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A man pushes a box of 40kg up an incline of 15°.If the man applied a horizontal force 200N and the box moves up the plane a distance of 20m at a constant velocity and the coefficient of friction is 0.10, find a)workdone by the man on the box b)workdone against friction.

$${A}\:{man}\:{pushes}\:{a}\:{box}\:{of}\:\mathrm{40}{kg}\:{up}\:{an} \\ $$$${incline}\:{of}\:\mathrm{15}°.{If}\:{the}\:{man}\:{applied} \\ $$$${a}\:{horizontal}\:{force}\:\mathrm{200}{N}\:{and}\:{the} \\ $$$${box}\:{moves}\:{up}\:{the}\:{plane}\:{a}\:{distance} \\ $$$${of}\:\mathrm{20}{m}\:{at}\:{a}\:{constant}\:{velocity}\:{and} \\ $$$${the}\:{coefficient}\:{of}\:{friction}\:{is}\:\mathrm{0}.\mathrm{10}, \\ $$$${find} \\ $$$$\left.{a}\right){workdone}\:{by}\:{the}\:{man}\:{on}\:{the} \\ $$$${box} \\ $$$$\left.{b}\right){workdone}\:{against}\:{friction}. \\ $$

Question Number 25307 Answers: 0 Comments: 0

An object constrained to move along the x-axis is acted upon by a force F(x) where a=5N/m, b=−2N/m. F(x)=ax+bx^2 The object is observed to proceed directly from x=1m to x=3m. How much work was done by the object by the force?Does the process of integration take into account the fact that the force F(x) changes sign in interval.

$${An}\:{object}\:{constrained}\:{to}\:{move} \\ $$$${along}\:{the}\:{x}-{axis}\:{is}\:{acted}\:{upon}\:{by} \\ $$$${a}\:{force}\:{F}\left({x}\right)\:{where}\:{a}=\mathrm{5}{N}/{m}, \\ $$$${b}=−\mathrm{2}{N}/{m}.\:{F}\left({x}\right)={ax}+{bx}^{\mathrm{2}} \\ $$$${The}\:{object}\:{is}\:{observed}\:{to}\:{proceed} \\ $$$${directly}\:{from}\:{x}=\mathrm{1}{m}\:{to}\:{x}=\mathrm{3}{m}. \\ $$$${How}\:{much}\:{work}\:{was}\:{done}\:{by}\:{the} \\ $$$${object}\:{by}\:{the}\:{force}?{Does}\:{the} \\ $$$${process}\:{of}\:{integration}\:{take}\:{into} \\ $$$${account}\:{the}\:{fact}\:{that}\:{the}\:{force} \\ $$$${F}\left({x}\right)\:{changes}\:{sign}\:{in}\:{interval}. \\ $$

Question Number 25350 Answers: 0 Comments: 0

If A and B are two points in the plane of a circle having radius r and mAB>2r ,prove that at least one of A or B is outside the circle.

$$\mathrm{If}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{two}\:\mathrm{points}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{plane}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{having} \\ $$$$\mathrm{radius}\:\mathrm{r}\:\mathrm{and}\:\mathrm{mAB}>\mathrm{2r}\:,\mathrm{prove}\:\mathrm{that}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one} \\ $$$$\mathrm{of}\:\mathrm{A}\:\mathrm{or}\:\mathrm{B}\:\mathrm{is}\:\mathrm{outside}\:\mathrm{the}\:\mathrm{circle}. \\ $$

Question Number 25300 Answers: 0 Comments: 2

Question Number 25295 Answers: 1 Comments: 0

X and Y can do a work in 30 days and 60 days respectively. If they work on alternate days beginning with X, in how many days will the work be completed?

$$\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{can}\:\mathrm{do}\:\mathrm{a}\:\mathrm{work}\:\mathrm{in}\:\mathrm{30}\:\mathrm{days}\:\mathrm{and} \\ $$$$\mathrm{60}\:\mathrm{days}\:\mathrm{respectively}.\:\mathrm{If}\:\mathrm{they}\:\mathrm{work}\:\mathrm{on} \\ $$$$\mathrm{alternate}\:\mathrm{days}\:\mathrm{beginning}\:\mathrm{with}\:\mathrm{X},\:\mathrm{in} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{days}\:\mathrm{will}\:\mathrm{the}\:\mathrm{work}\:\mathrm{be} \\ $$$$\mathrm{completed}? \\ $$

Question Number 25310 Answers: 0 Comments: 0

Question Number 25290 Answers: 2 Comments: 0

∫((x dx)/(√(a^4 +x^4 )))

$$\int\frac{{x}\:{dx}}{\sqrt{{a}^{\mathrm{4}} +{x}^{\mathrm{4}} }} \\ $$

Question Number 25288 Answers: 0 Comments: 0

(3x+(1/(2x)))^(10 ) by pascal triangle

$$\left(\mathrm{3}{x}+\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{10}\:} \:\:{by}\:{pascal}\:{triangle} \\ $$

Question Number 25287 Answers: 0 Comments: 0

limit_(x−0^− ) sin (log_e x)

$${limit}_{{x}−\mathrm{0}^{−} } \mathrm{sin}\:\left({log}_{{e}} {x}\right) \\ $$

Question Number 25283 Answers: 2 Comments: 1

Question Number 25280 Answers: 1 Comments: 0

Find the limit off(x) _(x→4) =(((x+2)/(x^2 −4)))

$${Find}\:{the}\:{limit}\:{off}\left({x}\right)\underset{{x}\rightarrow\mathrm{4}} {\:}=\left(\frac{{x}+\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{4}}\right) \\ $$

Question Number 25275 Answers: 0 Comments: 0

Question Number 25273 Answers: 0 Comments: 0

If x, y, z are in HP, then log (x+z)+log (x−2y+z) is equal to

$$\mathrm{If}\:\:{x},\:{y},\:{z}\:\mathrm{are}\:\mathrm{in}\:\mathrm{HP},\:\mathrm{then}\: \\ $$$$\mathrm{log}\:\left({x}+{z}\right)+\mathrm{log}\:\left({x}−\mathrm{2}{y}+{z}\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 25254 Answers: 1 Comments: 0

A charged sphere of mass 3×10^(−4) kg is suspended from a string.An electrical force acting horizontally on the sphere so that the string makes an angle 37° with the vertical when at rest. Find a)magnitude of the electric force b)the tension in the string.

$${A}\:{charged}\:{sphere}\:{of}\:{mass}\:\mathrm{3}×\mathrm{10}^{−\mathrm{4}} {kg}\:{is} \\ $$$${suspended}\:{from}\:{a}\:{string}.{An} \\ $$$${electrical}\:{force}\:{acting}\:{horizontally} \\ $$$${on}\:{the}\:{sphere}\:{so}\:{that}\:{the}\:{string} \\ $$$${makes}\:{an}\:{angle}\:\mathrm{37}°\:{with}\:{the}\:{vertical} \\ $$$${when}\:{at}\:{rest}.\:{Find} \\ $$$$\left.{a}\right){magnitude}\:{of}\:{the}\:{electric}\:{force} \\ $$$$\left.{b}\right){the}\:{tension}\:{in}\:{the}\:{string}. \\ $$

Question Number 25253 Answers: 1 Comments: 1

A 100kg man lowers himself to the ground from a height of 10m by means of a rope passed over a frictionless pulley and the other end attached to a 70kg sandbag. a)with what speed does the man hit the ground? b)could he have done anything to reduce the speed?

$${A}\:\mathrm{100}{kg}\:{man}\:{lowers}\:{himself}\:{to} \\ $$$${the}\:{ground}\:{from}\:{a}\:{height}\:{of}\:\mathrm{10}{m} \\ $$$${by}\:{means}\:{of}\:{a}\:{rope}\:{passed}\:{over}\:{a} \\ $$$${frictionless}\:{pulley}\:{and}\:{the}\:{other} \\ $$$${end}\:{attached}\:{to}\:{a}\:\mathrm{70}{kg}\:{sandbag}. \\ $$$$\left.{a}\right){with}\:{what}\:{speed}\:{does}\:{the}\:{man}\: \\ $$$${hit}\:{the}\:{ground}? \\ $$$$\left.{b}\right){could}\:{he}\:{have}\:{done}\:{anything}\:{to} \\ $$$${reduce}\:{the}\:{speed}? \\ $$

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