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AlgebraQuestion and Answers: Page 4

Question Number 223655 Answers: 3 Comments: 4

Question Number 223636 Answers: 0 Comments: 0

Factor the following expression: (((arctan(x^5 +1)))^(1/5) )^x^(−x^2 )

$$\mathrm{Factor}\:\mathrm{the}\:\mathrm{following}\:\mathrm{expression}: \\ $$$$\left(\sqrt[{\mathrm{5}}]{\mathrm{arctan}\left({x}^{\mathrm{5}} +\mathrm{1}\right)}\right)^{{x}^{−{x}^{\mathrm{2}} } } \\ $$

Question Number 223626 Answers: 1 Comments: 6

{ ((x^2 +y^2 +xy=25)),((y^2 +z^2 +yz=49)),((z^2 +x^2 +zx=64)) :} (x+y+z)^2 −100=??

$$\begin{cases}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{xy}=\mathrm{25}}\\{{y}^{\mathrm{2}} +{z}^{\mathrm{2}} +{yz}=\mathrm{49}}\\{{z}^{\mathrm{2}} +{x}^{\mathrm{2}} +{zx}=\mathrm{64}}\end{cases} \\ $$$$\left({x}+{y}+{z}\right)^{\mathrm{2}} −\mathrm{100}=?? \\ $$

Question Number 223615 Answers: 3 Comments: 0

40^(x−1) =2^(2x+1)

$$\mathrm{40}^{{x}−\mathrm{1}} =\mathrm{2}^{\mathrm{2}{x}+\mathrm{1}} \\ $$

Question Number 223585 Answers: 1 Comments: 1

Question Number 223571 Answers: 2 Comments: 0

S_1 = 1∙1! + 2∙2! + 3∙3! +...+ 16∙16! S_2 = 1∙1! + 2∙2! + 3∙3! +...+ 14∙14! Find: (S_1 /S_2 ) = ?

$$\mathrm{S}_{\mathrm{1}} \:=\:\mathrm{1}\centerdot\mathrm{1}!\:+\:\mathrm{2}\centerdot\mathrm{2}!\:+\:\mathrm{3}\centerdot\mathrm{3}!\:+...+\:\mathrm{16}\centerdot\mathrm{16}! \\ $$$$\mathrm{S}_{\mathrm{2}} \:=\:\mathrm{1}\centerdot\mathrm{1}!\:+\:\mathrm{2}\centerdot\mathrm{2}!\:+\:\mathrm{3}\centerdot\mathrm{3}!\:+...+\:\mathrm{14}\centerdot\mathrm{14}! \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{S}_{\mathrm{1}} }{\mathrm{S}_{\mathrm{2}} }\:=\:? \\ $$

Question Number 223569 Answers: 3 Comments: 0

Question Number 223508 Answers: 0 Comments: 0

Question Number 223487 Answers: 1 Comments: 0

Let Φ be the hyperbola xy = b², b ≠ 0, and P be a point on Φ. Let Q be the image of reflection of P about the origin. Construct a circle ω centred at P with radius PQ. ω cuts Φ at the points B, C, D, Q. Prove that ΔBCD is equilateral, no matter what the value of b is.

Question Number 223483 Answers: 1 Comments: 0

(x−1)(x−2)=1 (x−1)^(15) −(1/((x−1)^(15) ))=??

$$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)=\mathrm{1} \\ $$$$\left({x}−\mathrm{1}\right)^{\mathrm{15}} −\frac{\mathrm{1}}{\left({x}−\mathrm{1}\right)^{\mathrm{15}} }=?? \\ $$

Question Number 223474 Answers: 3 Comments: 1

(√(1+(√(1+x))))=(x)^(1/3)

$$\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+{x}}}=\sqrt[{\mathrm{3}}]{{x}} \\ $$

Question Number 223459 Answers: 4 Comments: 0

solve for x∈R (√(25−10x−x^2 ))+(√(15−x^2 ))=2(√5)

$${solve}\:{for}\:{x}\in{R} \\ $$$$\sqrt{\mathrm{25}−\mathrm{10}{x}−{x}^{\mathrm{2}} }+\sqrt{\mathrm{15}−{x}^{\mathrm{2}} }=\mathrm{2}\sqrt{\mathrm{5}} \\ $$

Question Number 223429 Answers: 2 Comments: 1

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