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Question Number 179228 Answers: 1 Comments: 0

prove in right triangle : a^2 +b^2 =c^2 −−−−−−

$${prove}\:{in}\:{right}\:{triangle}\::\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={c}^{\mathrm{2}} \\ $$$$−−−−−− \\ $$

Question Number 179226 Answers: 2 Comments: 1

Question Number 179198 Answers: 5 Comments: 2

Question Number 179195 Answers: 1 Comments: 0

a+(1/b)=tan59 b+(1/c)=tan60 c+(1/a)=tan61 (abc)^(2022) +(1/((abc)^(2022) ))=?

$${a}+\frac{\mathrm{1}}{{b}}={tan}\mathrm{59} \\ $$$${b}+\frac{\mathrm{1}}{{c}}={tan}\mathrm{60} \\ $$$${c}+\frac{\mathrm{1}}{{a}}={tan}\mathrm{61} \\ $$$$\left({abc}\right)^{\mathrm{2022}} +\frac{\mathrm{1}}{\left({abc}\right)^{\mathrm{2022}} }=? \\ $$

Question Number 179194 Answers: 2 Comments: 0

Evaluate the ∫ ((tan^5 x)/(cos^9 x)) dx

$${Evaluate}\:{the}\:\int\:\frac{\mathrm{tan}^{\mathrm{5}} \:{x}}{\mathrm{cos}^{\mathrm{9}} \:{x}}\:{dx} \\ $$

Question Number 179175 Answers: 0 Comments: 2

Find ∫x^5 (√(x^3 +1)) dx Answer: I= (2/(45)) (3x^3 −2) (√((x^3 +1)^3 )) + c

$$\:{Find}\:\int{x}^{\mathrm{5}} \:\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx} \\ $$$$\: \\ $$$$\:{Answer}:\:{I}=\:\frac{\mathrm{2}}{\mathrm{45}}\:\left(\mathrm{3}{x}^{\mathrm{3}} −\mathrm{2}\right)\:\sqrt{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{3}} }\:+\:{c} \\ $$$$ \\ $$

Question Number 180359 Answers: 1 Comments: 0

Question Number 180035 Answers: 0 Comments: 4

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Question Number 179159 Answers: 1 Comments: 1

Question Number 179157 Answers: 1 Comments: 0

If x = a^2 − bc, y = b^2 − ca, z = c^2 − ab then prove that, x^3 + y^3 + z^3 − 3xyz is a perfect square.

$$\mathrm{If}\:{x}\:=\:{a}^{\mathrm{2}} −\:{bc},\:{y}\:=\:{b}^{\mathrm{2}} \:−\:{ca},\:{z}\:=\:{c}^{\mathrm{2}} \:−\:{ab} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}, \\ $$$${x}^{\mathrm{3}} \:+\:{y}^{\mathrm{3}} \:+\:{z}^{\mathrm{3}} \:−\:\mathrm{3}{xyz}\:\mathrm{is}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$

Question Number 179181 Answers: 3 Comments: 0

Help-me! Use double integral to find the area of the region bounded by the following curves given in the plane shown below: y^2 = 4x and x^2 = 4y

$$\:\mathrm{Help}-\mathrm{me}! \\ $$$$\: \\ $$$$\:\mathrm{Use}\:\mathrm{double}\:\mathrm{integral}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \\ $$$$\:\mathrm{region}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{following}\:\mathrm{curves}\: \\ $$$$\:\mathrm{given}\:\mathrm{in}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{shown}\:\mathrm{below}: \\ $$$$\: \\ $$$$\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{4x}\:\mathrm{and}\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:=\:\mathrm{4y} \\ $$

Question Number 179156 Answers: 0 Comments: 0

Question Number 179140 Answers: 4 Comments: 0

(1/(3a)) = (1/(4b)) = (1/(6c)) and a+b+c=27 find a−c=?

$$\frac{\mathrm{1}}{\mathrm{3a}}\:=\:\frac{\mathrm{1}}{\mathrm{4b}}\:=\:\frac{\mathrm{1}}{\mathrm{6c}}\:\:\:\mathrm{and}\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{27} \\ $$$$\mathrm{find}\:\:\:\mathrm{a}−\mathrm{c}=? \\ $$

Question Number 179137 Answers: 1 Comments: 0

Question Number 179131 Answers: 1 Comments: 8

Question Number 179105 Answers: 2 Comments: 0

1. Compare: π^(2022e) and e^(2022𝛑) 2. Compute value of P = π^𝛑^𝛑^(...^𝛑 )

$$\mathrm{1}.\:\mathrm{Compare}:\:\:\:\pi^{\mathrm{2022}\boldsymbol{\mathrm{e}}} \:\:\:\mathrm{and}\:\:\:\mathrm{e}^{\mathrm{2022}\boldsymbol{\pi}} \\ $$$$\mathrm{2}.\:\mathrm{Compute}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{P}\:=\:\pi^{\boldsymbol{\pi}^{\boldsymbol{\pi}^{...^{\boldsymbol{\pi}} } } } \\ $$

Question Number 179100 Answers: 4 Comments: 2

if x^2 +y^2 +xy=5, find the range of x^2 +y^2 −xy. (x,y ∈R)

$${if}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{xy}=\mathrm{5},\:{find}\:{the}\:{range}\:{of} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −{xy}. \\ $$$$\left({x},{y}\:\in\mathbb{R}\right) \\ $$

Question Number 179095 Answers: 2 Comments: 1

Question Number 179094 Answers: 0 Comments: 1

determine 1)L^− [((s^3 +3)/(s(s^2 +9)))] 2)L^− [(4/((s^2 +2s+5)^2 ))] L^− is the inverse laplace transform

$${determine} \\ $$$$\left.\mathrm{1}\right)\mathcal{L}^{−} \left[\frac{{s}^{\mathrm{3}} +\mathrm{3}}{{s}\left({s}^{\mathrm{2}} +\mathrm{9}\right)}\right] \\ $$$$\left.\mathrm{2}\right)\mathcal{L}^{−} \left[\frac{\mathrm{4}}{\left({s}^{\mathrm{2}} +\mathrm{2}{s}+\mathrm{5}\right)^{\mathrm{2}} }\right] \\ $$$$\mathcal{L}^{−} \:{is}\:{the}\:{inverse}\:{laplace}\:{transform} \\ $$

Question Number 179093 Answers: 0 Comments: 0

find the laplace transform of f(t)= t^2 cos(2t) u(t) u(t) is unit step function u(t)= { ((1 t≥0)),((0 t<0)) :}

$$\:{find}\:{the}\:{laplace}\:{transform}\:{of} \\ $$$${f}\left({t}\right)=\:{t}^{\mathrm{2}} \:{cos}\left(\mathrm{2}{t}\right)\:{u}\left({t}\right) \\ $$$${u}\left({t}\right)\:{is}\:{unit}\:{step}\:{function}\: \\ $$$${u}\left({t}\right)=\begin{cases}{\mathrm{1}\:\:\:\:\:\:\:{t}\geqslant\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:{t}<\mathrm{0}}\end{cases} \\ $$$$ \\ $$

Question Number 179090 Answers: 1 Comments: 1

Given a>0, b>0, c>2, a+b=1. find the minimum value of ((3ac)/b)+(c/(ab))+(6/(c−2)).

$$\mathrm{Given}\:{a}>\mathrm{0},\:{b}>\mathrm{0},\:{c}>\mathrm{2},\:{a}+{b}=\mathrm{1}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\:\frac{\mathrm{3}{ac}}{{b}}+\frac{{c}}{{ab}}+\frac{\mathrm{6}}{{c}−\mathrm{2}}. \\ $$

Question Number 179088 Answers: 2 Comments: 0

Question Number 179073 Answers: 3 Comments: 0

Question Number 179107 Answers: 1 Comments: 0

I= ∫ (x^2 /(sin (2arctan (e^x )))) dx , Find I

$${I}=\:\int\:\frac{{x}^{\mathrm{2}} }{\mathrm{sin}\:\left(\mathrm{2arctan}\:\left({e}^{{x}} \right)\right)}\:{dx}\:\:,\:{Find}\:{I} \\ $$

Question Number 179066 Answers: 1 Comments: 0

If f(x)=∫ (x^2 /(x^2 +tan x)) dx then ∫ ((tan x)/(x^2 +tan x)) dx =?

$$\:\:\:\:\:\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\int\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$$$\:\:\:\:\mathrm{then}\:\int\:\frac{\mathrm{tan}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} +\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$

Question Number 179064 Answers: 1 Comments: 3

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