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Question Number 181466 Answers: 1 Comments: 0

3∙5^(2x+1) − 7∙2^(4x+1) = 19 x= ?

$$\:\mathrm{3}\centerdot\mathrm{5}^{\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{1}} \:−\:\mathrm{7}\centerdot\mathrm{2}^{\mathrm{4}\boldsymbol{\mathrm{x}}+\mathrm{1}} \:=\:\mathrm{19} \\ $$$$ \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\mathrm{x}}=\:? \\ $$$$ \\ $$$$ \\ $$

Question Number 181464 Answers: 0 Comments: 0

lim_(x→0) ((sin (tan x)−sin (x))/(x−tan (x))) =?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{tan}\:\mathrm{x}\right)−\mathrm{sin}\:\left(\mathrm{x}\right)}{\mathrm{x}−\mathrm{tan}\:\left(\mathrm{x}\right)}\:=? \\ $$

Question Number 174185 Answers: 1 Comments: 0

The circle x^2 +y^2 −2x−4y−20=0 is inscribed in a square. One vertex of the square is (−4, 7). Find the coordinates of the other vertices.

$$\mathrm{The}\:\mathrm{circle}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{4}{y}−\mathrm{20}=\mathrm{0}\:\mathrm{is} \\ $$$$\mathrm{inscribed}\:\mathrm{in}\:\mathrm{a}\:\mathrm{square}.\:\mathrm{One}\:\mathrm{vertex} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\mathrm{is}\:\left(−\mathrm{4},\:\mathrm{7}\right).\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{coordinates}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:\mathrm{vertices}. \\ $$

Question Number 174182 Answers: 0 Comments: 0

Question Number 174177 Answers: 4 Comments: 0

x^3 +(1/x^3 )=1 then prove that (((x^5 +(1/x^5 ))^3 −1)/(x^5 +(1/x^5 )))=3

$${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=\mathrm{1}\:\:\:\:\:{then}\:{prove}\:{that} \\ $$$$\frac{\left({x}^{\mathrm{5}} +\frac{\mathrm{1}}{{x}^{\mathrm{5}} }\right)^{\mathrm{3}} −\mathrm{1}}{{x}^{\mathrm{5}} +\frac{\mathrm{1}}{{x}^{\mathrm{5}} }}=\mathrm{3} \\ $$

Question Number 174194 Answers: 4 Comments: 0

Question Number 181462 Answers: 2 Comments: 1

Question Number 181461 Answers: 0 Comments: 0

Question Number 174153 Answers: 2 Comments: 1

Question Number 174152 Answers: 2 Comments: 0

lim_(x→0) ((1−sin ((π/2)cos x+2x))/(5x^2 )) =?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}\mathrm{cos}\:{x}+\mathrm{2}{x}\right)}{\mathrm{5}{x}^{\mathrm{2}} }\:=? \\ $$

Question Number 181450 Answers: 2 Comments: 0

∫_∞ ^(-∞) lnxdx

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{\infty} {\overset{-\infty} {\int}}\boldsymbol{\mathrm{lnxdx}} \\ $$

Question Number 174145 Answers: 0 Comments: 0

ANI = 7249000 and R = 8 Find: Σ_(p=1) ^(20) { ((ANI)/((1 + R)^p )) }

$$\mathrm{ANI}\:=\:\mathrm{7249000}\:\:\:\mathrm{and}\:\:\:\mathrm{R}\:=\:\mathrm{8} \\ $$$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{p}}=\mathrm{1}} {\overset{\mathrm{20}} {\sum}}\:\left\{\:\frac{\mathrm{ANI}}{\left(\mathrm{1}\:+\:\mathrm{R}\right)^{\boldsymbol{\mathrm{p}}} }\:\right\} \\ $$

Question Number 174144 Answers: 1 Comments: 0

If a,b∈N and a ∙ b = 100 a^6 ∙ b^8 how many digits can the product have at most? Answer: 17

$$\mathrm{If}\:\:\mathrm{a},\mathrm{b}\in\mathbb{N}\:\:\mathrm{and}\:\:\mathrm{a}\:\centerdot\:\mathrm{b}\:=\:\mathrm{100} \\ $$$$\mathrm{a}^{\mathrm{6}} \:\centerdot\:\mathrm{b}^{\mathrm{8}} \:\:\mathrm{how}\:\mathrm{many}\:\mathrm{digits}\:\mathrm{can}\:\mathrm{the}\:\mathrm{product} \\ $$$$\mathrm{have}\:\mathrm{at}\:\mathrm{most}? \\ $$$$\mathrm{Answer}:\:\:\mathrm{17} \\ $$

Question Number 174143 Answers: 2 Comments: 5

If 4^x = 5^y = 3^z find (a/b) + (a/c) Answer: (1;2)

$$\mathrm{If}\:\:\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{5}^{\boldsymbol{\mathrm{y}}} \:=\:\mathrm{3}^{\boldsymbol{\mathrm{z}}} \:\:\mathrm{find}\:\:\frac{\mathrm{a}}{\mathrm{b}}\:+\:\frac{\mathrm{a}}{\mathrm{c}} \\ $$$$\mathrm{Answer}:\:\:\left(\mathrm{1};\mathrm{2}\right) \\ $$

Question Number 174133 Answers: 0 Comments: 2

Question Number 174131 Answers: 0 Comments: 3

Question Number 174127 Answers: 1 Comments: 0

Q: p , q , r are roots of x^( 3) −7x^( 2) =(4−x)(x+2) find the value of : K = (1/( ((qr))^(1/3) )) + (1/( ((pr))^(1/3) )) + (1/( ((pq))^(1/3) )) = ?

$$ \\ $$$$\:\:\:{Q}:\:\:\:\:\:{p}\:,\:{q}\:,\:{r}\:\:\:\:{are}\:\:{roots}\:{of} \\ $$$$\:\:\:\:\:{x}^{\:\mathrm{3}} \:−\mathrm{7}{x}^{\:\mathrm{2}} =\left(\mathrm{4}−{x}\right)\left({x}+\mathrm{2}\right) \\ $$$$\:\:\:\:\:{find}\:\:{the}\:{value}\:{of}\:: \\ $$$$\:\:\:\mathrm{K}\:=\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{qr}}}\:\:+\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{pr}}}\:\:+\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{pq}}}\:=\:? \\ $$$$ \\ $$

Question Number 174124 Answers: 0 Comments: 7

C3^n −4C^(3n−1) =3^n find C for any n

$${C}\mathrm{3}^{{n}} −\mathrm{4}{C}^{\mathrm{3}{n}−\mathrm{1}} =\mathrm{3}^{{n}} \\ $$$${find}\:{C}\:\:{for}\:{any}\:{n}\: \\ $$

Question Number 174118 Answers: 1 Comments: 0

calculate Σ_(n=1) ^∞ (((−1)^n )/n) by using ψ (digamma)

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}}\:{by}\:{using} \\ $$$$\psi\:\:\left({digamma}\right) \\ $$

Question Number 174117 Answers: 1 Comments: 0

find ∫_0 ^1 (dx/(1+x^n )) interms of ψ (digamma)

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dx}}{\mathrm{1}+{x}^{{n}} }\:{interms}\:{of} \\ $$$$\psi\:\left({digamma}\right) \\ $$

Question Number 181440 Answers: 0 Comments: 0

Question Number 181439 Answers: 1 Comments: 0

Question Number 181438 Answers: 2 Comments: 1

If a + (1/b) = b + (1/c) = c + (1/a) then prove that abc = ±1. a ≠ b ≠ c

$$\mathrm{If}\:{a}\:+\:\frac{\mathrm{1}}{{b}}\:=\:{b}\:+\:\frac{\mathrm{1}}{{c}}\:=\:{c}\:+\:\frac{\mathrm{1}}{{a}}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${abc}\:=\:\pm\mathrm{1}.\:\:\:{a}\:\neq\:{b}\:\neq\:{c} \\ $$

Question Number 181437 Answers: 2 Comments: 0

Question Number 181435 Answers: 0 Comments: 0

((𝛅^2 u)/(𝛅t^2 )) = 4 ((𝛅^2 u)/(𝛅x^2 )) ; u∣_(t=0) =sin(x) ; ((𝛅u)/(𝛅t))∣_(t=0) =x

$$\:\:\:\frac{\boldsymbol{\delta}^{\mathrm{2}} \boldsymbol{\mathrm{u}}}{\boldsymbol{\delta\mathrm{t}}^{\mathrm{2}} }\:=\:\mathrm{4}\:\frac{\boldsymbol{\delta}^{\mathrm{2}} \boldsymbol{\mathrm{u}}}{\boldsymbol{\delta\mathrm{x}}^{\mathrm{2}} }\:\:\:;\:\:\boldsymbol{\mathrm{u}}\mid_{\boldsymbol{\mathrm{t}}=\mathrm{0}} =\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{x}}\right)\:\:\:;\:\:\:\frac{\boldsymbol{\delta\mathrm{u}}}{\boldsymbol{\delta\mathrm{t}}}\mid_{\boldsymbol{\mathrm{t}}=\mathrm{0}} =\boldsymbol{\mathrm{x}} \\ $$

Question Number 181432 Answers: 1 Comments: 5

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