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AlgebraQuestion and Answers: Page 66

Question Number 187951 Answers: 3 Comments: 0

please help me to solve 6x^2 +x−2=0

$${please}\:{help}\:{me}\:{to}\:{solve} \\ $$$$\mathrm{6}{x}^{\mathrm{2}} +{x}−\mathrm{2}=\mathrm{0} \\ $$

Question Number 187811 Answers: 1 Comments: 0

Question Number 187780 Answers: 1 Comments: 0

solve ⌊ (1/(4 )) + 2^( x) ⌋ + ⌊ (1/2) + 2^( x+1) ⌋=1

$$ \\ $$$$\:\:{solve} \\ $$$$\:\:\:\:\lfloor\:\:\frac{\mathrm{1}}{\mathrm{4}\:}\:+\:\mathrm{2}^{\:{x}} \:\rfloor\:+\:\lfloor\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{2}^{\:{x}+\mathrm{1}} \:\rfloor=\mathrm{1} \\ $$$$ \\ $$

Question Number 187731 Answers: 4 Comments: 0

Question Number 187695 Answers: 2 Comments: 0

If , f( x )= (( sin_ (cos (x) ))/( ^ (√( (π/x))))) ⇒ f ′ ((( π)/2) ) = ?

$$ \\ $$$$\:\:\:{If}\:,\:\:{f}\left(\:{x}\:\right)=\:\frac{\:\:{si}\underset{} {{n}}\:\left({cos}\:\left({x}\right)\:\right)}{\overset{} {\:}\sqrt{\:\frac{\pi}{{x}}}} \\ $$$$\:\:\:\:\Rightarrow\:\:\:{f}\:'\:\left(\frac{\:\pi}{\mathrm{2}}\:\right)\:=\:? \\ $$

Question Number 187690 Answers: 0 Comments: 0

Question Number 187595 Answers: 1 Comments: 1

Question Number 187556 Answers: 0 Comments: 1

Question Number 187534 Answers: 0 Comments: 0

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Question Number 187496 Answers: 1 Comments: 1

Question Number 187478 Answers: 1 Comments: 0

let a and b be positive integers such that ab + 1 divides a^2 + b^2 . show that ((a^2 + b^2 )/(ab + 1)) is the sequare of an integer.

$$\: \\ $$$$\:\:\:\boldsymbol{{let}}\:\boldsymbol{{a}}\:\boldsymbol{{and}}\:\boldsymbol{{b}}\:\boldsymbol{{be}}\:\boldsymbol{{positive}}\:\boldsymbol{{integers}}\:\:\:\:\: \\ $$$$\:\:\:\boldsymbol{{such}}\:\boldsymbol{{that}}\:\boldsymbol{{ab}}\:+\:\mathrm{1}\:\boldsymbol{{divides}}\:\boldsymbol{{a}}^{\mathrm{2}} \:+\:\boldsymbol{{b}}^{\mathrm{2}} .\:\:\:\:\: \\ $$$$\:\:\:\:\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\frac{\boldsymbol{{a}}^{\mathrm{2}} \:+\:\boldsymbol{{b}}^{\mathrm{2}} }{\boldsymbol{{ab}}\:+\:\mathrm{1}} \\ $$$$\:\:\:\:\:\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{sequare}}\:\boldsymbol{{of}}\:\boldsymbol{{an}}\:\boldsymbol{{integer}}. \\ $$$$ \\ $$

Question Number 187476 Answers: 1 Comments: 0

Question Number 187442 Answers: 1 Comments: 0

If (7^x /(1 + 7^x )) = (3/7) find ((2401^x )/(1 + 2401^x )) = ?

$$\mathrm{If}\:\:\:\:\:\frac{\mathrm{7}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}\:+\:\mathrm{7}^{\boldsymbol{\mathrm{x}}} }\:\:=\:\:\frac{\mathrm{3}}{\mathrm{7}}\:\:\:\:\:\mathrm{find}\:\:\:\:\frac{\mathrm{2401}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}\:+\:\mathrm{2401}^{\boldsymbol{\mathrm{x}}} }\:\:=\:\:? \\ $$

Question Number 187440 Answers: 0 Comments: 1

if y^(x−y) =(x^2 /y) then x−y=?

$${if}\:\:{y}^{{x}−{y}} =\frac{{x}^{\mathrm{2}} }{{y}}\:{then}\:{x}−{y}=? \\ $$

Question Number 187437 Answers: 1 Comments: 0

Question Number 187388 Answers: 2 Comments: 0

p^3 +q^3 =c , pq=(1/3) ∀ 0<c<(2/(3(√3))) Find p+q.

$${p}^{\mathrm{3}} +{q}^{\mathrm{3}} ={c}\:\:\:,\:\:{pq}=\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\forall\:\:\:\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$$${Find}\:{p}+{q}. \\ $$

Question Number 187381 Answers: 2 Comments: 0

3^x =5^y =225 Determiner: (1/x)+(1/y) ?

$$\mathrm{3}^{{x}} =\mathrm{5}^{{y}} =\mathrm{225} \\ $$$${Determiner}:\:\:\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}\:? \\ $$

Question Number 187373 Answers: 0 Comments: 0

Solve for natural numbers: 31 + Σ_(k=1) ^n ( ((n),(k) ) ∙ Σ_(m=1) ^n m^(n−k) ) = 31^(30)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{natural}\:\mathrm{numbers}: \\ $$$$\mathrm{31}\:+\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\left(\begin{pmatrix}{\mathrm{n}}\\{\mathrm{k}}\end{pmatrix}\:\:\centerdot\:\underset{\boldsymbol{\mathrm{m}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{m}^{\boldsymbol{\mathrm{n}}−\boldsymbol{\mathrm{k}}} \right)\:=\:\mathrm{31}^{\mathrm{30}} \\ $$

Question Number 187357 Answers: 1 Comments: 0

Question Number 187302 Answers: 0 Comments: 0

f(4)=44, f(m)=52,f(l)=−33 l,m are positive integers such that 4<m<l and f(x) is a polynomial with integer coefficients. Find l+m.

$${f}\left(\mathrm{4}\right)=\mathrm{44},\:{f}\left({m}\right)=\mathrm{52},{f}\left({l}\right)=−\mathrm{33} \\ $$$${l},{m}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{such}\:\mathrm{that}\:\mathrm{4}<{m}<{l} \\ $$$$\mathrm{and}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{with}\:\mathrm{integer}\:\mathrm{coefficients}. \\ $$$$\mathrm{Find}\:{l}+{m}. \\ $$

Question Number 187295 Answers: 0 Comments: 2

solve: ((√(4+(√4))^x )) +[(√(4−(√(4]^x )))) =4^x

$${solve}: \\ $$$$\left(\sqrt{\left.\mathrm{4}+\sqrt{\mathrm{4}}\right)\:^{{x}} }\:+\left[\sqrt{\mathrm{4}−\sqrt{\left.\mathrm{4}\right]^{{x}} }}\:=\mathrm{4}^{{x}} \right.\right. \\ $$

Question Number 187294 Answers: 0 Comments: 1

solve: −1−[x^x −5x+6]^x =1

$${solve}: \\ $$$$−\mathrm{1}−\left[{x}^{{x}} −\mathrm{5}{x}+\mathrm{6}\right]^{{x}} =\mathrm{1} \\ $$

Question Number 187288 Answers: 1 Comments: 0

logx+x!=2 x=?

$${logx}+{x}!=\mathrm{2} \\ $$$${x}=? \\ $$

Question Number 187255 Answers: 1 Comments: 0

Find the directional derivatives of the function f(x,y,z)=2x^2 +3y^2 +z^2 at the point p(2,1,3)

$${Find}\:{the}\:{directional}\:{derivatives}\:{of}\:{the} \\ $$$${function}\: \\ $$$${f}\left({x},\mathrm{y},\mathrm{z}\right)=\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:{at}\:{the}\:{point}\:{p}\left(\mathrm{2},\mathrm{1},\mathrm{3}\right) \\ $$

Question Number 187254 Answers: 1 Comments: 0

Question Number 187248 Answers: 0 Comments: 1

what is the cardinality of the set of prime numbers whose base ten digits sums up to 10

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{cardinality}\:\mathrm{of}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{whose} \\ $$$$\mathrm{base}\:\mathrm{ten}\:\mathrm{digits}\:\mathrm{sums}\:\mathrm{up}\:\mathrm{to}\:\mathrm{10} \\ $$

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