Question and Answers Forum

AllQuestion and Answers: Page 1005

Question Number 108413 Answers: 1 Comments: 0

228x=87 find x

$$\mathrm{228}{x}=\mathrm{87}\:{find}\:{x} \\ $$

Question Number 108407 Answers: 1 Comments: 0

The sides AB, BC, CA of a triangleABC have 3, 4 and 5 interior points respectively on them. The total number of triangles that can be constructed by using these points as vertices is

$$\mathrm{The}\:\mathrm{sides}\:\mathrm{AB},\:\mathrm{BC},\:\mathrm{CA}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangleABC} \\ $$$$\mathrm{have}\:\mathrm{3},\:\mathrm{4}\:\mathrm{and}\:\mathrm{5}\:\mathrm{interior}\:\mathrm{points}\:\mathrm{respectively} \\ $$$$\mathrm{on}\:\mathrm{them}.\:\mathrm{The}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{triangles} \\ $$$$\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{constructed}\:\mathrm{by}\:\mathrm{using}\:\mathrm{these} \\ $$$$\mathrm{points}\:\mathrm{as}\:\mathrm{vertices}\:\mathrm{is} \\ $$

Question Number 108406 Answers: 1 Comments: 0

solve the differential equation y^′ −2e^x y=2e^x (√y)

$$ \\ $$$$ \\ $$$$\:\:\:\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{differential}} \\ $$$$\boldsymbol{{equation}}\: \\ $$$$\boldsymbol{{y}}^{'} −\mathrm{2}{e}^{{x}} \boldsymbol{{y}}=\mathrm{2}{e}^{{x}} \sqrt{\boldsymbol{{y}}} \\ $$

Question Number 108401 Answers: 2 Comments: 2

((bobhans)/(⋱⋰)) I=∫_0 ^(π/2) ln (a^2 cos^2 θ + b^2 sin^2 θ ) dθ ?

$$\:\:\:\frac{\boldsymbol{{bobhans}}}{\ddots\iddots} \\ $$$$\:{I}=\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\:\left({a}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \:\theta\:+\:{b}^{\mathrm{2}} \:\mathrm{sin}^{\mathrm{2}} \:\theta\:\right)\:{d}\theta\:?\: \\ $$

Question Number 108399 Answers: 0 Comments: 2

Question Number 108391 Answers: 5 Comments: 0

((∡ BeMath ∡)/▽) I = ∫_0 ^π ((x dx)/(1+sin x))

$$\:\:\:\frac{\measuredangle\:\mathcal{B}{e}\mathcal{M}{ath}\:\measuredangle}{\bigtriangledown} \\ $$$${I}\:=\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{{x}\:{dx}}{\mathrm{1}+\mathrm{sin}\:{x}} \\ $$

Question Number 108389 Answers: 1 Comments: 0

Question Number 108384 Answers: 3 Comments: 0

(1)∫ ((√(sin x))/( (√(sin x)) + (√(cos x)))) dx ? (2) (d^2 y/dx^2 )−2(dy/dx) +y = e^x

$$\left(\mathrm{1}\right)\int\:\frac{\sqrt{\mathrm{sin}\:{x}}}{\:\sqrt{\mathrm{sin}\:{x}}\:+\:\sqrt{\mathrm{cos}\:{x}}}\:{dx}\:? \\ $$$$\left(\mathrm{2}\right)\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−\mathrm{2}\frac{{dy}}{{dx}}\:+{y}\:=\:{e}^{{x}} \\ $$

Question Number 108382 Answers: 2 Comments: 1

((bobhans)/(⋰⋱)) ∫_(π/2) ^π ∣ cos x−sin x ∣ dx ?

$$\:\:\:\frac{\boldsymbol{{bobhans}}}{\iddots\ddots} \\ $$$$\:\underset{\pi/\mathrm{2}} {\overset{\pi} {\int}}\mid\:\mathrm{cos}\:{x}−\mathrm{sin}\:{x}\:\mid\:{dx}\:? \\ $$$$ \\ $$

Question Number 108377 Answers: 1 Comments: 0

There are 20 white and 10 black balls in the box.In turn draw 4 balls and each draw ball is returned to the box before the next ball is drawn and the balls in the box are mixed.What is the probability that out of four balls taken out there will be two white balls?

$$\mathrm{There}\:\mathrm{are}\:\mathrm{20}\:\mathrm{white}\:\mathrm{and}\:\mathrm{10}\:\mathrm{black}\:\mathrm{balls} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{box}.\mathrm{In}\:\mathrm{turn}\:\mathrm{draw}\:\mathrm{4}\:\mathrm{balls}\:\mathrm{and} \\ $$$$\mathrm{each}\:\mathrm{draw}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{returned}\:\mathrm{to}\:\mathrm{the}\:\mathrm{box} \\ $$$$\mathrm{before}\:\mathrm{the}\:\mathrm{next}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{drawn}\:\mathrm{and}\:\mathrm{the}\: \\ $$$$\mathrm{balls}\:\mathrm{in}\:\mathrm{the}\:\mathrm{box}\:\mathrm{are}\:\mathrm{mixed}.\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{out}\:\mathrm{of}\:\mathrm{four}\:\mathrm{balls} \\ $$$$\mathrm{taken}\:\mathrm{out}\:\mathrm{there}\:\mathrm{will}\:\mathrm{be}\:\mathrm{two}\:\mathrm{white}\:\mathrm{balls}? \\ $$

Question Number 108453 Answers: 1 Comments: 0

If R=(7+4(√3))^(2n) = I+f, where I ∈ N and 0<f<1, then R(1−f) equals

$$\mathrm{If}\:\:{R}=\left(\mathrm{7}+\mathrm{4}\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} \:=\:{I}+{f},\:\mathrm{where}\:{I}\:\in\:{N} \\ $$$$\mathrm{and}\:\:\:\mathrm{0}<{f}<\mathrm{1},\:\mathrm{then}\:{R}\left(\mathrm{1}−{f}\right)\:\mathrm{equals} \\ $$

Question Number 108370 Answers: 0 Comments: 1