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AllQuestion and Answers: Page 239

Question Number 197776 Answers: 1 Comments: 3

Question Number 197772 Answers: 2 Comments: 1

Can anyone do this? ∫^( +∞) _( 1) ((t−1)/((1+t)^3 lnt))dt

$$\mathrm{Can}\:\mathrm{anyone}\:\mathrm{do}\:\mathrm{this}? \\ $$$$\underset{\:\mathrm{1}} {\int}^{\:+\infty} \frac{\mathrm{t}−\mathrm{1}}{\left(\mathrm{1}+\mathrm{t}\right)^{\mathrm{3}} \:\mathrm{lnt}}\mathrm{dt} \\ $$

Question Number 197771 Answers: 1 Comments: 0

Question Number 197767 Answers: 0 Comments: 1

Question Number 197766 Answers: 1 Comments: 1

∫_0 ^(π/2) (lim_(n→∞) nsin^(2n+1) x cos x)dx = ?

$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \left(\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}\mathrm{sin}^{\mathrm{2}{n}+\mathrm{1}} {x}\:\mathrm{cos}\:{x}\right){dx}\:\:=\:? \\ $$

Question Number 197763 Answers: 0 Comments: 0

Question Number 197753 Answers: 3 Comments: 0

Solve the equation: (√(5x^2 +14x+9))−(√(x^2 −x−20))=5(√(x+1))

$${Solve}\:{the}\:{equation}: \\ $$$$\sqrt{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{14}{x}+\mathrm{9}}−\sqrt{{x}^{\mathrm{2}} −{x}−\mathrm{20}}=\mathrm{5}\sqrt{{x}+\mathrm{1}} \\ $$

Question Number 197752 Answers: 1 Comments: 0

find minimum value of m such that m^(19) = 1800 (mod 2029)

$$\:\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{m} \\ $$$$\:\mathrm{such}\:\mathrm{that}\:\mathrm{m}^{\mathrm{19}} =\:\mathrm{1800}\:\left(\mathrm{mod}\:\mathrm{2029}\right) \\ $$

Question Number 197744 Answers: 1 Comments: 0

2∫_0 ^1 tan^(−1) x dx=?

$$\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}} {tan}^{−\mathrm{1}} {x}\:{dx}=? \\ $$

Question Number 197740 Answers: 3 Comments: 0

Question Number 197734 Answers: 1 Comments: 0

calcul ∫(lnx)^(√x) dx help pls

$$\boldsymbol{{c}}{alcul}\:\int\left(\boldsymbol{{lnx}}\right)^{\sqrt{\boldsymbol{{x}}}} \boldsymbol{{dx}} \\ $$$$\boldsymbol{{help}}\:\:\boldsymbol{{pls}} \\ $$

Question Number 197730 Answers: 2 Comments: 3

Question Number 197719 Answers: 0 Comments: 3

Determiner x

$$\mathrm{Determiner}\:\:\:\:\boldsymbol{\mathrm{x}} \\ $$

Question Number 197717 Answers: 0 Comments: 5

∡A=62 ∡C=43 Determiner: a=∡B c=∡D b=∡F

$$\measuredangle\boldsymbol{\mathrm{A}}=\mathrm{62}\:\:\:\measuredangle\boldsymbol{\mathrm{C}}=\mathrm{43} \\ $$$$\boldsymbol{\mathrm{Determiner}}:\:\:\mathrm{a}=\measuredangle\boldsymbol{\mathrm{B}}\:\:\:\:\mathrm{c}=\measuredangle\boldsymbol{\mathrm{D}}\:\:\:\:\:\mathrm{b}=\measuredangle\boldsymbol{\mathrm{F}} \\ $$

Question Number 197716 Answers: 0 Comments: 0

sen(x)y^(′′) +cos(x)y′+3x^3 y=tan((√x))

$${sen}\left({x}\right){y}^{''} +{cos}\left({x}\right){y}'+\mathrm{3}{x}^{\mathrm{3}} {y}={tan}\left(\sqrt{{x}}\right) \\ $$

Question Number 197708 Answers: 1 Comments: 0

x^a =x^(a+4) where a∈Z solve for x by showing steps

$$ \\ $$$${x}^{{a}} ={x}^{{a}+\mathrm{4}} \:\:\mathrm{where}\:{a}\in\mathbb{Z} \\ $$$$\mathrm{solve}\:\mathrm{for}\:{x}\:\mathrm{by}\:\mathrm{showing}\:\mathrm{steps} \\ $$

Question Number 197706 Answers: 1 Comments: 0

Question Number 197683 Answers: 2 Comments: 1

((a+3b)/(a+b−1))+((a+3b−1)/(a+b−3))=4 a+b=?

$$\frac{{a}+\mathrm{3}{b}}{{a}+{b}−\mathrm{1}}+\frac{{a}+\mathrm{3}{b}−\mathrm{1}}{{a}+{b}−\mathrm{3}}=\mathrm{4} \\ $$$${a}+{b}=? \\ $$

Question Number 197680 Answers: 1 Comments: 1

Question Number 197667 Answers: 1 Comments: 0

Question Number 197666 Answers: 0 Comments: 0

For the past 10 years M has deposited $40 at the end of each month in as saving bank paying 3% p.a. compoundedsemi annually. If they polic of the bank is to place eacht deposi at 3 %p.a. simple interest on ther fist of each month and compound semi annually find the amount to Ms credit

$$ \\ $$$$\mathrm{For}\:\mathrm{the}\:\mathrm{past}\:\mathrm{10}\:\mathrm{years}\:\mathrm{M}\:\mathrm{has}\:\mathrm{deposited} \\ $$$$\$\mathrm{40}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{each}\:\mathrm{month}\:\mathrm{in}\:\mathrm{as} \\ $$$$\mathrm{saving}\:\mathrm{bank}\:\mathrm{paying}\:\mathrm{3\%}\:\mathrm{p}.\mathrm{a}.\: \\ $$$$\mathrm{compoundedsemi}\:\mathrm{annually}.\:\mathrm{If}\:\mathrm{they} \\ $$$$\mathrm{polic}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bank}\:\mathrm{is}\:\mathrm{to}\:\mathrm{place}\:\mathrm{eacht} \\ $$$$\mathrm{deposi}\:\mathrm{at}\:\mathrm{3}\:\%\mathrm{p}.\mathrm{a}.\:\mathrm{simple}\:\mathrm{interest}\:\mathrm{on}\:\mathrm{ther} \\ $$$$\mathrm{fist}\:\mathrm{of}\:\mathrm{each}\:\mathrm{month}\:\mathrm{and}\:\mathrm{compound}\:\mathrm{semi}\: \\ $$$$\mathrm{annually}\:\mathrm{find}\:\mathrm{the}\:\mathrm{amount}\:\mathrm{to}\:\mathrm{Ms}\:\mathrm{credit} \\ $$

Question Number 197664 Answers: 0 Comments: 1

Question Number 197660 Answers: 1 Comments: 0

Question Number 197644 Answers: 1 Comments: 1

Question Number 197640 Answers: 1 Comments: 0

Water is leaking from a hemispheric bowl of radius 20cm at the rate of 0.5cm^3 /s. Find the rate at which surface area of the water decreasing when the water level is halfway from the top. Thank you

$${Water}\:{is}\:{leaking}\:{from}\:{a}\:{hemispheric} \\ $$$${bowl}\:{of}\:{radius}\:\mathrm{20}{cm}\:{at}\:{the}\:{rate}\:{of}\: \\ $$$$\mathrm{0}.\mathrm{5}{cm}^{\mathrm{3}} /{s}.\:{Find}\:{the}\:{rate}\:{at}\:{which}\:{surface} \\ $$$${area}\:{of}\:{the}\:{water}\:{decreasing}\:{when}\:{the} \\ $$$${water}\:{level}\:{is}\:{halfway}\:{from}\:{the}\:{top}. \\ $$$$ \\ $$$${Thank}\:{you} \\ $$

Question Number 197639 Answers: 1 Comments: 1

show that (1/((1−z)^n )) = Σ_(k=1) ^∞ (((n+k−1)!)/(k!(n−1)!)) z^k

$${show}\:{that}\:\frac{\mathrm{1}}{\left(\mathrm{1}−{z}\right)^{{n}} }\:=\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left({n}+{k}−\mathrm{1}\right)!}{{k}!\left({n}−\mathrm{1}\right)!}\:{z}^{{k}} \\ $$

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