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Question Number 12611 Answers: 1 Comments: 0

A drum of mass 100g is rolled into the deck of a lorry 1.5m above a horizontal floor using a plank 4m long. calculate the workdone against gravity during the process. (g = 10m/s^2 ).

$$\mathrm{A}\:\mathrm{drum}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{100g}\:\mathrm{is}\:\mathrm{rolled}\:\mathrm{into}\:\mathrm{the}\:\mathrm{deck}\:\mathrm{of}\:\mathrm{a}\:\mathrm{lorry}\:\mathrm{1}.\mathrm{5m}\:\mathrm{above}\:\mathrm{a}\: \\ $$$$\mathrm{horizontal}\:\mathrm{floor}\:\mathrm{using}\:\mathrm{a}\:\mathrm{plank}\:\mathrm{4m}\:\mathrm{long}.\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{workdone}\:\mathrm{against} \\ $$$$\mathrm{gravity}\:\mathrm{during}\:\mathrm{the}\:\mathrm{process}.\:\left(\mathrm{g}\:=\:\mathrm{10m}/\mathrm{s}^{\mathrm{2}} \right). \\ $$

Question Number 12610 Answers: 1 Comments: 0

A steam engine of efficiency 50% burns a 1g of coal to produce 10000J of energy. if it burns 20g per sec, calculate the output power.

$$\mathrm{A}\:\mathrm{steam}\:\mathrm{engine}\:\mathrm{of}\:\mathrm{efficiency}\:\mathrm{50\%}\:\mathrm{burns}\:\mathrm{a}\:\mathrm{1g}\:\mathrm{of}\:\mathrm{coal}\:\mathrm{to}\:\mathrm{produce}\:\mathrm{10000J} \\ $$$$\mathrm{of}\:\mathrm{energy}.\:\mathrm{if}\:\mathrm{it}\:\mathrm{burns}\:\mathrm{20g}\:\mathrm{per}\:\mathrm{sec},\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{output}\:\mathrm{power}. \\ $$

Question Number 12605 Answers: 1 Comments: 0

Question Number 12603 Answers: 1 Comments: 0

Q. value of θ = tan 3/4.

$${Q}.\:\mathrm{value}\:\mathrm{of}\:\:\theta\:=\:\mathrm{tan}\:\mathrm{3}/\mathrm{4}. \\ $$

Question Number 12601 Answers: 2 Comments: 0

y=(x^3 /3)+2x^2 −5x+7 find the critical points of the function

$$\boldsymbol{\mathrm{y}}=\frac{\boldsymbol{\mathrm{x}}^{\mathrm{3}} }{\mathrm{3}}+\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{\mathrm{x}}+\mathrm{7}\:\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{critical}}\:\:\boldsymbol{\mathrm{points}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{function}} \\ $$

Question Number 12596 Answers: 1 Comments: 0

y=−x^2 +bx+c x=−1 point function accepts a maximum value equal to 5. Find y(1).

Question Number 12591 Answers: 0 Comments: 1

This ∮(x)=3−(x^2 /(x^4 +3x^2 +1)) find the sphere of function values

$$\boldsymbol{\mathrm{This}} \\ $$$$\oint\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{3}−\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{x}}^{\mathrm{4}} +\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}\:\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{sphere}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{function}}\:\:\boldsymbol{\mathrm{values}} \\ $$

Question Number 12590 Answers: 0 Comments: 0

In a basic version of pocker , each players is dealth 5 cards from a standard 52 cards (no pocker). How many diferent 5 cards pocker hand are there ???

$$\mathrm{In}\:\mathrm{a}\:\mathrm{basic}\:\mathrm{version}\:\mathrm{of}\:\mathrm{pocker}\:,\:\mathrm{each}\:\mathrm{players}\:\mathrm{is}\:\mathrm{dealth}\:\mathrm{5}\:\mathrm{cards}\:\mathrm{from}\:\mathrm{a}\:\mathrm{standard} \\ $$$$\mathrm{52}\:\mathrm{cards}\:\left(\mathrm{no}\:\mathrm{pocker}\right).\:\mathrm{How}\:\mathrm{many}\:\mathrm{diferent}\:\mathrm{5}\:\mathrm{cards}\:\mathrm{pocker}\:\mathrm{hand}\:\mathrm{are}\:\mathrm{there}\:??? \\ $$

Question Number 12580 Answers: 1 Comments: 0

Find the smaillest value of the sum x(x+1)(x+2)(x+3).

$$\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{smaillest}}\:\:\boldsymbol{\mathrm{value}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{sum}} \\ $$$$\boldsymbol{\mathrm{x}}\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)\left(\boldsymbol{\mathrm{x}}+\mathrm{3}\right). \\ $$

Question Number 12577 Answers: 2 Comments: 0

Find the area generated when the curve x = a(θ − sinθ), (1 − cosθ) θ = 0, θ = π rotates about x−axis through 2π radian. Note: 1 − cosθ = 2 sin^2 ((θ/2))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{generated}\:\mathrm{when}\:\mathrm{the}\:\mathrm{curve}\:\:\mathrm{x}\:=\:\mathrm{a}\left(\theta\:−\:\mathrm{sin}\theta\right),\:\left(\mathrm{1}\:−\:\mathrm{cos}\theta\right) \\ $$$$\theta\:=\:\mathrm{0},\:\theta\:=\:\pi\:\:\mathrm{rotates}\:\mathrm{about}\:\mathrm{x}−\mathrm{axis}\:\mathrm{through}\:\mathrm{2}\pi\:\mathrm{radian}. \\ $$$$\mathrm{Note}:\:\mathrm{1}\:−\:\mathrm{cos}\theta\:=\:\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \left(\frac{\theta}{\mathrm{2}}\right) \\ $$

Question Number 12576 Answers: 1 Comments: 0

Given two functions f(x) and g(x) with f(1) = 7, g(2) = 1 , f′(1) = 204 and g′(x) = 22. What is the derivative of f(g(x)) at x = 2

$$\mathrm{Given}\:\mathrm{two}\:\mathrm{functions}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{with}\:\mathrm{f}\left(\mathrm{1}\right)\:=\:\mathrm{7},\:\mathrm{g}\left(\mathrm{2}\right)\:=\:\mathrm{1}\:,\:\mathrm{f}'\left(\mathrm{1}\right)\:=\:\mathrm{204} \\ $$$$\mathrm{and}\:\mathrm{g}'\left(\mathrm{x}\right)\:=\:\mathrm{22}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{derivative}\:\mathrm{of}\:\:\mathrm{f}\left(\mathrm{g}\left(\mathrm{x}\right)\right)\:\mathrm{at}\:\mathrm{x}\:=\:\mathrm{2} \\ $$

Question Number 12572 Answers: 2 Comments: 1

prove that if, sin(θ) = ((1 − x)/(1 + x)) then tan((x/4) − (θ/2)) = (√x)

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{if}, \\ $$$$\mathrm{sin}\left(\theta\right)\:=\:\frac{\mathrm{1}\:−\:\mathrm{x}}{\mathrm{1}\:+\:\mathrm{x}}\:\:\:\:\:\mathrm{then}\:\:\mathrm{tan}\left(\frac{\mathrm{x}}{\mathrm{4}}\:−\:\frac{\theta}{\mathrm{2}}\right)\:=\:\sqrt{\mathrm{x}} \\ $$

Question Number 12569 Answers: 0 Comments: 0

tank you

$${tank}\:{you} \\ $$

Question Number 12566 Answers: 1 Comments: 0

we give U_1 ,U_2 ,U_3 the terms of a geometric sequence .Determine U_1 ,U_2 ,U_3 such that : { ((U_1 .U_2 .U_3 =64)),((U_1 ^2 +U_2 ^2 +U_3 ^2 =84)) :}

$${we}\:{give}\:{U}_{\mathrm{1}} ,{U}_{\mathrm{2}} ,{U}_{\mathrm{3}} \:{the}\:{terms}\:{of}\:{a}\:{geometric}\:{sequence} \\ $$$$.{Determine}\:{U}_{\mathrm{1}} ,{U}_{\mathrm{2}} ,{U}_{\mathrm{3}} \:{such}\:{that}\:: \\ $$$$ \\ $$$$\begin{cases}{{U}_{\mathrm{1}} .{U}_{\mathrm{2}} .{U}_{\mathrm{3}} =\mathrm{64}}\\{{U}_{\mathrm{1}} ^{\mathrm{2}} +{U}_{\mathrm{2}} ^{\mathrm{2}} +{U}_{\mathrm{3}} ^{\mathrm{2}} =\mathrm{84}}\end{cases} \\ $$$$ \\ $$

Question Number 12562 Answers: 1 Comments: 1

y=−(x^3 /3)+2x^2 −3x maximum−minimum=?

$$\boldsymbol{\mathrm{y}}=−\frac{\boldsymbol{\mathrm{x}}^{\mathrm{3}} }{\mathrm{3}}+\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{\mathrm{x}} \\ $$$$\boldsymbol{\mathrm{maximum}}−\boldsymbol{\mathrm{minimum}}=? \\ $$

Question Number 12561 Answers: 0 Comments: 0

Prove mean, expected mean of binomial and bernoulli distribution

$$\mathrm{Prove}\:\mathrm{mean},\:\mathrm{expected}\:\mathrm{mean}\:\mathrm{of}\:\mathrm{binomial}\:\mathrm{and}\:\mathrm{bernoulli}\:\mathrm{distribution}\: \\ $$

Question Number 12558 Answers: 1 Comments: 0

This y=−x^2 +6x−12 find the values of the function area.

$$\boldsymbol{\mathrm{This}}\:\: \\ $$$$\boldsymbol{\mathrm{y}}=−\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{6}\boldsymbol{\mathrm{x}}−\mathrm{12}\:\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{values}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{function}}\:\boldsymbol{\mathrm{area}}. \\ $$

Question Number 12553 Answers: 0 Comments: 0

Using Laplace Transform, solve f(t) = ((sin 3t)/t)