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Question Number 22726 Answers: 1 Comments: 2

Question Number 22728 Answers: 0 Comments: 0

Question Number 22730 Answers: 1 Comments: 2

Question Number 22729 Answers: 2 Comments: 5

Question Number 22244 Answers: 1 Comments: 0

Solve the inequality : −9((x)^(1/4) )+(√x)+18 ≥ 0 .

$${Solve}\:{the}\:{inequality}\:: \\ $$$$\:−\mathrm{9}\left(\sqrt[{\mathrm{4}}]{{x}}\right)+\sqrt{{x}}+\mathrm{18}\:\geqslant\:\mathrm{0}\:. \\ $$

Question Number 22232 Answers: 1 Comments: 0

find (dy/dx) where sin^(−1) ((x/y))=x+y

$$\mathrm{find}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\mathrm{where}\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{x}}{\mathrm{y}}\right)=\mathrm{x}+\mathrm{y} \\ $$

Question Number 22731 Answers: 0 Comments: 0

Question Number 22247 Answers: 1 Comments: 0

I=∫(√)x^2 +a^2 dx

$$\mathrm{I}=\int\sqrt{}\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} \:\mathrm{dx} \\ $$

Question Number 22220 Answers: 1 Comments: 0

The number of integral solutions of the equation 4log_(x/2) ((√x))+2log_(4x) (x^2 )= 3log_(2x) (x^3 ) is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{integral}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\mathrm{4log}_{{x}/\mathrm{2}} \left(\sqrt{{x}}\right)+\mathrm{2log}_{\mathrm{4}{x}} \left({x}^{\mathrm{2}} \right)= \\ $$$$\mathrm{3log}_{\mathrm{2}{x}} \left({x}^{\mathrm{3}} \right)\:\mathrm{is} \\ $$

Question Number 22215 Answers: 3 Comments: 0

solve the inequation −x^2 +3x−2>0

$${solve}\:{the}\:{inequation}\:−{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{2}>\mathrm{0} \\ $$

Question Number 22210 Answers: 1 Comments: 0

∫((4x)/e^(3x) )dx

$$\int\frac{\mathrm{4}{x}}{{e}^{\mathrm{3}{x}} }{dx} \\ $$

Question Number 22203 Answers: 1 Comments: 1

lim_(x→∞) e^x cos x

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{e}^{{x}} \:\mathrm{cos}\:{x} \\ $$

Question Number 22221 Answers: 1 Comments: 1

∫ ((a_0 +b_0 x^2 )/((a+x)^2 ))dx

$$\int\:\:\frac{{a}_{\mathrm{0}} +{b}_{\mathrm{0}} {x}^{\mathrm{2}} }{\left({a}+{x}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 22199 Answers: 2 Comments: 3

Question Number 22193 Answers: 1 Comments: 1

A body of mass 0.1kg dropped from a height of 8m onto a hard floor and bounces back to a height of 2m. Calculate the chaange in momentum.If the body is in contact with the floor for 0.1s, what is the force exerted on the body?(g=10m/s^2 )

$$\mathrm{A}\:\mathrm{body}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{0}.\mathrm{1kg}\:\mathrm{dropped}\: \\ $$$$\mathrm{from}\:\mathrm{a}\:\mathrm{height}\:\mathrm{of}\:\mathrm{8m}\:\mathrm{onto}\:\mathrm{a}\:\mathrm{hard} \\ $$$$\mathrm{floor}\:\mathrm{and}\:\mathrm{bounces}\:\mathrm{back}\:\mathrm{to}\:\mathrm{a}\:\mathrm{height} \\ $$$$\mathrm{of}\:\mathrm{2m}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{chaange}\:\mathrm{in} \\ $$$$\mathrm{momentum}.\mathrm{If}\:\mathrm{the}\:\mathrm{body}\:\mathrm{is}\:\mathrm{in} \\ $$$$\mathrm{contact}\:\mathrm{with}\:\mathrm{the}\:\mathrm{floor}\:\mathrm{for}\:\mathrm{0}.\mathrm{1s}, \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{force}\:\mathrm{exerted}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{body}?\left(\mathrm{g}=\mathrm{10m}/\mathrm{s}^{\mathrm{2}} \right) \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 22177 Answers: 1 Comments: 0

(C_0 /2) − (C_1 /3) + (C_2 /4) − (C_3 /5) + ..........

$$\frac{{C}_{\mathrm{0}} }{\mathrm{2}}\:−\:\frac{{C}_{\mathrm{1}} }{\mathrm{3}}\:+\:\frac{{C}_{\mathrm{2}} }{\mathrm{4}}\:−\:\frac{{C}_{\mathrm{3}} }{\mathrm{5}}\:+\:.......... \\ $$

Question Number 22166 Answers: 1 Comments: 0

If∫_1 ^4 f(x) dx = 5 what is the value of ∫_0 ^1 f(3x +1) dx ?

$$\mathrm{If}\underset{\mathrm{1}} {\overset{\mathrm{4}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:\mathrm{5} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{f}\left(\mathrm{3}{x}\:+\mathrm{1}\right)\:{dx}\:? \\ $$

Question Number 22165 Answers: 1 Comments: 0

Question Number 22174 Answers: 1 Comments: 0

Question Number 22154 Answers: 2 Comments: 0

Given a,b,c real and positive numbers, and a + b + c = 1 Find the minimum value of ((a + b)/(abc))

$$\mathrm{Given}\:{a},{b},{c}\:\mathrm{real}\:\mathrm{and}\:\mathrm{positive}\:\mathrm{numbers},\:\mathrm{and} \\ $$$${a}\:+\:{b}\:+\:{c}\:=\:\mathrm{1} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\:\frac{{a}\:+\:{b}}{{abc}} \\ $$

Question Number 22162 Answers: 1 Comments: 0

use the appropite set law to show that (A−B)∪(B−A)=(A∪B)−(A∩B)

$${use}\:{the}\:{appropite}\:{set}\:{law}\:{to}\:{show}\: \\ $$$${that} \\ $$$$\left({A}−{B}\right)\cup\left({B}−{A}\right)=\left({A}\cup{B}\right)−\left({A}\cap{B}\right) \\ $$

Question Number 22151 Answers: 1 Comments: 0

integrate ∫((cosx−cos2x)/(1+cosx))dx

$${integrate} \\ $$$$\int\frac{{cosx}−{cos}\mathrm{2}{x}}{\mathrm{1}+{cosx}}{dx} \\ $$

Question Number 22145 Answers: 1 Comments: 3

A particle P is moving on a circle under the action of only one force acting always towards fixed point O on the circumference. Find ratio of (d^2 φ/dt^2 ) and ((dφ/dt))^2 .

$$\mathrm{A}\:\mathrm{particle}\:{P}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{on}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{under} \\ $$$$\mathrm{the}\:\mathrm{action}\:\mathrm{of}\:\mathrm{only}\:\mathrm{one}\:\mathrm{force}\:\mathrm{acting} \\ $$$$\mathrm{always}\:\mathrm{towards}\:\mathrm{fixed}\:\mathrm{point}\:{O}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{circumference}.\:\mathrm{Find}\:\mathrm{ratio}\:\mathrm{of}\:\frac{{d}^{\mathrm{2}} \phi}{{dt}^{\mathrm{2}} }\:\mathrm{and} \\ $$$$\left(\frac{{d}\phi}{{dt}}\right)^{\mathrm{2}} . \\ $$

Question Number 22139 Answers: 0 Comments: 3

The linear mass density, i.e. mass per unit length of the rope, varies from 0 to λ from one end to another. The acceleration of the combined system will be

$$\mathrm{The}\:\mathrm{linear}\:\mathrm{mass}\:\mathrm{density},\:{i}.{e}.\:\mathrm{mass}\:\mathrm{per} \\ $$$$\mathrm{unit}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rope},\:\mathrm{varies}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to} \\ $$$$\lambda\:\mathrm{from}\:\mathrm{one}\:\mathrm{end}\:\mathrm{to}\:\mathrm{another}.\:\mathrm{The} \\ $$$$\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{combined}\:\mathrm{system} \\ $$$$\mathrm{will}\:\mathrm{be} \\ $$

Question Number 22138 Answers: 0 Comments: 0

In the ground state, an element has 13 electrons in its M-shell. The element is

$$\mathrm{In}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{state},\:\mathrm{an}\:\mathrm{element}\:\mathrm{has}\:\mathrm{13} \\ $$$$\mathrm{electrons}\:\mathrm{in}\:\mathrm{its}\:\mathrm{M}-\mathrm{shell}.\:\mathrm{The}\:\mathrm{element}\:\mathrm{is} \\ $$

Question Number 22135 Answers: 1 Comments: 0

A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is

$$\mathrm{A}\:\mathrm{mass}\:{m}\:\mathrm{hangs}\:\mathrm{with}\:\mathrm{the}\:\mathrm{help}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{string}\:\mathrm{wrapped}\:\mathrm{around}\:\mathrm{a}\:\mathrm{pulley}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{frictionless}\:\mathrm{bearing}.\:\mathrm{The}\:\mathrm{pulley}\:\mathrm{has} \\ $$$$\mathrm{mass}\:{m}\:\mathrm{and}\:\mathrm{radius}\:{R}.\:\mathrm{Assuming}\:\mathrm{pulley} \\ $$$$\mathrm{to}\:\mathrm{be}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{uniform}\:\mathrm{circular}\:\mathrm{disc},\:\mathrm{the} \\ $$$$\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{mass}\:{m},\:\mathrm{if}\:\mathrm{the} \\ $$$$\mathrm{string}\:\mathrm{does}\:\mathrm{not}\:\mathrm{slip}\:\mathrm{on}\:\mathrm{the}\:\mathrm{pulley},\:\mathrm{is} \\ $$

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