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AlgebraQuestion and Answers: Page 67

Question Number 193769 Answers: 0 Comments: 0

Question Number 193757 Answers: 0 Comments: 0

Question Number 193714 Answers: 1 Comments: 3

Question Number 193707 Answers: 1 Comments: 0

Question Number 193688 Answers: 1 Comments: 0

Question Number 193687 Answers: 0 Comments: 2

Question Number 193651 Answers: 0 Comments: 1

determiner rayon R

$$\mathrm{determiner}\:\mathrm{rayon}\:\boldsymbol{\mathrm{R}} \\ $$

Question Number 193647 Answers: 2 Comments: 0

Question Number 193565 Answers: 1 Comments: 0

Question Number 193546 Answers: 2 Comments: 0

if a+b+c=1 find maximum ab +bc +ca a , b , c are non negative integers

$${if}\:{a}+{b}+{c}=\mathrm{1} \\ $$$${find}\:{maximum}\:{ab}\:+{bc}\:+{ca}\: \\ $$$${a}\:,\:{b}\:,\:{c}\:{are}\:{non}\:{negative}\:{integers} \\ $$$$ \\ $$

Question Number 193543 Answers: 0 Comments: 4

solve

$${solve} \\ $$

Question Number 193542 Answers: 1 Comments: 2

f(x) = x^3 +3x^2 −1 1) calcul h(X) = f(a+X) −b 2) determine a and b such that h is odd

$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{3}} +\mathrm{3x}^{\mathrm{2}} −\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calcul}\:\:\:\:\mathrm{h}\left(\mathrm{X}\right)\:=\:\mathrm{f}\left(\mathrm{a}+\mathrm{X}\right)\:−\mathrm{b} \\ $$2) determine a and b such that h is odd

Question Number 193525 Answers: 2 Comments: 0

((27t73)/(11)) and R=0 then t=? how is explontry solution

$$\:\:\:\:\:\frac{\mathrm{27t73}}{\mathrm{11}} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{R}=\mathrm{0}\:\:\:\mathrm{then}\:\mathrm{t}=? \\ $$$$\:\:\:\:\:\:\mathrm{how}\:\mathrm{is}\:\mathrm{explontry}\:\mathrm{solution} \\ $$

Question Number 193492 Answers: 1 Comments: 0

Question Number 193484 Answers: 0 Comments: 0

Nice problem: Find 8 distinctive numbers ∈N\{0} such that these are simultaniously true: (1) a+b+c+d = e+f+g+h (2) a^2 +b^2 +c^2 +d^2 = e^2 +f^2 +g^2 +h^2 (3) a^3 +b^3 +c^3 +d^3 = e^3 +f^3 +g^3 +h^3 [Find a method to generate such numbers]

$$\mathrm{Nice}\:\mathrm{problem}: \\ $$$$\mathrm{Find}\:\mathrm{8}\:\mathrm{distinctive}\:\mathrm{numbers}\:\in\mathbb{N}\backslash\left\{\mathrm{0}\right\}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{these}\:\mathrm{are}\:\mathrm{simultaniously}\:\mathrm{true}: \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\:{a}+{b}+{c}+{d}\:=\:{e}+{f}+{g}+{h} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} \:=\:{e}^{\mathrm{2}} +{f}^{\mathrm{2}} +{g}^{\mathrm{2}} +{h}^{\mathrm{2}} \\ $$$$\left(\mathrm{3}\right)\:\:\:\:\:{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} +{d}^{\mathrm{3}} \:=\:{e}^{\mathrm{3}} +{f}^{\mathrm{3}} +{g}^{\mathrm{3}} +{h}^{\mathrm{3}} \\ $$$$\left[\mathrm{Find}\:\mathrm{a}\:\mathrm{method}\:\mathrm{to}\:\mathrm{generate}\:\mathrm{such}\:\mathrm{numbers}\right] \\ $$

Question Number 193469 Answers: 0 Comments: 0

Question Number 193467 Answers: 3 Comments: 3

Proof : cot^(−1) ((((√(1+sint))+(√(1−sint)))/( (√(1+sint))−(√(1−sint)))))=(t/2)

$$\mathrm{Proof}\:: \\ $$$$\mathrm{cot}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{1}+\mathrm{sint}}+\sqrt{\mathrm{1}−\mathrm{sint}}}{\:\sqrt{\mathrm{1}+\mathrm{sint}}−\sqrt{\mathrm{1}−\mathrm{sint}}}\right)=\frac{\mathrm{t}}{\mathrm{2}}\: \\ $$

Question Number 193411 Answers: 2 Comments: 1

$$\:\:\:\:\: \\ $$$$ \\ $$

Question Number 193410 Answers: 2 Comments: 0

{ ((x=(√(3−(√(5+2(√3))))))),((y=(√(3+(√(5+2(√3))))))) :} x

$$\:\:\begin{cases}{\mathrm{x}=\sqrt{\mathrm{3}−\sqrt{\mathrm{5}+\mathrm{2}\sqrt{\mathrm{3}}}}}\\{\mathrm{y}=\sqrt{\mathrm{3}+\sqrt{\mathrm{5}+\mathrm{2}\sqrt{\mathrm{3}}}}}\end{cases}\: \\ $$$$\:\:\:\:\underbrace{\boldsymbol{{x}}} \\ $$

Question Number 193371 Answers: 3 Comments: 0

Reduce to first order and solve , showing each step in detail. 1. y′′ +(y′)^3 siny=0 2. y′′=1+(y′)^2

$$\mathrm{Reduce}\:\mathrm{to}\:\mathrm{first}\:\mathrm{order}\:\mathrm{and}\:\mathrm{solve}\:, \\ $$$$\mathrm{showing}\:\mathrm{each}\:\mathrm{step}\:\mathrm{in}\:\mathrm{detail}. \\ $$$$\mathrm{1}.\:\mathrm{y}''\:+\left(\mathrm{y}'\right)^{\mathrm{3}} \mathrm{siny}=\mathrm{0} \\ $$$$\mathrm{2}.\:\mathrm{y}''=\mathrm{1}+\left(\mathrm{y}'\right)^{\mathrm{2}} \\ $$$$ \\ $$

Question Number 193363 Answers: 1 Comments: 0

y = 4 × 10^(2x) Express x in terms of y, giving an exact simplified answer in terms of log base 10.

$${y}\:=\:\mathrm{4}\:×\:\mathrm{10}^{\mathrm{2}{x}} \\ $$$$\mathrm{Express}\:{x}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{y},\:\mathrm{giving}\:\mathrm{an}\:\mathrm{exact} \\ $$$$\mathrm{simplified}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{log}\:\mathrm{base}\:\mathrm{10}. \\ $$

Question Number 193356 Answers: 2 Comments: 0

Question Number 193346 Answers: 2 Comments: 0

(√(4x−3))−(√(2x−5))=2 solve for x

$$\sqrt{\mathrm{4x}−\mathrm{3}}−\sqrt{\mathrm{2x}−\mathrm{5}}=\mathrm{2} \\ $$$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x} \\ $$

Question Number 193339 Answers: 1 Comments: 0

Prove that a group G of prime order is cyclic.

$${Prove}\:{that}\:{a}\:{group}\:{G}\:{of}\:{prime}\:{order}\:{is}\:{cyclic}. \\ $$$$ \\ $$

Question Number 193314 Answers: 1 Comments: 0

a ,b, c > 0 & a^2 +b^2 +c^2 =3 prove that (((1+(3/(ab+bc+ca)) )^((a+b+c)^2 ) ))^(1/3) ≤(1+(a/b))(1+(b/c))(1+(c/a))

$$ \\ $$$$\boldsymbol{{a}}\:,\boldsymbol{{b}},\:\boldsymbol{{c}}\:\:>\:\mathrm{0}\:\&\:\:\boldsymbol{{a}}^{\mathrm{2}} +\boldsymbol{{b}}^{\mathrm{2}} +\boldsymbol{{c}}^{\mathrm{2}} =\mathrm{3}\:\boldsymbol{{prove}}\:\boldsymbol{{that}}\: \\ $$$$\sqrt[{\mathrm{3}}]{\left(\mathrm{1}+\frac{\mathrm{3}}{\boldsymbol{{ab}}+\boldsymbol{{bc}}+\boldsymbol{{ca}}}\:\right)^{\left(\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}\right)^{\mathrm{2}} } \:}\leqslant\left(\mathrm{1}+\frac{\boldsymbol{{a}}}{\boldsymbol{{b}}}\right)\left(\mathrm{1}+\frac{\boldsymbol{{b}}}{\boldsymbol{{c}}}\right)\left(\mathrm{1}+\frac{\boldsymbol{{c}}}{\boldsymbol{{a}}}\right) \\ $$

Question Number 193296 Answers: 2 Comments: 1

If a^2 + b^2 + c^2 = 16, x^2 + y^2 + z^2 = 25 and ax + by + cz = 20 then what is the value of ((a + b + c)/(x + y + z)) ?

$$\mathrm{If}\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:=\:\mathrm{16},\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{z}^{\mathrm{2}} \:=\:\mathrm{25} \\ $$$$\mathrm{and}\:{ax}\:+\:{by}\:+\:{cz}\:=\:\mathrm{20}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\frac{{a}\:+\:{b}\:+\:{c}}{{x}\:+\:{y}\:+\:{z}}\:? \\ $$

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