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Question Number 118265    Answers: 1   Comments: 0

Biochimica Isomeri di posizione del C_7 H_(16) CH_3 CH_2 CH_2 CH_2 CH_2 CH_2 CH_3 CH_3 CH_2 CH(CH_3 )CH_2 CH_2 CH_3 CH_3 CH(CH_3 )CH_2 CH_2 CH_2 CH_3 CH_3 CH(CH_3 )CH(CH_3 )CH_2 CH_3 Studiare la distillazione frazionata del petrolio

$$\mathrm{Biochimica} \\ $$$$\mathrm{Isomeri}\:\mathrm{di}\:\mathrm{posizione}\:\mathrm{del}\:\mathrm{C}_{\mathrm{7}} \mathrm{H}_{\mathrm{16}} \\ $$$$\mathrm{CH}_{\mathrm{3}} \mathrm{CH}_{\mathrm{2}} \mathrm{CH}_{\mathrm{2}} \mathrm{CH}_{\mathrm{2}} \mathrm{CH}_{\mathrm{2}} \mathrm{CH}_{\mathrm{2}} \mathrm{CH}_{\mathrm{3}} \\ $$$$\mathrm{CH}_{\mathrm{3}} \mathrm{CH}_{\mathrm{2}} \mathrm{CH}\left(\mathrm{CH}_{\mathrm{3}} \right)\mathrm{CH}_{\mathrm{2}} \mathrm{CH}_{\mathrm{2}} \mathrm{CH}_{\mathrm{3}} \\ $$$$\mathrm{CH}_{\mathrm{3}} \mathrm{CH}\left(\mathrm{CH}_{\mathrm{3}} \right)\mathrm{CH}_{\mathrm{2}} \mathrm{CH}_{\mathrm{2}} \mathrm{CH}_{\mathrm{2}} \mathrm{CH}_{\mathrm{3}} \\ $$$$\mathrm{CH}_{\mathrm{3}} \mathrm{CH}\left(\mathrm{CH}_{\mathrm{3}} \right)\mathrm{CH}\left(\mathrm{CH}_{\mathrm{3}} \right)\mathrm{CH}_{\mathrm{2}} \mathrm{CH}_{\mathrm{3}} \\ $$$$\mathrm{Studiare}\:\mathrm{la}\:\mathrm{distillazione}\:\mathrm{frazionata}\:\mathrm{del}\:\mathrm{petrolio} \\ $$

Question Number 118263    Answers: 0   Comments: 0

Question Number 118259    Answers: 0   Comments: 0

Svolgimento prova analoga alla verifica 1C 1) Scrivere l′insieme mediante elencazione A={x=8n+5,n∈N∧0<n≤3} Soluzione A={13;21;29} A={0;3;6;9;12} B={0;4;8;12} Scrivere A∩B A∪B Soluzione A∩B={0;12} A∪B={0;3;4;6;8;9;12} L′addizione non gode della proprieta^ invariantiva La divisione non gode della proprieta^ associativa (50:10):5≠50:(10:5) Indicare la proprieta^ corrispondente 35−7=(35−2)−(7−2) proprieta^ invariantiva della sottrazione (11+7)•5=5•(11+7) proprieta^ commutativa della moltiplicazione (7−2)•3=21−6 proprieta^ distributiva della moltiplicazione rispetto alla sottrazione 21−6=3•(7−2) raccoglimento a fattor comune

$$\mathrm{Svolgimento}\:\mathrm{prova}\:\mathrm{analoga}\:\mathrm{alla}\:\mathrm{verifica}\:\mathrm{1C} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Scrivere}\:\mathrm{l}'\mathrm{insieme}\:\mathrm{mediante}\:\mathrm{elencazione} \\ $$$$\mathrm{A}=\left\{\mathrm{x}=\mathrm{8n}+\mathrm{5},\mathrm{n}\in\mathbb{N}\wedge\mathrm{0}<\mathrm{n}\leqslant\mathrm{3}\right\} \\ $$$$\mathrm{Soluzione} \\ $$$$\mathrm{A}=\left\{\mathrm{13};\mathrm{21};\mathrm{29}\right\} \\ $$$$\mathrm{A}=\left\{\mathrm{0};\mathrm{3};\mathrm{6};\mathrm{9};\mathrm{12}\right\}\:\:\:\:\:\:\mathrm{B}=\left\{\mathrm{0};\mathrm{4};\mathrm{8};\mathrm{12}\right\} \\ $$$$\mathrm{Scrivere}\:\mathrm{A}\cap\mathrm{B}\:\:\:\:\:\:\:\mathrm{A}\cup\mathrm{B} \\ $$$$\mathrm{Soluzione} \\ $$$$\mathrm{A}\cap\mathrm{B}=\left\{\mathrm{0};\mathrm{12}\right\}\:\:\:\:\:\:\mathrm{A}\cup\mathrm{B}=\left\{\mathrm{0};\mathrm{3};\mathrm{4};\mathrm{6};\mathrm{8};\mathrm{9};\mathrm{12}\right\} \\ $$$$\mathrm{L}'\mathrm{addizione}\:\mathrm{non}\:\mathrm{gode}\:\mathrm{della}\:\mathrm{propriet}\grave {\mathrm{a}}\:\mathrm{invariantiva} \\ $$$$\mathrm{La}\:\mathrm{divisione}\:\mathrm{non}\:\mathrm{gode}\:\mathrm{della}\:\mathrm{propriet}\grave {\mathrm{a}}\:\mathrm{associativa} \\ $$$$\left(\mathrm{50}:\mathrm{10}\right):\mathrm{5}\neq\mathrm{50}:\left(\mathrm{10}:\mathrm{5}\right) \\ $$$$\mathrm{Indicare}\:\mathrm{la}\:\mathrm{propriet}\acute {\mathrm{a}}\:\mathrm{corrispondente} \\ $$$$\mathrm{35}−\mathrm{7}=\left(\mathrm{35}−\mathrm{2}\right)−\left(\mathrm{7}−\mathrm{2}\right)\:\:\:\:\:\:\mathrm{propriet}\acute {\mathrm{a}}\:\mathrm{invariantiva}\:\mathrm{della}\:\mathrm{sottrazione} \\ $$$$\left(\mathrm{11}+\mathrm{7}\right)\bullet\mathrm{5}=\mathrm{5}\bullet\left(\mathrm{11}+\mathrm{7}\right)\:\:\:\:\:\:\:\:\:\:\:\mathrm{propriet}\acute {\mathrm{a}}\:\mathrm{commutativa}\:\mathrm{della}\:\mathrm{moltiplicazione} \\ $$$$\left(\mathrm{7}−\mathrm{2}\right)\bullet\mathrm{3}=\mathrm{21}−\mathrm{6}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{propriet}\acute {\mathrm{a}}\:\mathrm{distributiva}\:\mathrm{della}\:\mathrm{moltiplicazione}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{rispetto}\:\mathrm{alla}\:\mathrm{sottrazione} \\ $$$$\mathrm{21}−\mathrm{6}=\mathrm{3}\bullet\left(\mathrm{7}−\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{raccoglimento}\:\mathrm{a}\:\mathrm{fattor}\:\mathrm{comune} \\ $$

Question Number 118251    Answers: 1   Comments: 0

Question Number 118278    Answers: 1   Comments: 0

Evaluate ∫_( 0) ^( (π/3)) tan^2 xsec((x/3))dx ★

$$\mathrm{Evaluate} \\ $$$$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{3}}} \mathrm{tan}^{\mathrm{2}} \mathrm{xsec}\left(\frac{\mathrm{x}}{\mathrm{3}}\right)\mathrm{dx} \\ $$$$\bigstar \\ $$

Question Number 118247    Answers: 2   Comments: 0

lim_(x→∞) ((1+x^4 ))^(1/4) − ((1+x^5 ))^(1/5) =?

$$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{4}}]{\mathrm{1}+{x}^{\mathrm{4}} }\:−\:\sqrt[{\mathrm{5}}]{\mathrm{1}+{x}^{\mathrm{5}} }\:=? \\ $$

Question Number 118246    Answers: 1   Comments: 0

∫_0 ^1 ((ln x)/(x+1)) dx =?

$$\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{ln}\:{x}}{{x}+\mathrm{1}}\:{dx}\:=? \\ $$

Question Number 118242    Answers: 1   Comments: 0

solve ∫_0 ^π ((xcosx)/((1+sin^2 x)))dx

$${solve} \\ $$$$\int_{\mathrm{0}} ^{\pi} \frac{{x}\mathrm{cos}{x}}{\left(\mathrm{1}+\mathrm{sin}^{\mathrm{2}} {x}\right)}{dx} \\ $$

Question Number 118239    Answers: 2   Comments: 0

Given that x,y,z are real numbers such that x+y+z=0 and xyz=−432. If a=(1/x)+(1/y)+(1/z), find the smallest possible value of a.

$$\mathrm{Given}\:\mathrm{that}\:{x},{y},{z}\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$${x}+{y}+{z}=\mathrm{0}\:\mathrm{and}\:{xyz}=−\mathrm{432}. \\ $$$$\mathrm{If}\:{a}=\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}+\frac{\mathrm{1}}{{z}},\:\mathrm{find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{possible} \\ $$$$\mathrm{value}\:\mathrm{of}\:{a}. \\ $$

Question Number 118231    Answers: 1   Comments: 0

Given a matrix A= (((−1 3 2)),(( 0 1 4)),((−2 3 2)) ) and A^(−1) = (1/(10))(kA+9I−A^2 ). find k.

$${Given}\:{a}\:{matrix}\:{A}=\:\begin{pmatrix}{−\mathrm{1}\:\:\:\:\:\:\mathrm{3}\:\:\:\:\:\mathrm{2}}\\{\:\:\:\mathrm{0}\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{4}}\\{−\mathrm{2}\:\:\:\:\:\mathrm{3}\:\:\:\:\:\mathrm{2}}\end{pmatrix} \\ $$$${and}\:{A}^{−\mathrm{1}} =\:\frac{\mathrm{1}}{\mathrm{10}}\left({kA}+\mathrm{9}{I}−{A}^{\mathrm{2}} \right). \\ $$$${find}\:{k}. \\ $$

Question Number 118230    Answers: 1   Comments: 0

If ∫ ((((√x))^5 )/(((√x))^7 +x^6 )) dx = p ln ((x^q /(x^q +1))) + C find the value of p and q.

$$\mathrm{If}\:\int\:\frac{\left(\sqrt{\mathrm{x}}\right)^{\mathrm{5}} }{\left(\sqrt{\mathrm{x}}\right)^{\mathrm{7}} +\mathrm{x}^{\mathrm{6}} }\:\mathrm{dx}\:=\:\mathrm{p}\:\mathrm{ln}\:\left(\frac{\mathrm{x}^{\mathrm{q}} }{\mathrm{x}^{\mathrm{q}} +\mathrm{1}}\right)\:+\:\mathrm{C}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}. \\ $$

Question Number 118228    Answers: 1   Comments: 0

lim_(x→0) ((Σ_(r=1) ^(10) (x+r)^(2020) )/((x^(1008) +1)(3x^(1012) +1))) =?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sum_{\mathrm{r}=\mathrm{1}} ^{\mathrm{10}} \left(\mathrm{x}+\mathrm{r}\right)^{\mathrm{2020}} }{\left(\mathrm{x}^{\mathrm{1008}} +\mathrm{1}\right)\left(\mathrm{3x}^{\mathrm{1012}} +\mathrm{1}\right)}\:=?\: \\ $$

Question Number 118227    Answers: 1   Comments: 0

If x = (√(42−(√(42−(√(42−...)))))) y = (√(x+(√(x+(√(x+...)))))) z=(√(y.(√(y.(√(y.(√(y...)))))))) . Find x+y+z .

$${If}\:{x}\:=\:\sqrt{\mathrm{42}−\sqrt{\mathrm{42}−\sqrt{\mathrm{42}−...}}} \\ $$$${y}\:=\:\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+...}}} \\ $$$${z}=\sqrt{{y}.\sqrt{{y}.\sqrt{{y}.\sqrt{{y}...}}}}\:.\:{Find}\:{x}+{y}+{z}\:. \\ $$

Question Number 118218    Answers: 3   Comments: 0

∫ sin^6 (2x)dx =?

$$\:\int\:\mathrm{sin}\:^{\mathrm{6}} \left(\mathrm{2}{x}\right){dx}\:=?\: \\ $$

Question Number 118210    Answers: 1   Comments: 0

Question Number 118209    Answers: 1   Comments: 0

Question Number 118203    Answers: 2   Comments: 0

Question Number 118260    Answers: 3   Comments: 1

∫ ((x^2 −1)/(x^4 +x^2 +1)) dx

$$\int\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}\:{dx} \\ $$

Question Number 118196    Answers: 1   Comments: 0

solve in N: b^3 (2b^2 +2b+1)=18360

$${solve}\:{in}\:\mathbb{N}: \\ $$$${b}^{\mathrm{3}} \left(\mathrm{2}{b}^{\mathrm{2}} +\mathrm{2}{b}+\mathrm{1}\right)=\mathrm{18360} \\ $$

Question Number 118193    Answers: 1   Comments: 0

Given A=n^2 −2n+2 , B=n^2 +2n+2 n ∈ N^∗ −{1}. Show that ∀ divisor of A which divise n can also divise 2. Show that all common divisor of A and B can divise 4n.

$${Given}\:{A}={n}^{\mathrm{2}} −\mathrm{2}{n}+\mathrm{2}\:,\:{B}={n}^{\mathrm{2}} +\mathrm{2}{n}+\mathrm{2} \\ $$$${n}\:\in\:\mathbb{N}^{\ast} −\left\{\mathrm{1}\right\}. \\ $$$${Show}\:{that}\:\forall\:{divisor}\:{of}\:{A}\:{which}\:{divise} \\ $$$${n}\:{can}\:{also}\:{divise}\:\mathrm{2}. \\ $$$${Show}\:{that}\:{all}\:{common}\:{divisor}\:{of}\: \\ $$$${A}\:{and}\:{B}\:{can}\:{divise}\:\mathrm{4}{n}. \\ $$

Question Number 118189    Answers: 0   Comments: 0

Question Number 118188    Answers: 1   Comments: 2

Question Number 118184    Answers: 2   Comments: 1

factorise x^4 +4

$${factorise}\:{x}^{\mathrm{4}} +\mathrm{4} \\ $$

Question Number 118181    Answers: 1   Comments: 1

find all numbers >1 from N which their cube are <18360

$${find}\:{all}\:{numbers}\:>\mathrm{1}\:{from}\:\mathbb{N}\:{which} \\ $$$${their}\:{cube}\:{are}\:<\mathrm{18360} \\ $$

Question Number 118180    Answers: 1   Comments: 0

show that if n is odd , n(n^2 +3) is even.

$${show}\:{that}\:{if}\:{n}\:{is}\:{odd}\:,\:{n}\left({n}^{\mathrm{2}} +\mathrm{3}\right)\:{is}\:{even}. \\ $$

Question Number 118172    Answers: 1   Comments: 0

Find the area of a rhombus with side 8 cm

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{rhombus}\:\mathrm{with}\:\mathrm{side}\:\:\mathrm{8}\:\mathrm{cm} \\ $$

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