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AlgebraQuestion and Answers: Page 356

Question Number 10542 Answers: 1 Comments: 0

Prove that: tan(sec^(−1) ((√(tan(θ)))))=(√(tan(θ)))(√(1−cot(θ)))

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{tan}\left(\mathrm{sec}^{−\mathrm{1}} \left(\sqrt{\mathrm{tan}\left(\theta\right)}\right)\right)=\sqrt{\mathrm{tan}\left(\theta\right)}\sqrt{\mathrm{1}−\mathrm{cot}\left(\theta\right)} \\ $$

Question Number 10515 Answers: 1 Comments: 0

2^a =6^((x/(x+y)) ) .3^a =6^(y/(x+y)) ⇒8^((y/x)+1) =?

$$\mathrm{2}^{{a}} =\mathrm{6}^{\frac{{x}}{{x}+{y}}\:} \:\:\:.\mathrm{3}^{{a}} \:=\mathrm{6}^{\frac{{y}}{{x}+{y}}} \:\Rightarrow\mathrm{8}^{\frac{{y}}{{x}}+\mathrm{1}} =? \\ $$

Question Number 10493 Answers: 2 Comments: 0

(1/(2!))+(2/(3!))+(3/(4!))+(4/(5!))+...+((17)/(18!))=?

$$\frac{\mathrm{1}}{\mathrm{2}!}+\frac{\mathrm{2}}{\mathrm{3}!}+\frac{\mathrm{3}}{\mathrm{4}!}+\frac{\mathrm{4}}{\mathrm{5}!}+...+\frac{\mathrm{17}}{\mathrm{18}!}=? \\ $$

Question Number 10492 Answers: 1 Comments: 0

3^(logx) −2^(logx−1) =2^(logx+1) −2×3^(logx−1) ⇒x=?

$$\mathrm{3}^{{logx}} −\mathrm{2}^{{logx}−\mathrm{1}} =\mathrm{2}^{{logx}+\mathrm{1}} −\mathrm{2}×\mathrm{3}^{{logx}−\mathrm{1}} \Rightarrow{x}=? \\ $$

Question Number 10470 Answers: 1 Comments: 0

Question Number 10464 Answers: 1 Comments: 0

Question Number 10463 Answers: 1 Comments: 0

x∈Z −1≤∣x−3∣<5 ⇒Σ=?

$${x}\in{Z} \\ $$$$−\mathrm{1}\leqslant\mid{x}−\mathrm{3}\mid<\mathrm{5}\:\Rightarrow\Sigma=? \\ $$

Question Number 10455 Answers: 5 Comments: 4

Question Number 10414 Answers: 2 Comments: 2

Question Number 10408 Answers: 1 Comments: 0

Question Number 10398 Answers: 2 Comments: 0

Question Number 10397 Answers: 1 Comments: 1

Question Number 10387 Answers: 1 Comments: 0

6 people a, b, c, d, e, and f stand in a line. The number of ways they can stand arranged is equal to 6! If two people have to stand next to each other, but everyone else do not matter, how many combinations combinations are there? e.g. (ab)cdef or cd(ba)ef

$$\mathrm{6}\:\mathrm{people}\:{a},\:{b},\:{c},\:{d},\:{e},\:\mathrm{and}\:{f}\:\mathrm{stand}\:\mathrm{in}\:\mathrm{a}\:\mathrm{line}. \\ $$$$\: \\ $$$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{they}\:\mathrm{can}\:\mathrm{stand}\:\mathrm{arranged} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{6}! \\ $$$$\: \\ $$$$\mathrm{If}\:\mathrm{two}\:\mathrm{people}\:\mathrm{have}\:\mathrm{to}\:\mathrm{stand}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}, \\ $$$$\mathrm{but}\:\mathrm{everyone}\:\mathrm{else}\:\mathrm{do}\:\mathrm{not}\:\mathrm{matter},\:\mathrm{how}\:\mathrm{many}\:\mathrm{combinations} \\ $$$$\mathrm{combinations}\:\mathrm{are}\:\mathrm{there}? \\ $$$$\: \\ $$$$\mathrm{e}.\mathrm{g}.\:\:\:\left({ab}\right){cdef}\:\:\:\:\mathrm{or}\:\:\:\:{cd}\left({ba}\right){ef} \\ $$

Question Number 10353 Answers: 0 Comments: 0

show that α^4 =−3hα^2 −gα and deduce that Σα^4 =−3hΣα^2 −gΣα and find Σα^2 ,Σα^3 ,Σα^4 in term of g and h.

$$\mathrm{show}\:\mathrm{that}\:\alpha^{\mathrm{4}} =−\mathrm{3h}\alpha^{\mathrm{2}} −\mathrm{g}\alpha\:\mathrm{and}\:\mathrm{deduce} \\ $$$$\mathrm{that}\:\Sigma\alpha^{\mathrm{4}} =−\mathrm{3h}\Sigma\alpha^{\mathrm{2}} −\mathrm{g}\Sigma\alpha\:\mathrm{and}\:\mathrm{find}\: \\ $$$$\Sigma\alpha^{\mathrm{2}} ,\Sigma\alpha^{\mathrm{3}} ,\Sigma\alpha^{\mathrm{4}} \:\:\mathrm{in}\:\mathrm{term}\:\mathrm{of}\:\mathrm{g}\:\mathrm{and}\:\mathrm{h}. \\ $$

Question Number 10352 Answers: 0 Comments: 0

show that α^3 =−3hα−g and use the similar expression to α,γ to deduce that α^3 =−3hΣα −g

$$\mathrm{show}\:\mathrm{that}\:\alpha^{\mathrm{3}} =−\mathrm{3h}\alpha−\mathrm{g}\:\:\:\mathrm{and}\:\:\mathrm{use}\:\mathrm{the}\: \\ $$$$\mathrm{similar}\:\mathrm{expression}\:\mathrm{to}\:\:\alpha,\gamma\:\:\mathrm{to}\:\mathrm{deduce}\: \\ $$$$\mathrm{that}\:\alpha^{\mathrm{3}} =−\mathrm{3h}\Sigma\alpha\:−\mathrm{g} \\ $$

Question Number 10347 Answers: 2 Comments: 0

A=1+2+3+...+n−2 B=15+16+.....+n A−B=42⇒n=?

$$\mathrm{A}=\mathrm{1}+\mathrm{2}+\mathrm{3}+...+\mathrm{n}−\mathrm{2} \\ $$$$\mathrm{B}=\mathrm{15}+\mathrm{16}+.....+\mathrm{n} \\ $$$$\mathrm{A}−\mathrm{B}=\mathrm{42}\Rightarrow\mathrm{n}=? \\ $$

Question Number 10340 Answers: 0 Comments: 1

A=1×2 +2×4 +3×6+...+14×28 B=1×3 +2×3 +...+14×29 ⇒B=?