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Question Number 208553 Answers: 3 Comments: 0

x^2 +xy+y^2 = 1

$$\:\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \mathrm{x}^{\mathrm{2}} +\mathrm{xy}+\mathrm{y}^{\mathrm{2}} =\:\mathrm{1} \\ $$

Question Number 208540 Answers: 2 Comments: 0

Question Number 208533 Answers: 2 Comments: 0

z′ = (1/2)(z+(1/z)) z and z′ are complex numbers show that z = 2e^(iθ) show that M′ describes a conic section

$${z}'\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left({z}+\frac{\mathrm{1}}{{z}}\right) \\ $$$${z}\:{and}\:{z}'\:{are}\:{complex}\:{numbers} \\ $$$${show}\:{that}\:{z}\:=\:\mathrm{2}{e}^{{i}\theta} \\ $$$${show}\:{that}\:{M}'\:{describes}\:{a}\:{conic}\:{section} \\ $$

Question Number 208526 Answers: 1 Comments: 2

Question Number 208520 Answers: 1 Comments: 0

Question Number 208519 Answers: 1 Comments: 0

If a^x = b^y (a/x) + (b/y) = 1 then, a^x + b^y = ?

$$\mathrm{If}\:\:\:\:\:\mathrm{a}^{\mathrm{x}} \:\:=\:\:\mathrm{b}^{\mathrm{y}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{a}}{\mathrm{x}}\:\:+\:\:\frac{\mathrm{b}}{\mathrm{y}}\:\:=\:\:\mathrm{1} \\ $$$$\mathrm{then},\:\:\:\:\mathrm{a}^{\mathrm{x}} \:\:+\:\:\mathrm{b}^{\mathrm{y}} \:\:=\:\:? \\ $$

Question Number 208515 Answers: 0 Comments: 0

∫_0 ^( ∞) ((ln^2 x)/(1+x^4 )) dx

$$\int_{\mathrm{0}} ^{\:\infty} \:\frac{{ln}^{\mathrm{2}} {x}}{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx} \\ $$

Question Number 208508 Answers: 1 Comments: 0

Evaluate and leave your answer in exponent form. 5^(2024) − 5^(2023) − 5^(2022) − 5^(2021) − 5^(2020) − 5^(2019) = ?

$$\mathrm{Evaluate}\:\mathrm{and}\:\mathrm{leave}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{exponent}\:\mathrm{form}. \\ $$$$\mathrm{5}^{\mathrm{2024}} \:−\:\:\mathrm{5}^{\mathrm{2023}} \:\:−\:\:\mathrm{5}^{\mathrm{2022}} \:\:−\:\:\mathrm{5}^{\mathrm{2021}} \:\:−\:\:\mathrm{5}^{\mathrm{2020}} \:\:−\:\:\mathrm{5}^{\mathrm{2019}} \:\:=\:\:? \\ $$

Question Number 208507 Answers: 0 Comments: 0

An aeroplane flies 25 km in the direction 60° North of East 35 km Straight East, then 15 km straight North. What direction is the pane from the straight point?

Question Number 208506 Answers: 2 Comments: 0

What is the smallest number which must added to 9454351626 so that it will become divisible by 11?

Question Number 208503 Answers: 0 Comments: 0

Question Number 208502 Answers: 1 Comments: 0

Question Number 208499 Answers: 0 Comments: 0

Question Number 208493 Answers: 2 Comments: 0

Question Number 208489 Answers: 1 Comments: 0

Question Number 208482 Answers: 0 Comments: 0

Question Number 208693 Answers: 2 Comments: 0

Calculate the area enclosed by the curve ((1/x)−2)^2 +((1/y)−2)^2 =1

$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{area}\:\mathrm{enclosed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{curve} \\ $$$$\left(\frac{\mathrm{1}}{{x}}−\mathrm{2}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{{y}}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{1} \\ $$

Question Number 208469 Answers: 1 Comments: 0

Find: ((61^3 + 24^3 )/(61^3 + 37^3 )) = ?

$$\mathrm{Find}:\:\:\:\:\:\frac{\mathrm{61}^{\mathrm{3}} \:\:+\:\:\mathrm{24}^{\mathrm{3}} }{\mathrm{61}^{\mathrm{3}} \:\:+\:\:\mathrm{37}^{\mathrm{3}} }\:\:=\:\:? \\ $$

Question Number 208468 Answers: 2 Comments: 0

Question Number 208467 Answers: 3 Comments: 0

Question Number 208466 Answers: 1 Comments: 0

Question Number 208465 Answers: 1 Comments: 0

Question Number 208463 Answers: 1 Comments: 0

Compare it: a = log_3 4 b = log_5 6 c = log_6 2

$$\mathrm{Compare}\:\mathrm{it}: \\ $$$$\mathrm{a}\:=\:\mathrm{log}_{\mathrm{3}} \:\mathrm{4} \\ $$$$\mathrm{b}\:=\:\mathrm{log}_{\mathrm{5}} \:\mathrm{6} \\ $$$$\mathrm{c}\:=\:\mathrm{log}_{\mathrm{6}} \:\mathrm{2} \\ $$

Question Number 208455 Answers: 1 Comments: 2

Question Number 208453 Answers: 2 Comments: 0

If f(x) = (((2a + 1)∙x + 1)/(x − a)) and f(x) = f^(−1) (x) Find: a^2 + 3 = ?

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\left(\mathrm{2a}\:+\:\mathrm{1}\right)\centerdot\mathrm{x}\:+\:\mathrm{1}}{\mathrm{x}\:−\:\mathrm{a}}\:\:\:\mathrm{and}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right) \\ $$$$\mathrm{Find}:\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{3}\:=\:? \\ $$

Question Number 208447 Answers: 0 Comments: 0

((√(x^2 +y^2 ))+(√(x^2 +y^2 −20y+100))+(√(x^2 −20x+y^2 +100)) )=?

$$\: \left(\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{20y}+\mathrm{100}}+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{20x}+\mathrm{y}^{\mathrm{2}} +\mathrm{100}}\:\right)=? \\ $$

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