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AlgebraQuestion and Answers: Page 85

Question Number 185395 Answers: 1 Comments: 0

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lim_(n→+∞) ((((_1 ^n )(_2 ^n )...(_n ^n )))^(1/n) /(e^(n/2) ×n^(−(1/2)) ))=?

$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\frac{\sqrt[{\mathrm{n}}]{\left(_{\mathrm{1}} ^{\mathrm{n}} \right)\left(_{\mathrm{2}} ^{\mathrm{n}} \right)...\left(_{\mathrm{n}} ^{\mathrm{n}} \right)}}{\mathrm{e}^{\frac{\mathrm{n}}{\mathrm{2}}} ×\mathrm{n}^{−\frac{\mathrm{1}}{\mathrm{2}}} }=? \\ $$

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Question Number 185315 Answers: 2 Comments: 0

Solve the equation: x! = x^2 − 3x + 20

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{x}!\:=\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{3x}\:+\:\mathrm{20} \\ $$

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A ball falls from a height of 10m and lands on the ground 75% of each time it falls, it gets up again; of the What is the total distance traveled by the ball? (a) 35m b) 40m c) 70m d) 75m

$$ \\ $$A ball falls from a height of 10m and lands on the ground 75% of each time it falls, it gets up again; of the What is the total distance traveled by the ball? (a) 35m b) 40m c) 70m d) 75m

Question Number 185210 Answers: 3 Comments: 2

x=((x^2 +1)/(α+1)) x=?

$${x}=\frac{{x}^{\mathrm{2}} +\mathrm{1}}{\alpha+\mathrm{1}}\:\:\:\:\:\:\:\:\:\:{x}=? \\ $$

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1+(1/(2+(1/(3+(1/(4+(1/⋱)))))))=???

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{3}+\frac{\mathrm{1}}{\mathrm{4}+\frac{\mathrm{1}}{\ddots}}}}=??? \\ $$

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y = sin (1/x) ⇒ y^′ = ?

$$\mathrm{y}\:=\:\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{x}}\:\:\Rightarrow\:\:\mathrm{y}^{'} \:=\:? \\ $$

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(∣y∣−∣x∣−2,8)(∣x∣−∣y∣−1,8) = 0 ∣y∣ = a ∣x∣ + a ∣∣x∣ − 1,1∣ + 5 At what value of a does the equation have 4 roots?

$$\left(\mid\mathrm{y}\mid−\mid\mathrm{x}\mid−\mathrm{2},\mathrm{8}\right)\left(\mid\mathrm{x}\mid−\mid\mathrm{y}\mid−\mathrm{1},\mathrm{8}\right)\:=\:\mathrm{0} \\ $$$$\mid\mathrm{y}\mid\:=\:\mathrm{a}\:\mid\mathrm{x}\mid\:+\:\mathrm{a}\:\mid\mid\mathrm{x}\mid\:−\:\mathrm{1},\mathrm{1}\mid\:+\:\mathrm{5} \\ $$$$\mathrm{At}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\:\boldsymbol{\mathrm{a}}\:\:\mathrm{does}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{have}\:\:\mathrm{4}\:\:\mathrm{roots}? \\ $$

Question Number 185127 Answers: 0 Comments: 3

{ (((√(x^2 − (5/9) + (√(y + x^2 − (5/9))))) = y)),(((√(y^2 − (4/9) + (√(x + y^2 − (4/9))))) = x)) :} Find: x , y = ?

$$\begin{cases}{\sqrt{\mathrm{x}^{\mathrm{2}} \:−\:\frac{\mathrm{5}}{\mathrm{9}}\:+\:\sqrt{\mathrm{y}\:+\:\mathrm{x}^{\mathrm{2}} \:−\:\frac{\mathrm{5}}{\mathrm{9}}}}\:=\:\mathrm{y}}\\{\sqrt{\mathrm{y}^{\mathrm{2}} \:−\:\frac{\mathrm{4}}{\mathrm{9}}\:+\:\sqrt{\mathrm{x}\:+\:\mathrm{y}^{\mathrm{2}} \:−\:\frac{\mathrm{4}}{\mathrm{9}}}}\:=\:\mathrm{x}}\end{cases} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{x}\:,\:\mathrm{y}\:=\:? \\ $$

Question Number 185128 Answers: 1 Comments: 0

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