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AlgebraQuestion and Answers: Page 1

Question Number 212711 Answers: 1 Comments: 0

f(x)=(1/(1−x)) y=f(x), z=f(y), f(z)=?

$$\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}−{x}} \\ $$$$\:{y}={f}\left({x}\right),\:{z}={f}\left({y}\right),\:{f}\left({z}\right)=? \\ $$

Question Number 212673 Answers: 3 Comments: 0

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

Question Number 212654 Answers: 1 Comments: 0

Question Number 212651 Answers: 1 Comments: 0

Question Number 212612 Answers: 1 Comments: 0

Solve the differential equation: (dy/dx) = cos(x + y)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}: \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:\:=\:\:\mathrm{cos}\left(\mathrm{x}\:+\:\mathrm{y}\right) \\ $$

Question Number 212609 Answers: 1 Comments: 0

If 0≤x≤2 Prove that: 2^x + 1 − (√(10,5x + 4)) ≤ 0

$$\mathrm{If}\:\:\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{2} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{1}\:−\:\sqrt{\mathrm{10},\mathrm{5x}\:+\:\mathrm{4}}\:\leqslant\:\mathrm{0} \\ $$

Question Number 212602 Answers: 0 Comments: 0

Question Number 212601 Answers: 0 Comments: 0

Question Number 212598 Answers: 1 Comments: 0

Help me to solve pls Q 212576

$$\mathrm{Help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{pls} \\ $$$$\mathrm{Q}\:\mathrm{212576}\: \\ $$

Question Number 212576 Answers: 0 Comments: 0

If ((x^2 − yz)/(a^2 − bc)) = ((y^2 − zx)/(b^2 − ca)) = ((z^2 − xy)/(c^2 − ab)) then prove that (x/a) = (y/b) = (z/c) .

$$\mathrm{If}\:\frac{{x}^{\mathrm{2}} \:−\:{yz}}{{a}^{\mathrm{2}} \:−\:{bc}}\:=\:\frac{{y}^{\mathrm{2}} \:−\:{zx}}{{b}^{\mathrm{2}} \:−\:{ca}}\:=\:\frac{{z}^{\mathrm{2}} \:−\:{xy}}{{c}^{\mathrm{2}} \:−\:{ab}}\:\mathrm{then}\: \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{x}}{{a}}\:=\:\frac{{y}}{{b}}\:=\:\frac{{z}}{{c}}\:. \\ $$

Question Number 212573 Answers: 0 Comments: 2

Prove that: ((5m^2 − n)/(n^2 + 3m)) = 1

$$\mathrm{Prove}\:\mathrm{that}:\:\:\:\frac{\mathrm{5m}^{\mathrm{2}} \:−\:\mathrm{n}}{\mathrm{n}^{\mathrm{2}} \:+\:\mathrm{3m}}\:=\:\mathrm{1} \\ $$

Question Number 212560 Answers: 0 Comments: 3

Exact solution just to this please: 9x^2 (x+1)^3 =3(3x^2 −1)(3x^2 +3x+1)

$${Exact}\:{solution}\:{just}\:{to}\:{this}\:{please}: \\ $$$$\mathrm{9}{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)^{\mathrm{3}} =\mathrm{3}\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{1}\right) \\ $$

Question Number 212552 Answers: 1 Comments: 0

^(Q:) In AB^Δ C : cos(A) +cos(B )+ 2cos(C )= 2 show that : a + b = 2c ■

$$ \\ $$$$\:\overset{\mathrm{Q}:} {\:}\:\mathrm{In}\:\mathrm{A}\overset{\Delta} {\mathrm{B}C}\::\:\:\:{cos}\left(\mathrm{A}\right)\:+{cos}\left(\mathrm{B}\:\right)+\:\mathrm{2}{cos}\left(\mathrm{C}\:\right)=\:\mathrm{2} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\::\:\:\:{a}\:+\:{b}\:=\:\mathrm{2}{c}\:\:\:\:\:\:\:\:\:\:\:\blacksquare\: \\ $$$$ \\ $$

Question Number 212550 Answers: 1 Comments: 0

the following equation has no root . find the relationship between a , b , c : 1: c≤2 2: c >2 3: c >ab 4: c≤ ab eq^n : (√( x+1+b +2(√(x+b)) )) + (√(x+1+a +2(√(x+a)))) = c

$$ \\ $$$$\:\:\:\:{the}\:{following}\:{equation}\:{has} \\ $$$$\:\:\:\:\:{no}\:{root}\:.\:{find}\:{the}\:{relationship} \\ $$$$\:\:\:{between}\:{a}\:,\:{b}\:,\:{c}\:: \\ $$$$\:\:\:\:\mathrm{1}:\:\:{c}\leqslant\mathrm{2} \\ $$$$\:\:\:\:\mathrm{2}:\:{c}\:>\mathrm{2} \\ $$$$\:\:\:\:\mathrm{3}:\:{c}\:>{ab} \\ $$$$\:\:\:\:\mathrm{4}:\:{c}\leqslant\:{ab} \\ $$$$\:\:\:\:{eq}^{{n}} \::\:\:\sqrt{\:{x}+\mathrm{1}+{b}\:+\mathrm{2}\sqrt{{x}+{b}}\:}\:+\:\sqrt{{x}+\mathrm{1}+{a}\:+\mathrm{2}\sqrt{{x}+{a}}}\:=\:{c} \\ $$$$ \\ $$

Question Number 212541 Answers: 1 Comments: 0

Find: x = ? sin(((88π^2 )/x)) = (1/(cos(3x)))

$$\mathrm{Find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$$$\mathrm{sin}\left(\frac{\mathrm{88}\pi^{\mathrm{2}} }{\mathrm{x}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{cos}\left(\mathrm{3x}\right)} \\ $$

Question Number 212531 Answers: 1 Comments: 0

Question Number 212522 Answers: 3 Comments: 0

in how many ways we can distribute 6 distinct balls in 3 identical boxes

$$\:\:\boldsymbol{{in}}\:\boldsymbol{{how}}\:\boldsymbol{{many}}\:\boldsymbol{{ways}}\:\boldsymbol{{we}} \\ $$$$\boldsymbol{{can}}\:\boldsymbol{{distribute}}\:\mathrm{6}\:\boldsymbol{{distinct}} \\ $$$$\boldsymbol{{balls}}\:\boldsymbol{{in}}\:\mathrm{3}\:\boldsymbol{{identical}}\:\boldsymbol{{boxes}} \\ $$

Question Number 212519 Answers: 1 Comments: 0

certificate: (x−1)∣(x^(2n+1) −1)and(x+1)∣(x^(2n+1) +1) All established [2024.10.16]

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}: \\ $$$$\:\:\:\:\:\left({x}−\mathrm{1}\right)\mid\left({x}^{\mathrm{2}{n}+\mathrm{1}} −\mathrm{1}\right)\mathrm{and}\left({x}+\mathrm{1}\right)\mid\left({x}^{\mathrm{2}{n}+\mathrm{1}} +\mathrm{1}\right) \\ $$$$\mathrm{All}\:\mathrm{established} \\ $$$$\left[\mathrm{2024}.\mathrm{10}.\mathrm{16}\right] \\ $$

Question Number 212516 Answers: 0 Comments: 0

Question Number 212508 Answers: 1 Comments: 1

Question Number 212506 Answers: 1 Comments: 0

Find: ((− ((18)/(1 + i (√3)))))^(1/4)

$$\mathrm{Find}:\:\:\:\:\:\:\sqrt[{\mathrm{4}}]{−\:\frac{\mathrm{18}}{\mathrm{1}\:+\:\boldsymbol{\mathrm{i}}\:\sqrt{\mathrm{3}}}} \\ $$

Question Number 212503 Answers: 0 Comments: 0

Question Number 212500 Answers: 1 Comments: 0

Can we exactly find r_(max) (a). r^2 +((2rt)/a)(t+2(√(ar)))=t^2 ∀ t is parameter

$${Can}\:{we}\:{exactly}\:{find}\:{r}_{{max}} \left({a}\right). \\ $$$${r}^{\mathrm{2}} +\frac{\mathrm{2}{rt}}{{a}}\left({t}+\mathrm{2}\sqrt{{ar}}\right)={t}^{\mathrm{2}} \:\:\:\:\forall\:{t}\:{is}\:{parameter} \\ $$

Question Number 212499 Answers: 2 Comments: 0

Given a,b,c and d are reals numbers such that { ((a^2 +b^2 =10)),((c^2 +d^2 =10 )),((ab+cd=0)) :} Find ac + bd.

$$\:\:\mathrm{Given}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{and}\:\mathrm{d}\:\mathrm{are}\:\mathrm{reals}\: \\ $$$$\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\:\:\:\begin{cases}{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} =\mathrm{10}}\\{\mathrm{c}^{\mathrm{2}} +\mathrm{d}^{\mathrm{2}} =\mathrm{10}\:}\\{\mathrm{ab}+\mathrm{cd}=\mathrm{0}}\end{cases} \\ $$$$\:\:\mathrm{Find}\:\mathrm{ac}\:+\:\mathrm{bd}. \\ $$

Question Number 212479 Answers: 1 Comments: 0

{ ((2x + 3y − z = 7)),((4x − y + 2z = 1)),((−x + 5y + 3z = 14)) :} find: x,y,z = ?

$$\begin{cases}{\mathrm{2x}\:+\:\mathrm{3y}\:−\:\mathrm{z}\:=\:\mathrm{7}}\\{\mathrm{4x}\:−\:\mathrm{y}\:+\:\mathrm{2z}\:=\:\mathrm{1}}\\{−\mathrm{x}\:+\:\mathrm{5y}\:+\:\mathrm{3z}\:=\:\mathrm{14}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\:\mathrm{x},\mathrm{y},\mathrm{z}\:=\:? \\ $$

Question Number 212470 Answers: 1 Comments: 0

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