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AllQuestion and Answers: Page 322

Question Number 187774 Answers: 2 Comments: 0

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Question Number 187762 Answers: 0 Comments: 0

if point P is any point inside △ABC with side lenghts a,b and c. prove that; ((PA)/a) + ((PB)/b) + ((PC)/c) ≥ (√(3 ))

$$ \\ $$$$\:\:\:\:\:\:\boldsymbol{{if}}\:\boldsymbol{{point}}\:\boldsymbol{{P}}\:\:\boldsymbol{{is}}\:\boldsymbol{{any}}\:\boldsymbol{{point}}\:\boldsymbol{{inside}}\:\:\: \\ $$$$\:\:\:\:\:\:\:\bigtriangleup\boldsymbol{{ABC}}\:\:\boldsymbol{{with}}\:\boldsymbol{{side}}\:\boldsymbol{{lenghts}}\:\boldsymbol{{a}},\boldsymbol{{b}}\:\boldsymbol{{and}}\:\boldsymbol{{c}}.\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{{prove}}\:\boldsymbol{{that}}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\boldsymbol{{PA}}}{\boldsymbol{{a}}}\:+\:\frac{\boldsymbol{{PB}}}{\boldsymbol{{b}}}\:+\:\frac{\boldsymbol{{PC}}}{\boldsymbol{{c}}}\:\geqslant\:\sqrt{\mathrm{3}\:} \\ $$$$ \\ $$

Question Number 187760 Answers: 1 Comments: 2

Question Number 187754 Answers: 1 Comments: 0

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$$\: \\ $$

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Question Number 187730 Answers: 1 Comments: 0

Evaluate lim(x,y)→(0,0) ((x^2 (y−1)^2 )/(x^2 +(y−1)^2 ))

$$\:{Evaluate}\: \\ $$$${lim}\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)\:\frac{{x}^{\mathrm{2}} \left({y}−\mathrm{1}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} +\left({y}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$

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Question Number 187716 Answers: 2 Comments: 0

Question Number 187714 Answers: 1 Comments: 2

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Question Number 187711 Answers: 0 Comments: 0

Evaluate lim(x,y)→(1,0) ((xy−y)/(x^2 +y^2 −2x+1))

$$\:{Evaluate}\:\: \\ $$$$\:\:\:{lim}\left({x},{y}\right)\rightarrow\left(\mathrm{1},\mathrm{0}\right)\:\:\frac{{xy}−{y}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}} \\ $$

Question Number 187703 Answers: 2 Comments: 0

∫ (1/(5x^2 − 2x − 4)) dx

$$\int\:\frac{\mathrm{1}}{\mathrm{5x}^{\mathrm{2}} \:\:−\:\:\mathrm{2x}\:\:−\:\:\mathrm{4}}\:\mathrm{dx} \\ $$

Question Number 187701 Answers: 1 Comments: 0

Question Number 187700 Answers: 0 Comments: 1

Find minimum area of the part y=x^2 and y=kx(x^2 −k), k>0

$$\:{Find}\:{minimum}\:{area}\:{of}\:{the}\:{part} \\ $$$$\:{y}={x}^{\mathrm{2}} \:{and}\:{y}={kx}\left({x}^{\mathrm{2}} −{k}\right),\:{k}>\mathrm{0}\: \\ $$

Question Number 187695 Answers: 2 Comments: 0

If , f( x )= (( sin_ (cos (x) ))/( ^ (√( (π/x))))) ⇒ f ′ ((( π)/2) ) = ?

$$ \\ $$$$\:\:\:{If}\:,\:\:{f}\left(\:{x}\:\right)=\:\frac{\:\:{si}\underset{} {{n}}\:\left({cos}\:\left({x}\right)\:\right)}{\overset{} {\:}\sqrt{\:\frac{\pi}{{x}}}} \\ $$$$\:\:\:\:\Rightarrow\:\:\:{f}\:'\:\left(\frac{\:\pi}{\mathrm{2}}\:\right)\:=\:? \\ $$

Question Number 187689 Answers: 2 Comments: 0

Question Number 187691 Answers: 0 Comments: 0

Misalkan P sebarang titik didalam 𝚫ABC sehingga PD, PE , dan PF masing masing tegak lurus dengan sisi BC,CA dan AB Jika panjang sisi BC,CA dan AB masing masing dinotasikan dengan a,b dan c. bila x,y dan z adalah sebarang bilangan real yang memenuhi xy + yz +xz ≥ 0 Tunjukkan bahwa; (y + z) ((PA)/a) + (z+x)((PB)/b) + (x + y) ((PC)/c) ≥ 2(√(xy + yz +zx))

$$\: \\ $$$$\:\:\:\boldsymbol{{Misalkan}}\:\boldsymbol{{P}}\:\boldsymbol{{sebarang}}\:\boldsymbol{{titik}}\:\boldsymbol{{didalam}}\:\boldsymbol{\Delta{ABC}}\:\:\boldsymbol{{sehingga}}\:\boldsymbol{{PD}},\:\boldsymbol{{PE}}\:,\:\boldsymbol{{dan}}\:\boldsymbol{{PF}}\:\: \\ $$$$\:\:\:\boldsymbol{{masing}}\:\boldsymbol{{masing}}\:\boldsymbol{{tegak}}\:\boldsymbol{{lurus}}\:\:\boldsymbol{{dengan}}\:\boldsymbol{{sisi}}\:\boldsymbol{{BC}},\boldsymbol{{CA}}\:\boldsymbol{{dan}}\:\boldsymbol{{AB}} \\ $$$$\:\:\:\boldsymbol{{Jika}}\:\boldsymbol{{panjang}}\:\boldsymbol{{sisi}}\:\boldsymbol{{BC}},\boldsymbol{{CA}}\:\boldsymbol{{dan}}\:\boldsymbol{{AB}}\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\boldsymbol{{masing}}\:\boldsymbol{{masing}}\:\boldsymbol{{dinotasikan}}\:\boldsymbol{{dengan}}\:\boldsymbol{{a}},\boldsymbol{{b}}\:\boldsymbol{{dan}}\:\boldsymbol{{c}}. \\ $$$$\:\:\:\boldsymbol{{bila}}\:\boldsymbol{{x}},\boldsymbol{{y}}\:\boldsymbol{{dan}}\:\boldsymbol{{z}}\:\boldsymbol{{adalah}}\:\boldsymbol{{sebarang}}\:\boldsymbol{{bilangan}}\:\boldsymbol{{real}}\:\boldsymbol{{yang}}\:\boldsymbol{{memenuhi}}\:\boldsymbol{{xy}}\:+\:\boldsymbol{{yz}}\:+\boldsymbol{{xz}}\:\geqslant\:\mathrm{0}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{Tunjukkan}}\:\boldsymbol{{bahwa}}; \\ $$$$\:\:\:\:\left(\boldsymbol{{y}}\:+\:\boldsymbol{{z}}\right)\:\frac{\boldsymbol{{PA}}}{\boldsymbol{{a}}}\:+\:\left(\boldsymbol{{z}}+\boldsymbol{{x}}\right)\frac{\boldsymbol{{PB}}}{\boldsymbol{{b}}}\:\:+\:\left(\boldsymbol{{x}}\:+\:\boldsymbol{{y}}\right)\:\frac{\boldsymbol{{PC}}}{\boldsymbol{{c}}}\:\:\geqslant\:\mathrm{2}\sqrt{\boldsymbol{{xy}}\:+\:\boldsymbol{{yz}}\:+\boldsymbol{{zx}}}\:\:\: \\ $$$$ \\ $$

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Question Number 187675 Answers: 1 Comments: 1

Question Number 187672 Answers: 2 Comments: 0

4^(−(1/x)) +6^(−(1/x)) = 9^(−(1/x)) x∈R

$$\mathrm{4}^{−\frac{\mathrm{1}}{{x}}} +\mathrm{6}^{−\frac{\mathrm{1}}{{x}}} \:=\:\mathrm{9}^{−\frac{\mathrm{1}}{{x}}} \\ $$$${x}\in\mathbb{R} \\ $$

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