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AllQuestion and Answers: Page 389

Question Number 182149 Answers: 4 Comments: 1

Question Number 182139 Answers: 1 Comments: 1

Find constant a, b, so that y(t)=(t+3)e^(2t) is solution of IVP y^′ =ay+e^(2t) , y(0)=b .

$$\mathrm{Find}\:\mathrm{constant}\:\mathrm{a},\:\mathrm{b},\:\mathrm{so}\:\mathrm{that} \\ $$$$\mathrm{y}\left(\mathrm{t}\right)=\left(\mathrm{t}+\mathrm{3}\right)\mathrm{e}^{\mathrm{2t}} \:\mathrm{is}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{IVP} \\ $$$$\mathrm{y}^{'} =\mathrm{ay}+\mathrm{e}^{\mathrm{2t}} ,\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{b} \\ $$$$ \\ $$$$. \\ $$

Question Number 182135 Answers: 2 Comments: 1

Question Number 182131 Answers: 2 Comments: 0

Solve ((x + a^2 + 2c^2 )/(b + c)) + ((x + b^2 + 2a^2 )/(c + a)) + ((x + c^2 + 2b^2 )/(a + b)) = 0

$$\mathrm{Solve} \\ $$$$\frac{{x}\:+\:{a}^{\mathrm{2}} \:+\:\mathrm{2}{c}^{\mathrm{2}} }{{b}\:+\:{c}}\:+\:\frac{{x}\:+\:{b}^{\mathrm{2}} \:+\:\mathrm{2}{a}^{\mathrm{2}} }{{c}\:+\:{a}}\:+\:\frac{{x}\:+\:{c}^{\mathrm{2}} \:+\:\mathrm{2}{b}^{\mathrm{2}} }{{a}\:+\:{b}}\:=\:\mathrm{0} \\ $$

Question Number 182129 Answers: 0 Comments: 0

Question Number 182128 Answers: 0 Comments: 0

Question Number 182114 Answers: 0 Comments: 1

Question Number 182109 Answers: 1 Comments: 0

f(x)=3x^2 −2x(√3)−8 g(x)=x^2 −(1/3) gof^(−1) (18)=?

$$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\mathrm{3}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{x}}\sqrt{\mathrm{3}}−\mathrm{8}\:\:\:\:\:\boldsymbol{{g}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{x}}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\boldsymbol{{gof}}^{−\mathrm{1}} \left(\mathrm{18}\right)=? \\ $$

Question Number 182108 Answers: 2 Comments: 0

A truck, P traveling at 54km/hr passes through a point at 10:30am, while another truck, Q traveling at 90km/hr passes through this same point 30 minutes later. At what time will truck Q overtake P?

Question Number 182103 Answers: 1 Comments: 1

Question Number 182093 Answers: 1 Comments: 2

Solve the equation: ((x−6)/(2020))+((x−5)/(2021))+((x−4)/(2022))=3

$${Solve}\:{the}\:{equation}: \\ $$$$\frac{{x}−\mathrm{6}}{\mathrm{2020}}+\frac{{x}−\mathrm{5}}{\mathrm{2021}}+\frac{{x}−\mathrm{4}}{\mathrm{2022}}=\mathrm{3} \\ $$

Question Number 182082 Answers: 0 Comments: 0

∫_0 ^∞ ∫_0 ^∞ Σ_(n=0) ^∞ Σ_(r=0) ^n (1)^r ∙((x^r y^(2022(n+2)) )/((n−r)!(r!)^2 (2022y^(2022) +2023)^2 ))dxdy

Question Number 182078 Answers: 2 Comments: 0

Question Number 182077 Answers: 1 Comments: 0

lim_(x→∞) x ln ((((x^2 +2x+2))^(1/4) /( ((16x^2 +2x))^(1/4) −(√x))) )=?

$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{x}\:\mathrm{ln}\:\left(\frac{\sqrt[{\mathrm{4}}]{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{2}}}{\:\sqrt[{\mathrm{4}}]{\mathrm{16x}^{\mathrm{2}} +\mathrm{2x}}\:−\sqrt{\mathrm{x}}}\:\right)=? \\ $$

Question Number 182075 Answers: 2 Comments: 1

Question Number 182074 Answers: 2 Comments: 0

Let x+ xy+ y= 54 ; x, y∈ N , Find x+ y

$${Let}\:{x}+\:{xy}+\:{y}=\:\mathrm{54}\:\:\:;\:{x},\:{y}\in\:\mathbb{N}\:,\:{Find}\:{x}+\:{y} \\ $$

Question Number 182073 Answers: 1 Comments: 0

Find the sum of the solutions of the equation: ∣(√x) − 2∣+ (√x) ((√x) − 4)+ 2= 0 ; x> 0

$${Find}\:{the}\:{sum}\:{of}\:{the}\:{solutions}\:{of}\:{the}\:{equation}: \\ $$$$\:\mid\sqrt{{x}}\:−\:\mathrm{2}\mid+\:\sqrt{{x}}\:\left(\sqrt{{x}}\:−\:\mathrm{4}\right)+\:\mathrm{2}=\:\mathrm{0}\:\:\:;\:{x}>\:\mathrm{0} \\ $$

Question Number 182069 Answers: 1 Comments: 1

(1+x^2 )(dy/dx)+3xy=5x solve

$$\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{3xy}=\mathrm{5x} \\ $$$$ \\ $$$$\mathrm{solve} \\ $$

Question Number 182066 Answers: 2 Comments: 0

Question Number 182091 Answers: 1 Comments: 1

Question Number 182050 Answers: 1 Comments: 0

A= [(a,b,c),((−2),3,6),(0,(−2),5) ]and B= [(1,2,4),(0,3,9),((−1),2,2) ] A×B= [((−1),3,(−1)),((−8),d,(31)),((−5),4,e) ]find the missing value

$${A}=\begin{bmatrix}{{a}}&{{b}}&{{c}}\\{−\mathrm{2}}&{\mathrm{3}}&{\mathrm{6}}\\{\mathrm{0}}&{−\mathrm{2}}&{\mathrm{5}}\end{bmatrix}{and}\:{B}=\begin{bmatrix}{\mathrm{1}}&{\mathrm{2}}&{\mathrm{4}}\\{\mathrm{0}}&{\mathrm{3}}&{\mathrm{9}}\\{−\mathrm{1}}&{\mathrm{2}}&{\mathrm{2}}\end{bmatrix} \\ $$$${A}×{B}=\begin{bmatrix}{−\mathrm{1}}&{\mathrm{3}}&{−\mathrm{1}}\\{−\mathrm{8}}&{{d}}&{\mathrm{31}}\\{−\mathrm{5}}&{\mathrm{4}}&{{e}}\end{bmatrix}{find}\:{the}\:{missing}\:{value} \\ $$

Question Number 182120 Answers: 2 Comments: 0

Question Number 182045 Answers: 2 Comments: 1

∫_(π/6) ^(π/3) (1/(1+(tanx)^(2013) )) dx = ?

$$ \\ $$$$\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{\mathrm{1}}{\mathrm{1}+\left({tanx}\right)^{\mathrm{2013}} }\:{dx}\:=\:? \\ $$$$ \\ $$

Question Number 182043 Answers: 0 Comments: 0

For a, b, c, d ∈ R a+b+c+d=0 ab, ac, ad, bc, bd, cd ≠0 Prove the inequality: ((ab)/((a+b)^2 ))+((ac)/((a+c)^2 ))+((ad)/((a+d)^2 ))+((bc)/((b+c)^2 ))+((bd)/((b+d)^2 ))+((cd)/((c+d)^2 ))≤−(3/2) When is equality reached?

$${For}\:{a},\:{b},\:{c},\:{d}\:\in\:\mathbb{R} \\ $$$${a}+{b}+{c}+{d}=\mathrm{0} \\ $$$${ab},\:{ac},\:{ad},\:{bc},\:{bd},\:{cd}\:\neq\mathrm{0} \\ $$$${Prove}\:{the}\:{inequality}: \\ $$$$\frac{{ab}}{\left({a}+{b}\right)^{\mathrm{2}} }+\frac{{ac}}{\left({a}+{c}\right)^{\mathrm{2}} }+\frac{{ad}}{\left({a}+{d}\right)^{\mathrm{2}} }+\frac{{bc}}{\left({b}+{c}\right)^{\mathrm{2}} }+\frac{{bd}}{\left({b}+{d}\right)^{\mathrm{2}} }+\frac{{cd}}{\left({c}+{d}\right)^{\mathrm{2}} }\leq−\frac{\mathrm{3}}{\mathrm{2}} \\ $$$${When}\:{is}\:{equality}\:{reached}? \\ $$

Question Number 182039 Answers: 1 Comments: 0

if f′′′(x)=f(x) find what is f(x)

$${if}\:{f}'''\left({x}\right)={f}\left({x}\right) \\ $$$${find}\:{what}\:{is}\:{f}\left({x}\right)\: \\ $$

Question Number 182037 Answers: 0 Comments: 0

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