Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 290

Question Number 182280    Answers: 1   Comments: 2

Question Number 182203    Answers: 0   Comments: 0

Let A={1^(p^2 −p) , 2^(p^2 −p) ,..., (p−1)^(p^2 −p) , p^2 −p+1} where p is any prime number Prove that for any value of p, however we split this set into two disjunctive sets, the arithmetic means of all elements of both sets cannot be equal to each other.

$${Let}\:{A}=\left\{\mathrm{1}^{{p}^{\mathrm{2}} −{p}} ,\:\mathrm{2}^{{p}^{\mathrm{2}} −{p}} ,...,\:\left({p}−\mathrm{1}\right)^{{p}^{\mathrm{2}} −{p}} ,\:{p}^{\mathrm{2}} −{p}+\mathrm{1}\right\} \\ $$$${where}\:{p}\:{is}\:{any}\:{prime}\:{number} \\ $$$${Prove}\:{that}\:{for}\:{any}\:{value}\:{of}\:{p}, \\ $$$${however}\:{we}\:{split}\:{this}\:{set}\:{into}\:{two} \\ $$$${disjunctive}\:{sets},\:{the}\:{arithmetic} \\ $$$${means}\:{of}\:{all}\:{elements}\:{of}\:{both}\:{sets} \\ $$$${cannot}\:{be}\:{equal}\:{to}\:{each}\:{other}. \\ $$

Question Number 182200    Answers: 2   Comments: 0

1. lim_(a→−x) ((sin(x^2 − a^2 ))/(x^3 + a^3 )) = ? 2. cot 80° (tan 10° + 2 tg 70°) = ?

$$\mathrm{1}.\:\:\:\underset{\boldsymbol{\mathrm{a}}\rightarrow−\boldsymbol{\mathrm{x}}} {\mathrm{lim}}\:\frac{\mathrm{sin}\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{a}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{a}^{\mathrm{3}} }\:=\:? \\ $$$$ \\ $$$$\mathrm{2}.\:\:\:\mathrm{cot}\:\mathrm{80}°\:\left(\mathrm{tan}\:\mathrm{10}°\:+\:\mathrm{2}\:\mathrm{tg}\:\mathrm{70}°\right)\:=\:? \\ $$

Question Number 182199    Answers: 2   Comments: 0

Let S={1, 2, 3, 4, 5, 6, 7} If we multiply atleast 2 numbers from this set with each other, what are the chances of the product to turn out to be divisible by 3?

$${Let}\:{S}=\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5},\:\mathrm{6},\:\mathrm{7}\right\} \\ $$$${If}\:{we}\:{multiply}\:{atleast}\:\mathrm{2}\:{numbers} \\ $$$${from}\:{this}\:{set}\:{with}\:{each}\:{other},\:{what} \\ $$$${are}\:{the}\:{chances}\:{of}\:{the}\:{product}\:{to} \\ $$$${turn}\:{out}\:{to}\:{be}\:{divisible}\:{by}\:\mathrm{3}? \\ $$

Question Number 182192    Answers: 1   Comments: 1

Question Number 182188    Answers: 2   Comments: 0

((((√5)+2))^(1/3) +(((√5)−2))^(1/3) )^(2014) =?

$$\left(\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}+\mathrm{2}}+\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}−\mathrm{2}}\right)^{\mathrm{2014}} =? \\ $$

Question Number 182183    Answers: 1   Comments: 0

∫_0 ^( 1) e^a a^n da=? n≥1 n∈N

$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \boldsymbol{{e}}^{\boldsymbol{{a}}} \boldsymbol{{a}}^{\boldsymbol{{n}}} \boldsymbol{{da}}=?\:\:\:\:\:\:\:\:\boldsymbol{{n}}\geqslant\mathrm{1}\:\:\:\:\boldsymbol{{n}}\in\boldsymbol{{N}} \\ $$

Question Number 182178    Answers: 1   Comments: 2

The Circle Has A Radius 5cm And the angle between sector from the chord is 73.7397952916880° and their right triangle is AB=4 cm AC=3 cm Find the area of arc triangle EDB with E^⌢ D^⌢ is arc

$${The}\:{Circle}\:{Has}\:{A}\:{Radius}\:\mathrm{5}{cm} \\ $$$${And}\:{the}\:{angle}\:{between} \\ $$$$\:{sector}\:{from}\:{the}\:{chord}\:{is} \\ $$$$\mathrm{73}.\mathrm{7397952916880}° \\ $$$${and}\:{their}\:{right}\:{triangle}\:{is} \\ $$$${AB}=\mathrm{4}\:{cm} \\ $$$${AC}=\mathrm{3}\:{cm} \\ $$$${Find}\:{the}\:{area}\:{of}\:{arc}\:{triangle} \\ $$$${EDB} \\ $$$${with}\:\overset{\frown} {{E}}\overset{\frown} {{D}}\:{is}\:{arc} \\ $$$$ \\ $$

Question Number 182176    Answers: 1   Comments: 0

Question Number 182170    Answers: 1   Comments: 0

Question Number 182165    Answers: 0   Comments: 1

Question Number 182155    Answers: 3   Comments: 1

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?

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

$$\:\:\:\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\underset{\boldsymbol{\mathrm{r}}=\mathrm{0}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\left(\mathrm{1}\right)^{\boldsymbol{\mathrm{r}}} \:\centerdot\frac{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{r}}} \boldsymbol{\mathrm{y}}^{\mathrm{2022}\left(\boldsymbol{\mathrm{n}}+\mathrm{2}\right)} }{\left(\boldsymbol{\mathrm{n}}−\boldsymbol{\mathrm{r}}\right)!\left(\boldsymbol{\mathrm{r}}!\right)^{\mathrm{2}} \left(\mathrm{2022}\boldsymbol{\mathrm{y}}^{\mathrm{2022}} +\mathrm{2023}\right)^{\mathrm{2}} }\boldsymbol{\mathrm{dxdy}} \\ $$$$ \\ $$$$ \\ $$

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))) )=?

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

  Pg 285      Pg 286      Pg 287      Pg 288      Pg 289      Pg 290      Pg 291      Pg 292      Pg 293      Pg 294   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com