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Question Number 47354 Answers: 0 Comments: 4

Question Number 47350 Answers: 3 Comments: 1

Question Number 47349 Answers: 1 Comments: 0

Question Number 47344 Answers: 1 Comments: 0

On the moon the acceleration of free fall is only about 1.6ms^(−2) . About how long should a boy be able to throw a ball there if he can throw it 10m high on earth? (g=10ms^(−2) )

$${On}\:{the}\:{moon}\:{the}\:{acceleration}\:{of} \\ $$$${free}\:{fall}\:{is}\:{only}\:{about}\:\mathrm{1}.\mathrm{6}{ms}^{−\mathrm{2}} . \\ $$$${About}\:{how}\:{long}\:{should}\:{a}\:{boy}\:{be} \\ $$$${able}\:{to}\:{throw}\:{a}\:{ball}\:{there}\:{if}\:{he}\:{can} \\ $$$${throw}\:{it}\:\mathrm{10}{m}\:{high}\:{on}\:{earth}? \\ $$$$\left({g}=\mathrm{10}{ms}^{−\mathrm{2}} \right) \\ $$

Question Number 47342 Answers: 2 Comments: 1

Question Number 47341 Answers: 0 Comments: 0

1.sketch the region of integration,reverse order of integration and hence evaluate the ∫_0 ^(2(√(ln3))) ∫_(y/2) ^(√(ln3)) e^x^2 dx dy

$$\mathrm{1}.\mathrm{sketch}\:\:\mathrm{the}\:\:\mathrm{region}\:\:\mathrm{of}\:\:\mathrm{integration},{reverse}\:\:{order}\:\:{of}\:\:{integration}\:\:{and}\:\:{hence}\:\:{evaluate}\:\:{the}\:\underset{\mathrm{0}} {\overset{\mathrm{2}\sqrt{{ln}\mathrm{3}}} {\int}}\:\underset{{y}/\mathrm{2}} {\overset{\sqrt{{ln}\mathrm{3}}} {\int}}\:\:{e}^{{x}^{\mathrm{2}} } \:{dx}\:{dy} \\ $$

Question Number 47333 Answers: 2 Comments: 0

An aircraft flying horizontally 100m above the ground and at 720km/h drops a bomb on a target on the ground.Determine the acute angle between the vertical and the line joining the aircraft and target at the instance when the bomb is released.(g=10ms^(−2) )

$${An}\:{aircraft}\:{flying}\:{horizontally} \\ $$$$\mathrm{100}{m}\:{above}\:{the}\:{ground}\:{and}\:{at}\:\mathrm{720}{km}/{h} \\ $$$${drops}\:{a}\:{bomb}\:{on}\:{a}\:{target}\:{on}\:{the} \\ $$$${ground}.{Determine}\:{the}\:{acute}\:{angle} \\ $$$${between}\:{the}\:{vertical}\:{and}\:{the}\:{line} \\ $$$${joining}\:{the}\:{aircraft}\:{and}\:{target}\:{at} \\ $$$${the}\:{instance}\:{when}\:{the}\:{bomb}\:{is} \\ $$$${released}.\left({g}=\mathrm{10}{ms}^{−\mathrm{2}} \right) \\ $$$$ \\ $$

Question Number 47331 Answers: 0 Comments: 1

this remained unsolved... ∣x−(3/4)∣×∣x+(5/4)∣=3; x∈C

$$\mathrm{this}\:\mathrm{remained}\:\mathrm{unsolved}... \\ $$$$\mid{x}−\frac{\mathrm{3}}{\mathrm{4}}\mid×\mid{x}+\frac{\mathrm{5}}{\mathrm{4}}\mid=\mathrm{3};\:{x}\in\mathbb{C} \\ $$

Question Number 47316 Answers: 1 Comments: 3

Question Number 47314 Answers: 1 Comments: 1

During random motion, gas molecules do not interact with each other . Hence Potential energy =0 ...... Pls explain why P.E = 0? P.E is stored form of energy,right?

$${During}\:{random}\:{motion},\:{gas}\:{molecules} \\ $$$${do}\:{not}\:{interact}\:{with}\:{each}\:{other}\:. \\ $$$${Hence}\:\:{Potential}\:{energy}\:=\mathrm{0}\:...... \\ $$$${Pls}\:{explain}\:{why}\:{P}.{E}\:=\:\mathrm{0}? \\ $$$${P}.{E}\:{is}\:{stored}\:{form}\:{of}\:{energy},{right}? \\ $$

Question Number 47310 Answers: 0 Comments: 1

Question Number 49003 Answers: 0 Comments: 2

∫((logx)/(√(1−x^x )))dx please help this

$$\int\frac{\boldsymbol{\mathrm{log}{x}}}{\sqrt{\mathrm{1}−\boldsymbol{{x}}^{\boldsymbol{{x}}} }}\boldsymbol{\mathrm{d}{x}} \\ $$$$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{help}}\:\boldsymbol{\mathrm{this}} \\ $$

Question Number 47302 Answers: 1 Comments: 0

A train which travels at a uniform speed due to mechanical fault after traveling for an hour goes at 3/5 th of the original speed and reaches the destination 2 hours late.If the fault occured after traveling another 50 miles the train would have reached 40 minutes earlier. What is the distance between the two stations ?

$${A}\:{train}\:{which}\:{travels}\:{at}\:{a}\:{uniform}\:{speed}\:{due}\:{to}\:{mechanical}\: \\ $$$${fault}\:{after}\:{traveling}\:{for}\:{an}\:{hour}\:{goes}\:{at}\:\mathrm{3}/\mathrm{5}\:{th}\:{of}\:{the}\:{original}\: \\ $$$${speed}\:{and}\:{reaches}\:{the}\:{destination}\:\mathrm{2}\:{hours}\:{late}.{If}\:{the}\:{fault} \\ $$$${occured}\:{after}\:{traveling}\:{another}\:\mathrm{50}\:{miles}\:{the}\:{train}\:{would}\:{have} \\ $$$${reached}\:\mathrm{40}\:{minutes}\:{earlier}.\:{What}\:{is}\:{the}\:{distance}\:{between}\:{the}\: \\ $$$${two}\:{stations}\:? \\ $$

Question Number 47301 Answers: 1 Comments: 0

If the equation x^2 +px+q =0 has roots a and b where p, q are non−zero constants. Then

$$\mathrm{If}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} +{px}+{q}\:=\mathrm{0}\:\mathrm{has}\:\mathrm{roots} \\ $$$${a}\:\mathrm{and}\:{b}\:\mathrm{where}\:{p},\:{q}\:\mathrm{are}\:\mathrm{non}−\mathrm{zero}\: \\ $$$$\mathrm{constants}.\:\mathrm{Then} \\ $$

Question Number 47295 Answers: 0 Comments: 6

calculate f(α) =∫_(−∞) ^(+∞) (dx/(x^2 +2x cosα +1)) 2) calculate g(α)=∫_(−∞) ^(+∞) ((sinα)/((x^2 +2x cosα+1)^2 ))dx 3) find f^((n)) (α) with n integr natural . 4) calculate ∫_(−∞) ^(+∞) (dx/(x^2 +x +1)) and ∫_(−∞) ^(+∞) (dx/((x^2 +x+1)^2 ))

$${calculate}\:{f}\left(\alpha\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:+\mathrm{2}{x}\:{cos}\alpha\:+\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left(\alpha\right)=\int_{−\infty} ^{+\infty} \:\:\frac{{sin}\alpha}{\left({x}^{\mathrm{2}} \:+\mathrm{2}{x}\:{cos}\alpha+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{f}^{\left({n}\right)} \left(\alpha\right)\:{with}\:{n}\:{integr}\:{natural}\:. \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:+{x}\:+\mathrm{1}}\:{and}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 47291 Answers: 1 Comments: 0

solve for x∈C: ∣x−(3/4)∣×∣x+(5/4)∣=3

$$\mathrm{solve}\:\mathrm{for}\:{x}\in\mathbb{C}: \\ $$$$\mid{x}−\frac{\mathrm{3}}{\mathrm{4}}\mid×\mid{x}+\frac{\mathrm{5}}{\mathrm{4}}\mid=\mathrm{3} \\ $$

Question Number 47283 Answers: 0 Comments: 1

A stone tied to a string is made to resolve in a horizontal circle of radius 4m with another speed of 2rads^(−1) .With what tangential velocity will the stone be off the circle if the string cuts?

$${A}\:{stone}\:{tied}\:{to}\:{a}\:{string}\:{is}\:{made}\:{to} \\ $$$${resolve}\:{in}\:{a}\:{horizontal}\:{circle}\:{of} \\ $$$${radius}\:\mathrm{4}{m}\:{with}\:{another}\:{speed}\:{of} \\ $$$$\mathrm{2}{rads}^{−\mathrm{1}} .{With}\:{what}\:{tangential} \\ $$$${velocity}\:{will}\:{the}\:{stone}\:{be}\:{off}\:{the} \\ $$$${circle}\:{if}\:{the}\:{string}\:{cuts}? \\ $$

Question Number 47282 Answers: 2 Comments: 0

Question Number 47311 Answers: 0 Comments: 1

Question Number 47280 Answers: 0 Comments: 0

A geometric progression bas three terms a ,b ,c whose sum is 42.If 6 is added to each of the firs two term and 3 to the third ,a new G.P. result whose first term is the same as n. Find a,band?c.

$${A}\:{geometric}\:{progression}\:{bas}\:{three} \\ $$$${terms}\:{a}\:,{b}\:,{c}\:{whose}\:{sum}\:{is}\:\mathrm{42}.{If}\:\mathrm{6} \\ $$$${is}\:{added}\:{to}\:{each}\:{of}\:{the}\:{firs}\:{two}\:{term} \\ $$$${and}\:\mathrm{3}\:{to}\:{the}\:{third}\:,{a}\:{new}\:{G}.{P}.\:{result} \\ $$$${whose}\:{first}\:{term}\:{is}\:{the}\:{same}\:{as}\:{n}. \\ $$$${Find}\:{a},{band}?{c}. \\ $$

Question Number 47272 Answers: 2 Comments: 1

Question Number 47259 Answers: 0 Comments: 0

∫_0 ^1 ((tan^(−1) ((x/(x+1))))/(tan^(−1) (((1−2x^2 +2x)/2))))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \left(\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}+\mathrm{1}}\right)}{\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \left(\frac{\mathrm{1}−\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}\boldsymbol{\mathrm{dx}} \\ $$

Question Number 47289 Answers: 0 Comments: 4

Pls can Q47194 be solved by using the cosine rule?If possible please show me with the required diagram. Thanks in advance.

$${Pls}\:{can}\:{Q}\mathrm{47194}\:{be}\:{solved}\:{by}\:{using} \\ $$$${the}\:{cosine}\:{rule}?{If}\:{possible}\:{please} \\ $$$${show}\:{me}\:{with}\:{the}\:{required}\:{diagram}. \\ $$$${Thanks}\:{in}\:{advance}. \\ $$

Question Number 47250 Answers: 1 Comments: 0

Question Number 47248 Answers: 0 Comments: 1

calculate ∫_(−1) ^1 ((ln(x+2))/((x+4)^2 −1))dx

$${calculate}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\:\frac{{ln}\left({x}+\mathrm{2}\right)}{\left({x}+\mathrm{4}\right)^{\mathrm{2}} −\mathrm{1}}{dx} \\ $$

Question Number 47243 Answers: 1 Comments: 0

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