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Question Number 86789 by TawaTawa1 last updated on 31/Mar/20

Commented by jagoll last updated on 31/Mar/20

Answered by jagoll last updated on 31/Mar/20

Commented by jagoll last updated on 31/Mar/20

miss tawa. i think you can solve it

$$\mathrm{miss}\:\mathrm{tawa}.\:\mathrm{i}\:\mathrm{think}\:\mathrm{you}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{it} \\ $$

Commented by TawaTawa1 last updated on 31/Mar/20

I appreciate your time sir. God bless you

$$\mathrm{I}\:\mathrm{appreciate}\:\mathrm{your}\:\mathrm{time}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you} \\ $$

Commented by TawaTawa1 last updated on 31/Mar/20

I did not understand the first step.

$$\mathrm{I}\:\mathrm{did}\:\mathrm{not}\:\mathrm{understand}\:\mathrm{the}\:\mathrm{first}\:\mathrm{step}. \\ $$

Commented by jagoll last updated on 31/Mar/20

i use descartes theorem

$$\mathrm{i}\:\mathrm{use}\:\mathrm{descartes}\:\mathrm{theorem} \\ $$

Commented by TawaTawa1 last updated on 31/Mar/20

But sir, you have not find the area. What is the area sir please. Area of the shaded

$$\mathrm{But}\:\mathrm{sir},\:\mathrm{you}\:\mathrm{have}\:\mathrm{not}\:\mathrm{find}\:\mathrm{the}\:\mathrm{area}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{sir}\:\mathrm{please}. \\ $$$$\mathrm{Area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{shaded} \\ $$

Commented by jagoll last updated on 31/Mar/20

the area can already be calculated by substracting the area of the triangle with the area of the circle

$$\mathrm{the}\:\mathrm{area}\:\mathrm{can}\:\mathrm{already}\:\mathrm{be}\:\mathrm{calculated} \\ $$$$\mathrm{by}\:\mathrm{substracting}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{triangle}\:\mathrm{with}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle} \\ $$

Commented by TawaTawa1 last updated on 31/Mar/20

The three circle?

$$\mathrm{The}\:\mathrm{three}\:\mathrm{circle}? \\ $$

Commented by TawaTawa1 last updated on 01/Apr/20

Sir jagoll please complete solution. Please sir.

$$\mathrm{Sir}\:\mathrm{jagoll}\:\mathrm{please}\:\mathrm{complete}\:\mathrm{solution}.\:\mathrm{Please}\:\mathrm{sir}. \\ $$

Commented by jagoll last updated on 01/Apr/20

my answer same with mr w

$$\mathrm{my}\:\mathrm{answer}\:\mathrm{same}\:\mathrm{with}\:\mathrm{mr}\:\mathrm{w}\: \\ $$

Answered by mr W last updated on 31/Mar/20

((5/2))^2 +(5−r)^2 =((5/2)+r)^2 ⇒r=(5/3) tan θ=((5−(5/3))/(5/2))=(4/3) A_(shaded) =((5(5−(5/3)))/2)−2×(1/2)((5/2))^2 θ−(1/2)((5/3))^2 (π−2θ) =((25)/3)−((25)/4)θ−(1/2)×((25)/9)(π−2θ) =((25)/(36))(12−2π−5θ) =((25)/(36))(12−2π−5 tan^(−1) (4/3))

$$\left(\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} +\left(\mathrm{5}−{r}\right)^{\mathrm{2}} =\left(\frac{\mathrm{5}}{\mathrm{2}}+{r}\right)^{\mathrm{2}} \\ $$$$\Rightarrow{r}=\frac{\mathrm{5}}{\mathrm{3}} \\ $$$$\mathrm{tan}\:\theta=\frac{\mathrm{5}−\frac{\mathrm{5}}{\mathrm{3}}}{\frac{\mathrm{5}}{\mathrm{2}}}=\frac{\mathrm{4}}{\mathrm{3}} \\ $$$${A}_{{shaded}} =\frac{\mathrm{5}\left(\mathrm{5}−\frac{\mathrm{5}}{\mathrm{3}}\right)}{\mathrm{2}}−\mathrm{2}×\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} \theta−\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{5}}{\mathrm{3}}\right)^{\mathrm{2}} \left(\pi−\mathrm{2}\theta\right) \\ $$$$=\frac{\mathrm{25}}{\mathrm{3}}−\frac{\mathrm{25}}{\mathrm{4}}\theta−\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{25}}{\mathrm{9}}\left(\pi−\mathrm{2}\theta\right) \\ $$$$=\frac{\mathrm{25}}{\mathrm{36}}\left(\mathrm{12}−\mathrm{2}\pi−\mathrm{5}\theta\right) \\ $$$$=\frac{\mathrm{25}}{\mathrm{36}}\left(\mathrm{12}−\mathrm{2}\pi−\mathrm{5}\:\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{4}}{\mathrm{3}}\right) \\ $$

Commented by TawaTawa1 last updated on 31/Mar/20

God bless you sir.

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

Commented by TawaTawa1 last updated on 01/Apr/20

Sir i got − 180.51 when i press calculator. Can the area be negative or there is a mistake somewhere.

$$\mathrm{Sir}\:\mathrm{i}\:\mathrm{got}\:\:\:−\:\mathrm{180}.\mathrm{51}\:\:\:\mathrm{when}\:\mathrm{i}\:\mathrm{press}\:\mathrm{calculator}. \\ $$$$\mathrm{Can}\:\mathrm{the}\:\mathrm{area}\:\mathrm{be}\:\mathrm{negative}\:\mathrm{or}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{mistake}\:\mathrm{somewhere}. \\ $$

Commented by mr W last updated on 01/Apr/20

sorry. i can′t teach you how to use calculator. it seems you don′t make difference between rad and degree, i just guess.

$${sorry}.\:{i}\:{can}'{t}\:{teach}\:{you}\:{how}\:{to}\:{use}\: \\ $$$${calculator}.\:{it}\:{seems}\:{you}\:{don}'{t}\:{make} \\ $$$${difference}\:{between}\:{rad}\:{and}\:{degree}, \\ $$$${i}\:{just}\:{guess}. \\ $$

Commented by john santu last updated on 01/Apr/20

= 0.750235

$$=\:\mathrm{0}.\mathrm{750235} \\ $$

Commented by TawaTawa1 last updated on 01/Apr/20

Sir did you use π = 180 degree.

$$\boldsymbol{\mathrm{Sir}}\:\boldsymbol{\mathrm{did}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{use}}\:\:\:\pi\:\:=\:\:\mathrm{180}\:\mathrm{degree}. \\ $$

Commented by john santu last updated on 01/Apr/20

Commented by TawaTawa1 last updated on 01/Apr/20

Ohh. You work in radian sir. I appreciate.

$$\mathrm{Ohh}.\:\mathrm{You}\:\mathrm{work}\:\mathrm{in}\:\mathrm{radian}\:\mathrm{sir}.\:\:\mathrm{I}\:\mathrm{appreciate}. \\ $$

Commented by TawaTawa1 last updated on 01/Apr/20

Am sorry sir mrW. I press i work in degree.

$$\mathrm{Am}\:\mathrm{sorry}\:\mathrm{sir}\:\:\mathrm{mrW}.\:\:\mathrm{I}\:\mathrm{press}\:\mathrm{i}\:\mathrm{work}\:\mathrm{in}\:\mathrm{degree}. \\ $$

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