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Question Number 75895    Answers: 1   Comments: 0

A garrison had provisions for 1500 men for 30 days. After some days, 300 more men joined the garrison. The provisions lasted for a total of 26 days from the beginning. After how many days did the new men join?

$$\mathrm{A}\:\mathrm{garrison}\:\mathrm{had}\:\mathrm{provisions}\:\mathrm{for}\:\mathrm{1500}\:\mathrm{men} \\ $$$$\mathrm{for}\:\mathrm{30}\:\mathrm{days}.\:\mathrm{After}\:\mathrm{some}\:\mathrm{days},\:\mathrm{300}\:\mathrm{more} \\ $$$$\mathrm{men}\:\mathrm{joined}\:\mathrm{the}\:\mathrm{garrison}.\:\mathrm{The}\:\mathrm{provisions} \\ $$$$\mathrm{lasted}\:\mathrm{for}\:\mathrm{a}\:\mathrm{total}\:\mathrm{of}\:\mathrm{26}\:\mathrm{days}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{beginning}.\:\mathrm{After}\:\mathrm{how}\:\mathrm{many}\:\mathrm{days}\:\mathrm{did} \\ $$$$\mathrm{the}\:\mathrm{new}\:\mathrm{men}\:\mathrm{join}? \\ $$

Question Number 75894    Answers: 0   Comments: 0

When 616 is divided by a certain positive number, which is 66(2/3)% of the quotient, it leaves 16 as the remainder. Find the divisor.

$$\mathrm{When}\:\mathrm{616}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{a}\:\mathrm{certain}\: \\ $$$$\mathrm{positive}\:\mathrm{number},\:\mathrm{which}\:\mathrm{is}\:\mathrm{66}\frac{\mathrm{2}}{\mathrm{3}}\%\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{quotient},\:\mathrm{it}\:\mathrm{leaves}\:\mathrm{16}\:\mathrm{as}\:\mathrm{the}\:\mathrm{remainder}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{divisor}. \\ $$

Question Number 75890    Answers: 0   Comments: 0

calculate ∫_0 ^∞ ((arctan(2x+3))/(x^2 +4))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}+\mathrm{3}\right)}{{x}^{\mathrm{2}} +\mathrm{4}}{dx} \\ $$

Question Number 75889    Answers: 0   Comments: 0

find ∫ (√((x+1)(x+2)(2x−1)))dx

$${find}\:\int\:\sqrt{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left(\mathrm{2}{x}−\mathrm{1}\right)}{dx} \\ $$

Question Number 75888    Answers: 0   Comments: 1

find ∫_0 ^1 (√(1+x^4 ))dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 75883    Answers: 0   Comments: 2

If a^4 + b^4 + c^4 + d^4 = 16 Prove that, a^5 + b^5 + c^5 + d^5 ≤ 32

$$\mathrm{If}\:\:\:\:\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \:+\:\mathrm{d}^{\mathrm{4}} \:\:\:=\:\:\:\mathrm{16} \\ $$$$\mathrm{Prove}\:\mathrm{that},\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{5}} \:+\:\mathrm{b}^{\mathrm{5}} \:+\:\mathrm{c}^{\mathrm{5}} \:+\:\mathrm{d}^{\mathrm{5}} \:\:\:\leqslant\:\:\:\mathrm{32} \\ $$

Question Number 75879    Answers: 1   Comments: 0

Question Number 75873    Answers: 1   Comments: 0

∫xe^x dx

$$\int{xe}^{{x}} {dx} \\ $$

Question Number 75868    Answers: 0   Comments: 0

PROVE THAT sin3° sin39° sin75° = sin 9° sin 24° sin 30°

$${PROVE}\:\:{THAT} \\ $$$$ \\ $$$$\mathrm{sin3}°\:\mathrm{sin39}°\:\mathrm{sin75}°\:=\:\mathrm{sin}\:\mathrm{9}°\:\mathrm{sin}\:\mathrm{24}°\:\mathrm{sin}\:\mathrm{30}° \\ $$

Question Number 75860    Answers: 1   Comments: 0

complete and balance S+HNO_3 →

$${complete}\:{and}\:{balance}\: \\ $$$${S}+{HNO}_{\mathrm{3}} \rightarrow \\ $$$$ \\ $$

Question Number 75851    Answers: 1   Comments: 0

Question Number 75849    Answers: 0   Comments: 0

In a AB^△ C: { ((a+b+c=2(h_a +h_b +h_c ))),((a^2 +b^2 +c^2 =6abc)),((h_a ^2 +h_b ^2 +h_c ^2 =6h_a .h_b .h_c )) :} find:∡A

$$\boldsymbol{\mathrm{In}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{A}}\overset{\bigtriangleup} {\boldsymbol{\mathrm{B}C}}: \\ $$$$\begin{cases}{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}=\mathrm{2}\left(\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{a}}} +\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{b}}} +\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{c}}} \right)}\\{\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} +\boldsymbol{\mathrm{c}}^{\mathrm{2}} =\mathrm{6}\boldsymbol{\mathrm{abc}}}\\{\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{a}}} ^{\mathrm{2}} +\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{b}}} ^{\mathrm{2}} +\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{c}}} ^{\mathrm{2}} =\mathrm{6}\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{a}}} .\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{b}}} .\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{c}}} }\end{cases} \\ $$$$\boldsymbol{\mathrm{find}}:\measuredangle\boldsymbol{\mathrm{A}} \\ $$

Question Number 75848    Answers: 2   Comments: 1

∫_0 ^( (𝛑/2)) ((sin4x)/(1+sinx+cosx))dx=?

$$\underset{\mathrm{0}} {\overset{\:\:\:\:\:\:\:\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\int}}\frac{\boldsymbol{\mathrm{sin}}\mathrm{4}\boldsymbol{\mathrm{x}}}{\mathrm{1}+\boldsymbol{\mathrm{sinx}}+\boldsymbol{\mathrm{cosx}}}\boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 75840    Answers: 1   Comments: 0

If x^(200) < 3^(300) , then greatest possible integral value of x is _____.

$$\mathrm{If}\:\:{x}^{\mathrm{200}} \:<\:\mathrm{3}^{\mathrm{300}} \:,\:\mathrm{then}\:\mathrm{greatest}\:\mathrm{possible} \\ $$$$\mathrm{integral}\:\mathrm{value}\:\mathrm{of}\:\:\:{x}\:\:\mathrm{is}\:\_\_\_\_\_. \\ $$

Question Number 75838    Answers: 0   Comments: 1

Question Number 75845    Answers: 1   Comments: 2

{ ((x+yz=x^2 )),((y+xz=y^2 )),((z+xy=z^2 )) :} solve for x,y,z.

$$\begin{cases}{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{yz}}=\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\\{\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{xz}}=\boldsymbol{\mathrm{y}}^{\mathrm{2}} }\\{\boldsymbol{\mathrm{z}}+\boldsymbol{\mathrm{xy}}=\boldsymbol{\mathrm{z}}^{\mathrm{2}} }\end{cases}\:\:\:\:\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}},\boldsymbol{\mathrm{z}}. \\ $$

Question Number 75830    Answers: 1   Comments: 5

Question Number 75828    Answers: 1   Comments: 1

Σ_(n=1) ^∞ (1/(10^n ))

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{10}^{{n}} } \\ $$

Question Number 75826    Answers: 1   Comments: 1

Question Number 75846    Answers: 2   Comments: 0

sin^5 x+(√2)sinx=1 , x∈[0,2𝛑]

$$\boldsymbol{\mathrm{sin}}^{\mathrm{5}} \boldsymbol{\mathrm{x}}+\sqrt{\mathrm{2}}\boldsymbol{\mathrm{sinx}}=\mathrm{1}\:\:\:\:\:\:\:\:,\:\:\boldsymbol{\mathrm{x}}\in\left[\mathrm{0},\mathrm{2}\boldsymbol{\pi}\right] \\ $$

Question Number 75847    Answers: 0   Comments: 2

{ ((((tgx−tgy)/(1−tgx.tgy))=tg(x/2))),(( ((tgx+tgy)/(1+tgxtgy))=tg(y/2))) :}

$$\begin{cases}{\frac{\boldsymbol{\mathrm{tgx}}−\boldsymbol{\mathrm{tgy}}}{\mathrm{1}−\boldsymbol{\mathrm{tgx}}.\boldsymbol{\mathrm{tgy}}}=\boldsymbol{\mathrm{tg}}\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}}\\{\:\:\frac{\boldsymbol{\mathrm{tgx}}+\boldsymbol{\mathrm{tgy}}}{\mathrm{1}+\boldsymbol{\mathrm{tgxtgy}}}=\boldsymbol{\mathrm{tg}}\frac{\boldsymbol{\mathrm{y}}}{\mathrm{2}}}\end{cases} \\ $$

Question Number 75825    Answers: 0   Comments: 0

Question Number 75822    Answers: 0   Comments: 0

Question Number 75821    Answers: 0   Comments: 1

Question Number 75818    Answers: 1   Comments: 3

Given the increasing sequence : 1, 4, 8, 13, ... a. Find U_(2019) b. Find S_(2019) U_n is nth−term of the sequence S_n is sum of n − term of the sequence Arithmetic Sequence Degree Two

$${Given}\:\:{the}\:\:{increasing}\:\:{sequence}\:: \\ $$$$\mathrm{1},\:\mathrm{4},\:\mathrm{8},\:\mathrm{13},\:... \\ $$$${a}.\:{Find}\:\:{U}_{\mathrm{2019}} \\ $$$${b}.\:{Find}\:\:{S}_{\mathrm{2019}} \\ $$$${U}_{{n}} \:\:{is}\:\:{nth}−{term}\:\:{of}\:\:{the}\:\:{sequence} \\ $$$${S}_{{n}} \:\:{is}\:\:{sum}\:\:{of}\:\:{n}\:−\:{term}\:\:{of}\:\:{the}\:\:{sequence} \\ $$$${Arithmetic}\:\:{Sequence}\:\:{Degree}\:\:{Two} \\ $$

Question Number 75814    Answers: 1   Comments: 1

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