Question-89412

Question Number 89412 by I want to learn more last updated on 17/Apr/20

Commented by I want to learn more last updated on 17/Apr/20

Please is the answer: ((39)/8) square unit.

$$\mathrm{Please}\:\mathrm{is}\:\mathrm{the}\:\mathrm{answer}:\:\:\:\frac{\mathrm{39}}{\mathrm{8}}\:\mathrm{square}\:\mathrm{unit}. \\ $$

Commented by jagoll last updated on 17/Apr/20

x = (1/4)(4+3y) y^2 = 4x ⇒ x=(1/4)y^2 (1/4)y^2 = (3/4)y+1 (1/4)y^2 −(3/4)y−1=0 Δ= (9/(16))−4((1/4))(−1)= ((25)/(16)) area = ((Δ(√Δ))/(6.a^2 )) = ((((25)/(16))×(5/4))/(6×(1/(16)))) = ((125)/(64))×((16)/6) = ((125)/(4×6)) = ((125)/(24))

$${x}\:=\:\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{4}+\mathrm{3}{y}\right)\: \\ $$$${y}^{\mathrm{2}} \:=\:\mathrm{4}{x}\:\Rightarrow\:{x}=\frac{\mathrm{1}}{\mathrm{4}}{y}^{\mathrm{2}} \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}{y}^{\mathrm{2}} \:=\:\frac{\mathrm{3}}{\mathrm{4}}{y}+\mathrm{1} \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}{y}^{\mathrm{2}} −\frac{\mathrm{3}}{\mathrm{4}}{y}−\mathrm{1}=\mathrm{0} \\ $$$$\Delta=\:\frac{\mathrm{9}}{\mathrm{16}}−\mathrm{4}\left(\frac{\mathrm{1}}{\mathrm{4}}\right)\left(−\mathrm{1}\right)=\:\frac{\mathrm{25}}{\mathrm{16}} \\ $$$${area}\:=\:\frac{\Delta\sqrt{\Delta}}{\mathrm{6}.{a}^{\mathrm{2}} }\:=\:\frac{\frac{\mathrm{25}}{\mathrm{16}}×\frac{\mathrm{5}}{\mathrm{4}}}{\mathrm{6}×\frac{\mathrm{1}}{\mathrm{16}}} \\ $$$$=\:\frac{\mathrm{125}}{\mathrm{64}}×\frac{\mathrm{16}}{\mathrm{6}}\:=\:\frac{\mathrm{125}}{\mathrm{4}×\mathrm{6}}\:=\:\frac{\mathrm{125}}{\mathrm{24}} \\ $$

Commented by jagoll last updated on 17/Apr/20

Commented by I want to learn more last updated on 17/Apr/20

Commented by I want to learn more last updated on 17/Apr/20

Sir, wolfram says ((125)/(24)), where is the error sir or wolfram wrong. Thanks

$$\mathrm{Sir},\:\mathrm{wolfram}\:\mathrm{says}\:\:\:\:\frac{\mathrm{125}}{\mathrm{24}},\:\:\:\mathrm{where}\:\mathrm{is}\:\mathrm{the}\:\mathrm{error}\:\mathrm{sir}\:\mathrm{or}\:\mathrm{wolfram}\:\mathrm{wrong}.\:\mathrm{Thanks} \\ $$

Commented by I want to learn more last updated on 17/Apr/20