Question and Answers Forum

AllQuestion and Answers: Page 1037

Question Number 115268 Answers: 1 Comments: 0

(√(4^x −5.2^(x+1) +25)) +(√(9^x −2.3^(x+2) +17)) ≤ 2^x −5

$$\sqrt{\mathrm{4}^{{x}} −\mathrm{5}.\mathrm{2}^{{x}+\mathrm{1}} +\mathrm{25}}\:+\sqrt{\mathrm{9}^{{x}} −\mathrm{2}.\mathrm{3}^{{x}+\mathrm{2}} +\mathrm{17}}\:\leqslant\:\mathrm{2}^{{x}} −\mathrm{5} \\ $$

Question Number 115267 Answers: 1 Comments: 0

If f(x) is a differentiable function defined ∀x∈R such that (f(x))^3 −x+f(x)=0 then ∫_0 ^(√2) f^(−1) (x) dx =

$${If}\:{f}\left({x}\right)\:{is}\:{a}\:{differentiable}\:{function} \\ $$$${defined}\:\:\forall{x}\in\mathbb{R}\:{such}\:{that}\:\left({f}\left({x}\right)\right)^{\mathrm{3}} −{x}+{f}\left({x}\right)=\mathrm{0} \\ $$$${then}\:\underset{\mathrm{0}} {\overset{\sqrt{\mathrm{2}}} {\int}}\:{f}^{−\mathrm{1}} \left({x}\right)\:{dx}\:=\: \\ $$

Question Number 115261 Answers: 2 Comments: 0

Equation of circle touching the line ∣x−2∣+∣y−3∣ = 4 will be

$${Equation}\:{of}\:{circle}\:{touching}\:{the}\:{line}\: \\ $$$$\mid{x}−\mathrm{2}\mid+\mid{y}−\mathrm{3}\mid\:=\:\mathrm{4}\:{will}\:{be}\: \\ $$

Question Number 115260 Answers: 2 Comments: 1

Let f be a real valued function defined on the interval (−1,1) such that e^(−x) .f(x)=2+∫_0 ^x (√(t^4 +1)) dt ∀x∈(−1,1) and let g be the inverse function of f . Find the value of g′(2).

$${Let}\:{f}\:{be}\:{a}\:{real}\:{valued}\:{function}\:{defined} \\ $$$${on}\:{the}\:{interval}\:\left(−\mathrm{1},\mathrm{1}\right)\:{such}\:{that}\: \\ $$$${e}^{−{x}} .{f}\left({x}\right)=\mathrm{2}+\underset{\mathrm{0}} {\overset{{x}} {\int}}\:\sqrt{{t}^{\mathrm{4}} +\mathrm{1}}\:{dt}\:\forall{x}\in\left(−\mathrm{1},\mathrm{1}\right) \\ $$$${and}\:{let}\:{g}\:{be}\:{the}\:{inverse}\:{function}\:{of}\:{f} \\ $$$$.\:{Find}\:{the}\:{value}\:{of}\:{g}'\left(\mathrm{2}\right). \\ $$

Question Number 115258 Answers: 1 Comments: 0

A vector of magnitude 2 along a bisector of the angle between the two vectors 2i^ −2j^ +k^ and i^ +2j^ −2k^ is __

$${A}\:{vector}\:{of}\:{magnitude}\:\mathrm{2}\:{along}\:{a}\:{bisector} \\ $$$${of}\:{the}\:{angle}\:{between}\:{the}\:{two}\:{vectors} \\ $$$$\mathrm{2}\hat {{i}}−\mathrm{2}\hat {{j}}+\hat {{k}}\:{and}\:\hat {{i}}+\mathrm{2}\hat {{j}}−\mathrm{2}\hat {{k}}\:{is}\:\_\_ \\ $$

Question Number 115255 Answers: 0 Comments: 0

Express cosec 3x in terms of cosec x.

$$\mathrm{Express}\:\mathrm{cosec}\:\mathrm{3x}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{cosec}\:\mathrm{x}. \\ $$

Question Number 115253 Answers: 1 Comments: 0

Express sin 4x interm of sin x.

$$\mathrm{Express}\:\mathrm{sin}\:\mathrm{4x}\:\mathrm{interm}\:\mathrm{of}\:\mathrm{sin}\:\mathrm{x}. \\ $$

Question Number 115250 Answers: 0 Comments: 0

If mr Fosu sells the car after covering a mileage of 128km. find the i. value of the car if the rate of depreciation is $ 0.03 per km ii. the range of values for which Mr Fosu could sell the car so that he does not lose more than $,2000 or gain more tban $3,000 on the depreciated value.

$$\mathrm{If}\:\mathrm{mr}\:\mathrm{Fosu}\:\mathrm{sells}\:\mathrm{the}\:\mathrm{car}\:\mathrm{after}\:\mathrm{covering}\: \\ $$$$\mathrm{a}\:\mathrm{mileage}\:\mathrm{of}\:\mathrm{128km}.\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{i}.\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car}\:\mathrm{if}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\: \\ $$$$\mathrm{depreciation}\:\mathrm{is}\:\$\:\mathrm{0}.\mathrm{03}\:\mathrm{per}\:\mathrm{km} \\ $$$$\mathrm{ii}.\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{values}\:\mathrm{for}\:\mathrm{which}\:\mathrm{Mr} \\ $$$$\mathrm{Fosu}\:\mathrm{could}\:\mathrm{sell}\:\mathrm{the}\:\mathrm{car}\:\mathrm{so}\:\mathrm{that}\:\mathrm{he}\:\mathrm{does} \\ $$$$\mathrm{not}\:\mathrm{lose}\:\mathrm{more}\:\mathrm{than}\:\$,\mathrm{2000}\:\mathrm{or}\:\mathrm{gain}\:\mathrm{more}\:\mathrm{tban}\: \\ $$$$\$\mathrm{3},\mathrm{000}\:\mathrm{on}\:\mathrm{the}\:\mathrm{depreciated}\:\mathrm{value}. \\ $$

Question Number 115248 Answers: 1 Comments: 0

Express cos 4x interm of cos x.

$$\mathrm{Express}\:\mathrm{cos}\:\mathrm{4x}\:\mathrm{interm}\:\mathrm{of}\:\mathrm{cos}\:\mathrm{x}. \\ $$

Question Number 115246 Answers: 0 Comments: 1

5^((x+1)^2 ) + 625 ≤ 5^(x^2 +2) + 5^(2x+3)

$$\:\:\:\:\mathrm{5}^{\left({x}+\mathrm{1}\right)^{\mathrm{2}} } \:+\:\mathrm{625}\:\leqslant\:\mathrm{5}^{{x}^{\mathrm{2}} +\mathrm{2}} \:+\:\mathrm{5}^{\mathrm{2}{x}+\mathrm{3}} \\ $$

Question Number 115238 Answers: 2 Comments: 0

64^(x^2 −(3/4)x) ≤ ((√8))^x^3

$$\:\:\:\mathrm{64}^{{x}^{\mathrm{2}} −\frac{\mathrm{3}}{\mathrm{4}}{x}} \:\leqslant\:\left(\sqrt{\mathrm{8}}\right)^{{x}^{\mathrm{3}} } \: \\ $$

Question Number 115237 Answers: 2 Comments: 0

Question Number 115230 Answers: 0 Comments: 6

2 women and 4 men will sit on the 8 available seats and surround the round table . The many possible arrangements of them sitting if they sat randomly

$$\mathrm{2}\:{women}\:{and}\:\mathrm{4}\:{men}\:{will}\:{sit}\:{on}\:{the} \\ $$$$\mathrm{8}\:{available}\:{seats}\:{and}\:{surround}\: \\ $$$${the}\:{round}\:{table}\:.\:{The}\:{many}\:{possible} \\ $$$${arrangements}\:{of}\:{them}\:{sitting} \\ $$$${if}\:{they}\:{sat}\:{randomly} \\ $$

Question Number 115229 Answers: 2 Comments: 0

find the mean value of y=(5/(2−x−3x^2 )) between x=−(1/3) and x=(1/3)

$${find}\:{the}\:{mean}\:{value}\:{of}\: \\ $$$${y}=\frac{\mathrm{5}}{\mathrm{2}−{x}−\mathrm{3}{x}^{\mathrm{2}} }\:\:{between}\:{x}=−\frac{\mathrm{1}}{\mathrm{3}}\:{and} \\ $$$${x}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$

Question Number 115222 Answers: 1 Comments: 0

.... nice math ... nice integral prove :: Ψ=9∫_0 ^( ∞) x^5 e^(−x^3 ) ln(1+x)dx =^(???) Γ((1/3))−Γ((2/3))+Γ((3/3)) m.n.july.1970

$$\:\:\:\:\:\:....\:{nice}\:\:{math}\:... \\ $$$$ \\ $$$$\:\:\:\:{nice}\:\:{integral}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\::: \\ $$$$\Psi=\mathrm{9}\int_{\mathrm{0}} ^{\:\infty} {x}^{\mathrm{5}} {e}^{−{x}^{\mathrm{3}} } {ln}\left(\mathrm{1}+{x}\right){dx}\:\overset{???} {=}\:\Gamma\left(\frac{\mathrm{1}}{\mathrm{3}}\right)−\Gamma\left(\frac{\mathrm{2}}{\mathrm{3}}\right)+\Gamma\left(\frac{\mathrm{3}}{\mathrm{3}}\right)\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.{july}.\mathrm{1970} \\ $$$$\:\: \\ $$

Question Number 115215 Answers: 2 Comments: 7

solve ∫_0 ^1 ln^2 (1−x^2 )dx

$${solve} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 115224 Answers: 2 Comments: 0

Question Number 115205 Answers: 1 Comments: 0

Question Number 115203 Answers: 2 Comments: 1

Question Number 115201 Answers: 1 Comments: 1

Question Number 115218 Answers: 0 Comments: 0

Show that ∀n∈N, ∀u_0 ,u_1 ,...,u_n ,v_0 ,v_1 ,...v_n ∈C ∀k≤n; u_k =Σ_(i=0) ^k ((k),(i) )v_i ⇔∀k≤n; v_k =Σ_(i=0) ^k (−1)^(k−1) ((k),(i) )u_i

$$\mathrm{Show}\:\mathrm{that}\:\forall\mathrm{n}\in\mathbb{N},\:\forall\mathrm{u}_{\mathrm{0}} ,\mathrm{u}_{\mathrm{1}} ,...,\mathrm{u}_{\mathrm{n}} ,\mathrm{v}_{\mathrm{0}} ,\mathrm{v}_{\mathrm{1}} ,...\mathrm{v}_{\mathrm{n}} \in\mathbb{C} \\ $$$$\forall\mathrm{k}\leqslant\mathrm{n};\:\mathrm{u}_{\mathrm{k}} =\sum_{\mathrm{i}=\mathrm{0}} ^{\mathrm{k}} \begin{pmatrix}{\mathrm{k}}\\{\mathrm{i}}\end{pmatrix}\mathrm{v}_{\mathrm{i}} \Leftrightarrow\forall\mathrm{k}\leqslant\mathrm{n};\:\mathrm{v}_{\mathrm{k}} =\sum_{\mathrm{i}=\mathrm{0}} ^{\mathrm{k}} \left(−\mathrm{1}\right)^{\mathrm{k}−\mathrm{1}} \begin{pmatrix}{\mathrm{k}}\\{\mathrm{i}}\end{pmatrix}\mathrm{u}_{\mathrm{i}} \\ $$

Question Number 115195 Answers: 1 Comments: 0

lim_(x→(π/8)) ((cot 4x−cos 4x)/((π−8x)^3 )) ?

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{8}}} {\mathrm{lim}}\:\frac{\mathrm{cot}\:\mathrm{4}{x}−\mathrm{cos}\:\mathrm{4}{x}}{\left(\pi−\mathrm{8}{x}\right)^{\mathrm{3}} }\:?\: \\ $$

Question Number 115194 Answers: 0 Comments: 0

Find a three−digits number whose digits form a geometry progression ;if you known that after substract that number by 495 ,get a number written by the same digits as the number you are looking for but in the reverse order;if the digits of the number obtained after substraction(from left right)reduced by 1,1 and 2 respectively ,you obtain an arithmetic progression

$$\mathrm{Find}\:\mathrm{a}\:\mathrm{three}−\mathrm{digits}\:\mathrm{number}\:\mathrm{whose} \\ $$$$\mathrm{digits}\:\mathrm{form}\:\mathrm{a}\:\mathrm{geometry}\:\mathrm{progression} \\ $$$$;\mathrm{if}\:\mathrm{you}\:\mathrm{known}\:\mathrm{that}\:\mathrm{after}\:\mathrm{substract}\:\mathrm{that} \\ $$$$\mathrm{number}\:\mathrm{by}\:\mathrm{495}\:,\mathrm{get}\:\mathrm{a}\:\mathrm{number} \\ $$$$\mathrm{written}\:\mathrm{by}\:\mathrm{the}\:\mathrm{same}\:\mathrm{digits}\:\mathrm{as}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{you}\:\mathrm{are}\:\mathrm{looking}\:\mathrm{for}\:\mathrm{but}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{reverse}\:\mathrm{order};\mathrm{if}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{obtained}\:\mathrm{after} \\ $$$$\mathrm{substraction}\left(\mathrm{from}\:\mathrm{left}\:\mathrm{right}\right)\mathrm{reduced} \\ $$$$\mathrm{by}\:\mathrm{1},\mathrm{1}\:\mathrm{and}\:\mathrm{2}\:\mathrm{respectively}\:,\mathrm{you}\:\mathrm{obtain} \\ $$$$\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{progression} \\ $$

Question Number 115193 Answers: 1 Comments: 1

...advanced mathematics... :: digamma limit :: if k>0 then prove that lim_(x→0) (1/x)(ψ(((k+x)/(2x))) − ψ((k/(2x)))) =(1/k) ✓ m.n.july.1970...

$$\:\:\:\:\:\:\:\:\:\:\:...{advanced}\:\:{mathematics}...\:\: \\ $$$$\:\:\:\:\:\:\:::\:\:\:{digamma}\:\:{limit}\:\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:{if}\:\:\:{k}>\mathrm{0}\:\:{then} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{1}}{{x}}\left(\psi\left(\frac{{k}+{x}}{\mathrm{2}{x}}\right)\:−\:\psi\left(\frac{{k}}{\mathrm{2}{x}}\right)\right)\:=\frac{\mathrm{1}}{{k}}\:\:\:\:\checkmark \\ $$$$ \\ $$$$\:\:\:\:\:{m}.{n}.{july}.\mathrm{1970}... \\ $$$$\: \\ $$

Question Number 115174 Answers: 2 Comments: 0

lim_(x→1) ((tan (cos^(−1) ((1/x))))/( (√(x−1)))) = ?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{x}}\right)\right)}{\:\sqrt{{x}−\mathrm{1}}}\:=\:? \\ $$

Question Number 115170 Answers: 3 Comments: 0

(1)Given ((P _(n−1)^(2n+1) )/(P _n^(2n−1) )) = (3/5) , find n = ? (2) in how many ways can 6 persons stand in a queue? (3) how many different 4 letter words can be formed by using letters of EDUCATION using each letter at most once ?

$$\left(\mathrm{1}\right){Given}\:\frac{{P}\:_{{n}−\mathrm{1}} ^{\mathrm{2}{n}+\mathrm{1}} }{{P}\:_{{n}} ^{\mathrm{2}{n}−\mathrm{1}} }\:=\:\frac{\mathrm{3}}{\mathrm{5}}\:,\:{find}\:{n}\:=\:? \\ $$$$\left(\mathrm{2}\right)\:{in}\:{how}\:{many}\:{ways}\:{can}\:\mathrm{6}\:{persons} \\ $$$${stand}\:{in}\:{a}\:{queue}? \\ $$$$\left(\mathrm{3}\right)\:{how}\:{many}\:{different}\:\mathrm{4}\:{letter}\:{words} \\ $$$${can}\:{be}\:{formed}\:{by}\:{using}\:{letters}\:{of}\: \\ $$$${EDUCATION}\:{using}\:{each}\:{letter}\:{at}\: \\ $$$${most}\:{once}\:? \\ $$$$ \\ $$

Pg 1032 Pg 1033 Pg 1034 Pg 1035 Pg 1036 Pg 1037 Pg 1038 Pg 1039 Pg 1040 Pg 1041

Contact: info@tinkutara.com