Question and Answers Forum

AllQuestion and Answers: Page 1378

Question Number 75896 Answers: 1 Comments: 0

One pipe can fill a tank in 40 minutes and an outlet pipe can empty the full tank in 24 minutes. If both the pipes are opened simultaneously, what time will it take for the full tank to be emptied?

$$\mathrm{One}\:\mathrm{pipe}\:\mathrm{can}\:\mathrm{fill}\:\mathrm{a}\:\mathrm{tank}\:\mathrm{in}\:\mathrm{40}\:\mathrm{minutes} \\ $$$$\mathrm{and}\:\mathrm{an}\:\mathrm{outlet}\:\mathrm{pipe}\:\mathrm{can}\:\mathrm{empty}\:\mathrm{the}\:\mathrm{full} \\ $$$$\mathrm{tank}\:\mathrm{in}\:\mathrm{24}\:\mathrm{minutes}.\:\mathrm{If}\:\mathrm{both}\:\mathrm{the}\:\mathrm{pipes} \\ $$$$\mathrm{are}\:\mathrm{opened}\:\mathrm{simultaneously},\:\mathrm{what}\:\mathrm{time} \\ $$$$\mathrm{will}\:\mathrm{it}\:\mathrm{take}\:\mathrm{for}\:\mathrm{the}\:\mathrm{full}\:\mathrm{tank}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{emptied}? \\ $$

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

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

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

Pg 1373 Pg 1374 Pg 1375 Pg 1376 Pg 1377 Pg 1378 Pg 1379 Pg 1380 Pg 1381 Pg 1382

Contact: [email protected]