm{2}\:\:−\:\:\mathrm{3x}\right)^{−\:\mathrm{7}} \:\:\:\:=\:\:\:−\:\left(\mathrm{2}\:\:−\:\:\mathrm{3x}\right)^{−\:\mathrm{7}} \\ $$$$=\:\:\:−\:\:\frac{\mathrm{8008}\:\:×\:\:\mathrm{2}^{\mathrm{10}} }{\mathrm{3}^{\mathrm{17}} } \\ $$

Question Number 116915 Answers: 2 Comments: 0