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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

Question Number 191483 Answers: 0 Comments: 0

Compute the min−max polynomial q_1 ^∗ (x) to e^x on interval [−1, 1]. Anyone??

$$\mathrm{Compute}\:\mathrm{the}\:\mathrm{min}−\mathrm{max}\:\mathrm{polynomial} \\ $$$$\mathrm{q}_{\mathrm{1}} ^{\ast} \left(\mathrm{x}\right)\:\mathrm{to}\:\mathrm{e}^{\mathrm{x}} \:\mathrm{on}\:\mathrm{interval}\:\left[−\mathrm{1},\:\mathrm{1}\right]. \\ $$$$ \\ $$$$\mathrm{Anyone}?? \\ $$

Question Number 191477 Answers: 1 Comments: 0

Prove that ((tan y+sec y−1)/(tan y−sec y+1))=tan y+sec y

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$ \\ $$$$\frac{\mathrm{tan}\:\mathrm{y}+\mathrm{sec}\:\mathrm{y}−\mathrm{1}}{\mathrm{tan}\:\mathrm{y}−\mathrm{sec}\:\mathrm{y}+\mathrm{1}}=\mathrm{tan}\:\mathrm{y}+\mathrm{sec}\:\mathrm{y} \\ $$$$ \\ $$

Question Number 191458 Answers: 2 Comments: 0

Question Number 191457 Answers: 2 Comments: 3

Question Number 191456 Answers: 0 Comments: 0

Question Number 191455 Answers: 2 Comments: 0

Question Number 191454 Answers: 1 Comments: 2

Question Number 191516 Answers: 0 Comments: 0

Question Number 191451 Answers: 1 Comments: 0

x+(1/x)=5 and x∙y=4 find x^2 +((1/y))^2 =?

$${x}+\frac{\mathrm{1}}{{x}}=\mathrm{5}\:\:{and}\:{x}\centerdot{y}=\mathrm{4}\:{find} \\ $$$${x}^{\mathrm{2}} +\left(\frac{\mathrm{1}}{{y}}\right)^{\mathrm{2}} =? \\ $$

Question Number 191450 Answers: 0 Comments: 0

x+(1/x)=5 and x∙y=4 faind x^4 +((1/y))^3 =?

$${x}+\frac{\mathrm{1}}{{x}}=\mathrm{5}\:\:{and}\:\:{x}\centerdot{y}=\mathrm{4} \\ $$$${faind}\:\:\:\:{x}^{\mathrm{4}} +\left(\frac{\mathrm{1}}{{y}}\right)^{\mathrm{3}} =? \\ $$

Question Number 191445 Answers: 0 Comments: 0

Factorize (x − 998)(x − 999)−(((1000)/(999^2 )))

$$\mathrm{Factorize} \\ $$$$\left({x}\:−\:\mathrm{998}\right)\left({x}\:−\:\mathrm{999}\right)−\left(\frac{\mathrm{1000}}{\mathrm{999}^{\mathrm{2}} }\right) \\ $$

Question Number 191443 Answers: 2 Comments: 0

(3^(100) + 2^(100) ), 4^(100) which is greater? Give proof.

$$\left(\mathrm{3}^{\mathrm{100}} \:+\:\mathrm{2}^{\mathrm{100}} \right),\:\mathrm{4}^{\mathrm{100}} \:\mathrm{which}\:\mathrm{is}\:\mathrm{greater}? \\ $$$$\mathrm{Give}\:\mathrm{proof}. \\ $$

Question Number 191442 Answers: 0 Comments: 0

Question Number 191440 Answers: 0 Comments: 0

Question Number 191439 Answers: 0 Comments: 0

Question Number 191436 Answers: 1 Comments: 0

Factorize x^2 + (1/a) (bx + c)

$$\mathrm{Factorize} \\ $$$$\boldsymbol{{x}}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\boldsymbol{{a}}}\:\left(\boldsymbol{{bx}}\:+\:\boldsymbol{{c}}\right) \\ $$

Question Number 191435 Answers: 0 Comments: 0

It is given that I_1 =∫xg[x(1−x)]dx , I_2 = ∫g[x(1−x)]dx. Find (I_2 /I_1 ). Thanks.

$$\:{It}\:{is}\:{given}\:{that}\:{I}_{\mathrm{1}} =\int{xg}\left[{x}\left(\mathrm{1}−{x}\right)\right]{dx}\:,\: \\ $$$${I}_{\mathrm{2}} =\:\int{g}\left[{x}\left(\mathrm{1}−{x}\right)\right]{dx}.\:{Find}\:\frac{{I}_{\mathrm{2}} }{{I}_{\mathrm{1}} }.\:{Thanks}. \\ $$

Question Number 191410 Answers: 1 Comments: 0

Three villages A, B and C are on a straight road and B is the mid-way between A and C. A motor cyclist moving with a uniform acceleration passes A, B and C. The speeds with which the motorcyclist passes A and C are 20ms^(−1) and 40ms^− respectively. find the speed with which the motor cyclist passes B.

$$\:{Three}\:{villages}\:{A},\:{B}\:{and}\:{C}\:{are}\:{on}\:{a}\: \\ $$$$\:{straight}\:{road}\:{and}\:{B}\:{is}\:{the}\:{mid}-{way} \\ $$$${between}\:{A}\:{and}\:{C}.\:{A}\:{motor}\:{cyclist} \\ $$$${moving}\:{with}\:{a}\:{uniform}\:{acceleration} \\ $$$${passes}\:{A},\:{B}\:{and}\:{C}.\:{The}\:{speeds}\:{with}\: \\ $$$${which}\:{the}\:{motorcyclist}\:{passes}\:{A}\:{and}\: \\ $$$${C}\:{are}\:\mathrm{20}{ms}^{−\mathrm{1}} \:{and}\:\mathrm{40}{ms}^{−} \:{respectively}. \\ $$$${find}\:{the}\:{speed}\:{with}\:{which}\:{the}\:{motor} \\ $$$${cyclist}\:{passes}\:{B}. \\ $$

Question Number 191409 Answers: 1 Comments: 0

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