Question and Answers Forum

AllQuestion and Answers: Page 425

Question Number 177361 Answers: 1 Comments: 0

4(16^((x+4)) × 5.2^(2x) =13

$$\mathrm{4}\left(\mathrm{16}^{\left({x}+\mathrm{4}\right)} \:×\:\mathrm{5}.\mathrm{2}^{\mathrm{2}{x}} =\mathrm{13}\right. \\ $$

Question Number 177360 Answers: 1 Comments: 0

1/2 log_4 36 ×log_6 64

$$\mathrm{1}/\mathrm{2}\:{log}_{\mathrm{4}} \mathrm{36}\:×{log}_{\mathrm{6}} \mathrm{64} \\ $$

Question Number 177375 Answers: 0 Comments: 5

soit k un entier naturel non nul ,S un nombre fini de nombres premiers impair −Demontrer qu il existe au plus une maniere(a rotation et symetrie axiale) de disposer les elements de S sur un cercle de sorte que le priduit de 2 nombres places l′un a cote de l′autre soit toujours de la forme (x^2 +x+k),x un entier naturel non nul. Extrait de Olimpiad de Mathematiques (France 2022).

$$\mathrm{soit}\:\mathrm{k}\:\mathrm{un}\:\mathrm{entier}\:\mathrm{naturel}\:\mathrm{non}\:\mathrm{nul}\:,\mathrm{S}\:\mathrm{un}\:\mathrm{nombre}\:\mathrm{fini}\:\mathrm{de}\: \\ $$$$\mathrm{nombres}\:\mathrm{premiers}\:\mathrm{impair} \\ $$$$−\mathrm{Demontrer}\:\mathrm{qu}\:\mathrm{il}\:\mathrm{existe}\:\mathrm{au}\:\mathrm{plus}\:\mathrm{une}\:\mathrm{maniere}\left(\mathrm{a}\:\mathrm{rotation}\:\mathrm{et}\:\mathrm{symetrie}\:\mathrm{axiale}\right) \\ $$$$\mathrm{de}\:\mathrm{disposer}\:\mathrm{les}\:\mathrm{elements}\:\mathrm{de}\:\mathrm{S}\:\mathrm{sur}\:\mathrm{un}\:\mathrm{cercle}\:\mathrm{de}\:\mathrm{sorte}\:\mathrm{que}\:\mathrm{le}\:\mathrm{priduit}\:\mathrm{de}\:\mathrm{2}\:\mathrm{nombres}\: \\ $$$$\mathrm{places}\:\mathrm{l}'\mathrm{un}\:\mathrm{a}\:\mathrm{cote}\:\mathrm{de}\:\mathrm{l}'\mathrm{autre}\:\mathrm{soit}\:\mathrm{toujours}\:\mathrm{de}\:\mathrm{la}\:\mathrm{forme}\:\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{k}}\right),\mathrm{x}\:\mathrm{un}\:\mathrm{entier}\:\mathrm{naturel}\:\mathrm{non}\:\mathrm{nul}. \\ $$$$\:\:\:\:\:\:\:{Extrait}\:{de}\:{Olimpiad}\:{de}\:{Mathematiques}\:\left({France}\:\mathrm{2022}\right). \\ $$$$ \\ $$

Question Number 177353 Answers: 4 Comments: 1

Question Number 177336 Answers: 0 Comments: 3

A tank GM by 4m by 3m. calculate one−third of its volume. please help!

$$\mathrm{A}\:\mathrm{tank}\:\mathrm{GM}\:\mathrm{by}\:\mathrm{4m}\:\mathrm{by}\:\mathrm{3m}.\:\mathrm{calculate} \\ $$$$\mathrm{one}−\mathrm{third}\:\mathrm{of}\:\mathrm{its}\:\mathrm{volume}. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}! \\ $$

Question Number 177331 Answers: 1 Comments: 0

a+b+c=0 a^2 +b^2 +c^2 =4 a^4 +b^4 +c^4 =?

$${a}+{b}+{c}=\mathrm{0} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{4} \\ $$$${a}^{\mathrm{4}} +{b}^{\mathrm{4}} +{c}^{\mathrm{4}} =? \\ $$

Question Number 177332 Answers: 1 Comments: 1

Question Number 177320 Answers: 1 Comments: 0

Question Number 177306 Answers: 2 Comments: 0

Resoudre l equaation acos x+bsin x=c (a,b,c)∈R^3

$${Resoudre}\:{l}\:{equaation} \\ $$$$\:\:{a}\mathrm{cos}\:{x}+{b}\mathrm{sin}\:{x}={c} \\ $$$$\left({a},{b},{c}\right)\in\mathbb{R}^{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 177298 Answers: 1 Comments: 0

Prove that ∫_0 ^(π/2) ((sin^2 x)/((sin x+cos x)))dx=(1/( (√2)))log ((√2)+1)

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}{\left(\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)}\mathrm{dx}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{log}\:\left(\sqrt{\mathrm{2}}+\mathrm{1}\right) \\ $$

Question Number 177296 Answers: 2 Comments: 1

Evaluate ∫_0 ^π (x/(a^2 cos^2 x+b^2 sin^2 x))dx

$$\:\:\mathrm{Evaluate}\: \\ $$$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{x}}{\mathrm{a}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{b}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$$$ \\ $$

Question Number 177280 Answers: 3 Comments: 1

by ussing demover find (cos(π/2) + i cos(π/8))^(−5)

$${by}\:{ussing}\:{demover}\:{find}\: \\ $$$$ \\ $$$$\left({cos}\frac{\pi}{\mathrm{2}}\:\:+\:{i}\:{cos}\frac{\pi}{\mathrm{8}}\right)^{−\mathrm{5}} \:\: \\ $$

Question Number 177279 Answers: 0 Comments: 0

Question Number 177253 Answers: 2 Comments: 0

The base of a right pyramid is a hexagon of side 16 cm, and its lateral surface is 720 sq. cm. Is. the height of the pyramid will be

$$ \\ $$The base of a right pyramid is a hexagon of side 16 cm, and its lateral surface is 720 sq. cm. Is. the height of the pyramid will be

Question Number 177242 Answers: 1 Comments: 0

∫ ((3x^(16) +5x^(14) )/((x^5 +x^2 +1)^4 ))dx

$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{\mathrm{3x}^{\mathrm{16}} +\mathrm{5x}^{\mathrm{14}} }{\left(\mathrm{x}^{\mathrm{5}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{4}} }\mathrm{dx} \\ $$$$ \\ $$

Question Number 177241 Answers: 1 Comments: 0

∫ ((sin x)/(sin (x−a)))dx

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\left(\mathrm{x}−\mathrm{a}\right)}\mathrm{dx} \\ $$

Question Number 177240 Answers: 1 Comments: 2

Imagine that a hole is drilled from one point on the earth surface to the other side through the diameter of the earth and small of mass ^′ m^′ released into the hole. show that the hole of mass excute simple harmonic motion and find its period of revolution

$$\mathrm{Imagine}\:\mathrm{that}\:\mathrm{a}\:\mathrm{hole}\:\mathrm{is}\:\mathrm{drilled} \\ $$$$\mathrm{from}\:\mathrm{one}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{earth}\: \\ $$$$\mathrm{surface}\:\mathrm{to}\:\mathrm{the}\:\mathrm{other}\:\mathrm{side}\:\mathrm{through}\:\mathrm{the} \\ $$$$\mathrm{diameter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{and}\:\mathrm{small} \\ $$$$\mathrm{of}\:\mathrm{mass}\:\:^{'} \mathrm{m}^{'} \:\mathrm{released}\:\mathrm{into}\:\mathrm{the}\:\mathrm{hole}. \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{hole}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{excute} \\ $$$$\mathrm{simple}\:\mathrm{harmonic}\:\mathrm{motion}\:\mathrm{and} \\ $$$$\mathrm{find}\:\mathrm{its}\:\mathrm{period}\:\mathrm{of}\:\mathrm{revolution} \\ $$

Question Number 177221 Answers: 0 Comments: 0