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AlgebraQuestion and Answers: Page 70

Question Number 189201 Answers: 1 Comments: 0

In △ABC holds: (√2) a cos (B/2) cos (C/2) = s ⇒ sec (2B) + tan (2B) = ((c + b)/(c − b))

$$\mathrm{In}\:\:\:\bigtriangleup\mathrm{ABC}\:\:\:\mathrm{holds}: \\ $$$$\sqrt{\mathrm{2}}\:\mathrm{a}\:\mathrm{cos}\:\frac{\mathrm{B}}{\mathrm{2}}\:\mathrm{cos}\:\frac{\mathrm{C}}{\mathrm{2}}\:=\:\mathrm{s} \\ $$$$\Rightarrow\:\mathrm{sec}\:\left(\mathrm{2B}\right)\:+\:\mathrm{tan}\:\left(\mathrm{2B}\right)\:=\:\frac{\mathrm{c}\:+\:\mathrm{b}}{\mathrm{c}\:−\:\mathrm{b}} \\ $$

Question Number 189135 Answers: 2 Comments: 0

Question Number 189137 Answers: 0 Comments: 2

It is known that x is rational x (√(28 + 3(√(28 + 3(√(28 + 3(√?))))))) Find the dufference of possible vaules of x

$$\mathrm{It}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}\:\:\mathrm{x}\:\:\mathrm{is}\:\mathrm{rational} \\ $$$$\mathrm{x}\:\sqrt{\mathrm{28}\:+\:\mathrm{3}\sqrt{\mathrm{28}\:+\:\mathrm{3}\sqrt{\mathrm{28}\:+\:\mathrm{3}\sqrt{?}}}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{dufference}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{vaules} \\ $$$$\mathrm{of}\:\:\boldsymbol{\mathrm{x}} \\ $$

Question Number 189133 Answers: 1 Comments: 0

Convert hexadecimal number 4 A F_(16) to decimal

$$\mathrm{Convert}\:\mathrm{hexadecimal}\:\mathrm{number} \\ $$$$\mathrm{4}\:\mathrm{A}\:\mathrm{F}_{\mathrm{16}} \:\:\mathrm{to}\:\mathrm{decimal} \\ $$

Question Number 189131 Answers: 2 Comments: 0

Question Number 189124 Answers: 1 Comments: 0

Question Number 189132 Answers: 1 Comments: 0

Find the value of a+b+c+d+e in the system of equations: { ((13a+2b+c+6d+2e=96)),((5a+9b+2c+7d+3e=75)),((7a+8b+17c+11d+7e=99)),((3a+3b+3c+d+8e=55)),((a+7b+6c+4d+9e=79)) :}

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}: \\ $$$$\begin{cases}{\mathrm{13a}+\mathrm{2b}+\mathrm{c}+\mathrm{6d}+\mathrm{2e}=\mathrm{96}}\\{\mathrm{5a}+\mathrm{9b}+\mathrm{2c}+\mathrm{7d}+\mathrm{3e}=\mathrm{75}}\\{\mathrm{7a}+\mathrm{8b}+\mathrm{17c}+\mathrm{11d}+\mathrm{7e}=\mathrm{99}}\\{\mathrm{3a}+\mathrm{3b}+\mathrm{3c}+\mathrm{d}+\mathrm{8e}=\mathrm{55}}\\{\mathrm{a}+\mathrm{7b}+\mathrm{6c}+\mathrm{4d}+\mathrm{9e}=\mathrm{79}}\end{cases} \\ $$

Question Number 189077 Answers: 0 Comments: 0

Question Number 189070 Answers: 1 Comments: 0

Question Number 189025 Answers: 0 Comments: 0

Question Number 189024 Answers: 0 Comments: 0

Question Number 189022 Answers: 3 Comments: 0

if ((√(1+x^2 ))+x)((√(1+y^2 ))+y)=1 with x,y ∈R, find (x+y)^2 =?

$${if}\:\left(\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }+{x}\right)\left(\sqrt{\mathrm{1}+{y}^{\mathrm{2}} }+{y}\right)=\mathrm{1}\: \\ $$$${with}\:{x},{y}\:\in{R},\:{find}\:\left({x}+{y}\right)^{\mathrm{2}} =? \\ $$

Question Number 189013 Answers: 2 Comments: 0

Suppose (G, ∙ ) and (H, ∗ ) are groups. Take homomorphism φ : G → H. Suppose ∃g∈G : ∣g∣ = n, then ∣φ(g)∣ ≤ n. Does ∀g∈G, ∣g∣ = ∣φ(g)∣ ⇒ G ≅ H ?

$$\mathrm{Suppose}\:\left({G},\:\centerdot\:\right)\:\mathrm{and}\:\left({H},\:\ast\:\right)\:\mathrm{are}\:\mathrm{groups}. \\ $$$$\mathrm{Take}\:\mathrm{homomorphism}\:\phi\::\:{G}\:\rightarrow\:{H}. \\ $$$$\mathrm{Suppose}\:\exists{g}\in{G}\::\:\mid{g}\mid\:=\:{n},\:\mathrm{then}\:\mid\phi\left({g}\right)\mid\:\leqslant\:{n}. \\ $$$$\: \\ $$$$\mathrm{Does}\:\forall{g}\in{G},\:\mid{g}\mid\:=\:\mid\phi\left({g}\right)\mid\:\Rightarrow\:{G}\:\cong\:{H}\:? \\ $$

Question Number 188928 Answers: 0 Comments: 0

Question Number 188908 Answers: 1 Comments: 0

the radius of a circle is 12cmunits find the perimeter of a regular inscribed a. triangle b.heptagon c. decagon

$${the}\:{radius}\:{of}\:{a}\:{circle}\:{is}\:\mathrm{12}{cmunits} \\ $$$${find}\:{the}\:{perimeter}\:{of}\:{a}\:{regular}\: \\ $$$${inscribed}\: \\ $$$${a}.\:{triangle} \\ $$$${b}.{heptagon} \\ $$$${c}.\:{decagon} \\ $$

Question Number 188898 Answers: 0 Comments: 0

In △ABC holds: Σ ((2 + (√3) tan (B/2))/(1 + 3 tan^2 (A/2))) ≥ (9/2)

$$\mathrm{In}\:\bigtriangleup\mathrm{ABC}\:\mathrm{holds}:\:\:\:\Sigma\:\frac{\mathrm{2}\:+\:\sqrt{\mathrm{3}}\:\mathrm{tan}\:\frac{\mathrm{B}}{\mathrm{2}}}{\mathrm{1}\:+\:\mathrm{3}\:\mathrm{tan}^{\mathrm{2}} \:\frac{\mathrm{A}}{\mathrm{2}}}\:\geqslant\:\frac{\mathrm{9}}{\mathrm{2}} \\ $$

Question Number 188879 Answers: 2 Comments: 3

Find the sum of all three digit numbers started with odd number when each digit are different. Please help...

$${Find}\:{the}\:{sum}\:{of}\:{all}\:{three}\:{digit}\:{numbers} \\ $$$${started}\:{with}\:{odd}\:{number}\:{when}\:{each}\:{digit} \\ $$$${are}\:{different}. \\ $$$$ \\ $$$${Please}\:{help}... \\ $$

Question Number 188864 Answers: 0 Comments: 0

Question Number 188786 Answers: 1 Comments: 1

Question Number 188776 Answers: 3 Comments: 1

Prove that n^2 +3n+2 is divisible by 2 for any n∈Z

$$\mathrm{Prove}\:\mathrm{that}\:{n}^{\mathrm{2}} +\mathrm{3}{n}+\mathrm{2}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{2} \\ $$$$\mathrm{for}\:\mathrm{any}\:{n}\in\mathbb{Z} \\ $$

Question Number 188774 Answers: 1 Comments: 0

Question Number 188753 Answers: 1 Comments: 0

x^2 − y^2 = 2023 x, y ∈ N How many pair of (x, y)

$$\:{x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:=\:\mathrm{2023}\:\:\:\:\:\:\:\:\:{x},\:{y}\:\in\:\mathrm{N} \\ $$$$\:\mathrm{H}{ow}\:{many}\:{pair}\:{of}\:\left({x},\:{y}\right) \\ $$

Question Number 188704 Answers: 1 Comments: 0

Question Number 188660 Answers: 2 Comments: 0

solve x^4 +4x=1

$${solve}\:{x}^{\mathrm{4}} +\mathrm{4}{x}=\mathrm{1} \\ $$

Question Number 188653 Answers: 0 Comments: 1

In how many different ways can the letters of the word ABRAKADABRA be arranged?

$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{different}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the} \\ $$$$\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\mathrm{ABRAKADABRA} \\ $$$$\mathrm{be}\:\mathrm{arranged}? \\ $$

Question Number 188648 Answers: 1 Comments: 0

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