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AlgebraQuestion and Answers: Page 300

Question Number 60255 Answers: 0 Comments: 0

b=(((kT)/P))^(1/3) . distance molekular prove.

$$\boldsymbol{\mathrm{b}}=\sqrt[{\mathrm{3}}]{\frac{\boldsymbol{\mathrm{kT}}}{\boldsymbol{\mathrm{P}}}}.\:\boldsymbol{\mathrm{distance}}\:\:\boldsymbol{\mathrm{molekular}} \\ $$$$\boldsymbol{\mathrm{prove}}. \\ $$

Question Number 60175 Answers: 0 Comments: 2

solving u^v =w with u, v, w ∈C finding all possible solutions I tested this with several values and found no mistake. please review and comment. I hope this will help at least some of you.

$$\mathrm{solving}\:{u}^{{v}} ={w}\:\mathrm{with}\:{u},\:{v},\:{w}\:\in\mathbb{C} \\ $$$$\mathrm{finding}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions} \\ $$$$\mathrm{I}\:\mathrm{tested}\:\mathrm{this}\:\mathrm{with}\:\mathrm{several}\:\mathrm{values}\:\mathrm{and}\:\mathrm{found} \\ $$$$\mathrm{no}\:\mathrm{mistake}.\:\mathrm{please}\:\mathrm{review}\:\mathrm{and}\:\mathrm{comment}. \\ $$$$\mathrm{I}\:\mathrm{hope}\:\mathrm{this}\:\mathrm{will}\:\mathrm{help}\:\mathrm{at}\:\mathrm{least}\:\mathrm{some}\:\mathrm{of}\:\mathrm{you}. \\ $$

Question Number 60156 Answers: 3 Comments: 2

Prove by principle of mathematical induction sin(x) + sin(2x) + sin(3x) + ... + sin(nx) = ((cos((1/2)x) − cos(n + (1/2))x)/(2 sin((1/2)x)))

$$\mathrm{Prove}\:\mathrm{by}\:\mathrm{principle}\:\mathrm{of}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{sin}\left(\mathrm{x}\right)\:+\:\mathrm{sin}\left(\mathrm{2x}\right)\:+\:\mathrm{sin}\left(\mathrm{3x}\right)\:+\:...\:+\:\mathrm{sin}\left(\mathrm{nx}\right)\:\:=\:\:\frac{\mathrm{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)\:−\:\mathrm{cos}\left(\mathrm{n}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}}{\mathrm{2}\:\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)} \\ $$

Question Number 60056 Answers: 1 Comments: 1

Question Number 60052 Answers: 0 Comments: 0

Question Number 60039 Answers: 2 Comments: 3

find all solutions for z∈C z^i =(1/2)−(1/2)i z^(1−i) =1+i

$$\mathrm{find}\:\mathrm{all}\:\mathrm{solutions}\:\mathrm{for}\:{z}\in\mathbb{C} \\ $$$${z}^{\mathrm{i}} =\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{i} \\ $$$${z}^{\mathrm{1}−\mathrm{i}} =\mathrm{1}+\mathrm{i} \\ $$

Question Number 59977 Answers: 1 Comments: 0

4×(5+5)

$$\mathrm{4}×\left(\mathrm{5}+\mathrm{5}\right) \\ $$

Question Number 59929 Answers: 0 Comments: 0

Use long division to solve 7485/5

$$\mathrm{Use}\:\mathrm{long}\:\mathrm{division}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{7485}/\mathrm{5} \\ $$

Question Number 59833 Answers: 1 Comments: 0

Question Number 59678 Answers: 0 Comments: 0

Determine a,b,c in terms of α,β,γ. (a/b)−c=γ (b/c)−a=α (c/a)−b=β

$$\mathcal{D}{etermine}\:{a},{b},{c}\:{in}\:{terms}\:{of}\:\alpha,\beta,\gamma. \\ $$$$\:\:\:\:\frac{{a}}{{b}}−{c}=\gamma \\ $$$$\:\:\:\:\frac{{b}}{{c}}−{a}=\alpha \\ $$$$\:\:\:\:\frac{{c}}{{a}}−{b}=\beta \\ $$

Question Number 59615 Answers: 1 Comments: 0

6+((1/5)×7)

$$\mathrm{6}+\left(\frac{\mathrm{1}}{\mathrm{5}}×\mathrm{7}\right) \\ $$

Question Number 59614 Answers: 1 Comments: 0

1(1/7)+1(1/(14))

$$\mathrm{1}\frac{\mathrm{1}}{\mathrm{7}}+\mathrm{1}\frac{\mathrm{1}}{\mathrm{14}} \\ $$

Question Number 59581 Answers: 2 Comments: 0

Determine a , b , c in terms of α , β , γ. ab+c=γ bc+a=α ca+b=β

$$\mathcal{D}{etermine}\:{a}\:,\:{b}\:,\:{c}\:{in}\:{terms}\:{of}\:\alpha\:,\:\beta\:,\:\gamma. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ab}+{c}=\gamma\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{bc}+{a}=\alpha \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ca}+{b}=\beta \\ $$

Question Number 59552 Answers: 1 Comments: 0

(1/4)+((1/4)+(1/8))

$$\frac{\mathrm{1}}{\mathrm{4}}+\left(\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{8}}\right) \\ $$

Question Number 59551 Answers: 1 Comments: 0

1.8×1.6

$$\mathrm{1}.\mathrm{8}×\mathrm{1}.\mathrm{6} \\ $$

Question Number 59550 Answers: 1 Comments: 0

9+(5×4+5^3 )

$$\mathrm{9}+\left(\mathrm{5}×\mathrm{4}+\mathrm{5}^{\mathrm{3}} \right) \\ $$

Question Number 59549 Answers: 2 Comments: 0

(1/5)×i i=7

$$\frac{\mathrm{1}}{\mathrm{5}}×\mathrm{i}\:\:\mathrm{i}=\mathrm{7} \\ $$

Question Number 59547 Answers: 1 Comments: 0

4+t×c t=3 c=6

$$\mathrm{4}+\mathrm{t}×\mathrm{c}\:\mathrm{t}=\mathrm{3}\:\mathrm{c}=\mathrm{6} \\ $$

Question Number 59499 Answers: 1 Comments: 3

Question Number 59482 Answers: 0 Comments: 0

Question Number 59439 Answers: 0 Comments: 0

Question Number 59409 Answers: 0 Comments: 2

Question Number 59336 Answers: 1 Comments: 0

Find the nth term of the AP: 2, − (2/5) , − (2/(11)) , ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{AP}:\:\:\:\:\:\mathrm{2},\:\:\:\:−\:\frac{\mathrm{2}}{\mathrm{5}}\:,\:\:\:\:\:−\:\frac{\mathrm{2}}{\mathrm{11}}\:,\:... \\ $$

Question Number 59313 Answers: 1 Comments: 0

c+6×t c=3 t=5

$$\mathrm{c}+\mathrm{6}×\mathrm{t}\:\:\mathrm{c}=\mathrm{3}\:\:\mathrm{t}=\mathrm{5} \\ $$

Question Number 59270 Answers: 1 Comments: 0

Solve the equation 3x^(1/2) +5−2x^(1/2) =0

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{3x}^{\frac{\mathrm{1}}{\mathrm{2}}} +\mathrm{5}−\mathrm{2x}^{\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{0} \\ $$

Question Number 59166 Answers: 0 Comments: 0

67{[4×(3+5)+6]}

$$\mathrm{67}\left\{\left[\mathrm{4}×\left(\mathrm{3}+\mathrm{5}\right)+\mathrm{6}\right]\right\} \\ $$

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