Question and Answers Forum

AllQuestion and Answers: Page 302

Question Number 191518 Answers: 0 Comments: 1

Question Number 191602 Answers: 1 Comments: 1

Question Number 191597 Answers: 0 Comments: 0

Prove H_x → cot ( x ) x!→ sin ( x )

$${Prove} \\ $$$$ \\ $$$$\mathrm{H}_{{x}} \:\rightarrow\:\mathrm{cot}\:\left(\:\mathrm{x}\:\right)\: \\ $$$$\mathrm{x}!\rightarrow\:\:\mathrm{sin}\:\left(\:\mathrm{x}\:\right) \\ $$

Question Number 191595 Answers: 1 Comments: 0

a = ((xy)/(x + y)) , b = ((xz)/(x + z)) and c = ((yz)/(y + z)) . Represent x in a, b, c form. [x, y, z ≠ 0]

$${a}\:=\:\frac{{xy}}{{x}\:+\:{y}}\:,\:{b}\:=\:\frac{{xz}}{{x}\:+\:{z}}\:\mathrm{and}\:{c}\:=\:\frac{{yz}}{{y}\:+\:{z}}\:. \\ $$$$\mathrm{Represent}\:{x}\:\mathrm{in}\:{a},\:{b},\:{c}\:\mathrm{form}.\:\left[{x},\:{y},\:{z}\:\neq\:\mathrm{0}\right] \\ $$

Question Number 191611 Answers: 1 Comments: 0

if x^2 −x+1 = 0 and α and β are thd roots of this equation then evaluate ((α^(100) +β^(100) )/(α^(100) −β^(100) ))

$${if}\:{x}^{\mathrm{2}} −{x}+\mathrm{1}\:=\:\mathrm{0}\:{and}\:\alpha\:{and}\:\beta\:{are}\:{thd}\:{roots} \\ $$$${of}\:{this}\:{equation}\:{then}\:{evaluate}\:\frac{\alpha^{\mathrm{100}} +\beta^{\mathrm{100}} }{\alpha^{\mathrm{100}} −\beta^{\mathrm{100}} } \\ $$

Question Number 191512 Answers: 1 Comments: 0

Q: the equation ⌊ cos(4x )⌋=m.cos(2x) has no solution . x∈ (0, (π/2) ) find the acceptable real values for ”m”.

$$ \\ $$$$\:\:\:\:\:{Q}:\:\:\:\:\:\:\:{the}\:{equation}\: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\lfloor\:\mathrm{cos}\left(\mathrm{4}{x}\:\right)\rfloor={m}.\mathrm{cos}\left(\mathrm{2}{x}\right) \\ $$$$\:\:\:{has}\:{no}\:\:{solution}\:.\:\:{x}\in\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\:\right) \\ $$$$\:\:\:\:{find}\:{the}\:{acceptable} \\ $$$$\:\:\:\:\:\:\:{real}\:{values}\:{for}\:\:\:\:''{m}''. \\ $$

Question Number 191510 Answers: 0 Comments: 3

now I can write in arabic language but I cant use it to wrie equations for example ax^2 + bx + c = 0 + + = ^2 I get this please try to solve this problem thank you so much Mohammed Alwan Yemen

$${now}\:{I}\:{can}\:{write}\:{in}\:{arabic} \\ $$$${language}\:{but}\:{I}\:{cant}\:{use}\: \\ $$$${it}\:{to}\:{wrie}\:{equations} \\ $$$${for}\:{example} \\ $$$${ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0} \\ $$$$\:+\:+\:=\: \\ $$$$ ^{\mathrm{2}} \\ $$$${I}\:{get}\:{this}\: \\ $$$${please}\:{try}\:{to}\:{solve}\:{this}\: \\ $$$${problem}\: \\ $$$${thank}\:{you}\:{so}\:{much} \\ $$$${Mohammed}\:{Alwan} \\ $$$${Yemen} \\ $$

Question Number 191508 Answers: 0 Comments: 0

Question Number 191507 Answers: 1 Comments: 0

Question Number 191501 Answers: 1 Comments: 2

find a solution; e^x = ln(x)

$$ \\ $$$$\:\:\:\:{find}\:{a}\:{solution}; \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{{e}}^{\boldsymbol{{x}}} \:=\:\boldsymbol{{ln}}\left(\boldsymbol{{x}}\right) \\ $$$$ \\ $$

Question Number 191499 Answers: 0 Comments: 6

x + ln(1−x) = 0.1614, find x?1II I think we can use Lambert BOSSES, help your boy!

$$\mathrm{x}\:+\:\mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)\:=\:\mathrm{0}.\mathrm{1614},\:\mathrm{find}\:\mathrm{x}?\mathrm{1II} \\ $$$$\mathrm{I}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{use}\:\mathrm{Lambert} \\ $$$$ \\ $$$$\mathrm{BOSSES},\:\mathrm{help}\:\mathrm{your}\:\mathrm{boy}! \\ $$

Question Number 191498 Answers: 0 Comments: 0

If A(((2c)/a) , (c/b)), B((c/a) , 0) and C(((1 + c)/a) , (1/b)) are three points, then prove that, i. (((AB)^2 + (BC)^2 )/((CA)^2 )) = ((c^2 + 1)/((c − 1)^2 )) ii. (AB)^2 + (BC)^2 − (AC)^2 = ((2c(a^2 + b^2 ))/(a^2 b^2 ))

$$\mathrm{If}\:\mathrm{A}\left(\frac{\mathrm{2}{c}}{{a}}\:,\:\frac{{c}}{{b}}\right),\:\mathrm{B}\left(\frac{{c}}{{a}}\:,\:\mathrm{0}\right)\:\mathrm{and}\:\mathrm{C}\left(\frac{\mathrm{1}\:+\:{c}}{{a}}\:,\:\frac{\mathrm{1}}{{b}}\right) \\ $$$$\mathrm{are}\:\mathrm{three}\:\mathrm{points},\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that},\: \\ $$$$\mathrm{i}.\:\:\frac{\left(\mathrm{AB}\right)^{\mathrm{2}} \:+\:\left(\mathrm{BC}\right)^{\mathrm{2}} }{\left(\mathrm{CA}\right)^{\mathrm{2}} }\:=\:\frac{{c}^{\mathrm{2}} \:+\:\mathrm{1}}{\left({c}\:−\:\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\mathrm{ii}.\:\left(\mathrm{AB}\right)^{\mathrm{2}} \:+\:\left(\mathrm{BC}\right)^{\mathrm{2}} \:−\:\left(\mathrm{AC}\right)^{\mathrm{2}} \:=\:\frac{\mathrm{2}{c}\left({a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \right)}{{a}^{\mathrm{2}} {b}^{\mathrm{2}} } \\ $$

Question Number 191486 Answers: 1 Comments: 0

a(√a) + b(√b) = 183 and b(√a) + a(√b) = 182 What is the value of (9/5) (a + b) ?

$${a}\sqrt{{a}}\:+\:{b}\sqrt{{b}}\:=\:\mathrm{183}\:\mathrm{and}\:{b}\sqrt{{a}}\:+\:{a}\sqrt{{b}}\:=\:\mathrm{182} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{9}}{\mathrm{5}}\:\left({a}\:+\:{b}\right)\:? \\ $$

Question Number 191484 Answers: 2 Comments: 0

(x + (√(1 + x^2 )))(y + (√(1 + y^2 ))) = 1 What is the value of (x + y)^2 ?

$$\left({x}\:+\:\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\left({y}\:+\:\sqrt{\mathrm{1}\:+\:{y}^{\mathrm{2}} }\right)\:=\:\mathrm{1} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left({x}\:+\:{y}\right)^{\mathrm{2}} \:? \\ $$

Question Number 191474 Answers: 1 Comments: 1

If A+B+C=π Prove that cos 2A+cos 2B+cos2C+1=−4cosAcos Bcos C

$$\mathrm{If}\:\mathrm{A}+\mathrm{B}+\mathrm{C}=\pi \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{cos}\:\mathrm{2A}+\mathrm{cos}\:\mathrm{2B}+\mathrm{cos2C}+\mathrm{1}=−\mathrm{4cosAcos}\:\mathrm{Bcos}\:\mathrm{C} \\ $$$$ \\ $$

Question Number 191473 Answers: 0 Comments: 0