Read the passage below and fill in each blank space with the most appropriate word.

Biology
Read the passage below and fill in each blank space with the most appropriate word.

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Answer

2×∠AOM=2×30∘=60∘.2 \times \angle AOM = 2 \times 30^\circ = 60^\circ.

1. Mesure de l'angle AOBAOB

Step 1: Le point BB est le symétrique de MM par rapport à la droite (OA)(OA).

Par symétrie axiale,

∠AOB=2×∠AOM=2×30∘=60∘.\angle AOB = 2 \times \angle AOM = 2 \times 30^\circ = 60^\circ.

Step 2: Conversion en radians.

Formule : θrad=θdeg×π180\theta_{\rm rad} = \theta_{\rm deg} \times \dfrac{\pi}{180}.

60∘×π180=60π180=π3 rad.60^\circ \times \dfrac{\pi}{180} = \dfrac{60\pi}{180} = \dfrac{\pi}{3} \, \rm rad.

∠AOB=60∘\angle AOB = 60^\circ ou π3 rad\dfrac{\pi}{3} \, \rm rad.

2. Longueur de l'arc AMAM

Step 1: Angle central ∠AOM=30∘\angle AOM = 30^\circ.

Conversion en radians :

30∘×π180=π6 rad.30^\circ \times \dfrac{\pi}{180} = \dfrac{\pi}{6} \, \rm rad.

Step 2: Formule de la longueur d'arc : l=rθl = r \theta (θ\theta en radians).

l=7 cm×π6=7π6 cm.l = 7 \, \rm cm \times \dfrac{\pi}{6} = \dfrac{7\pi}{6} \, \rm cm.

3. Mesure de l'angle MCDMCD

Step 1: Positions angulaires (par rapport à OAOA) : MM à 30∘30^\circ, CC à 90∘90^\circ, DD à 270∘270^\circ.

Angle central ∠MOC=90∘−30∘=60∘\angle MOC = 90^\circ - 30^\circ = 60^\circ.

Longueur MCMC (formule des cordes : 2rsin⁡(θ2)2r \sin(\frac{\theta}{2})) :

MC=2×7 cm×sin⁡(60∘2)=14 cm×sin⁡30∘=14×0.5=7 cm.MC = 2 \times 7 \, \rm cm \times \sin\left(\frac{60^\circ}{2}\right) = 14 \, \rm cm \times \sin 30^\circ = 14 \times 0.5 = 7 \, \rm cm.

Step 2: Longueur CDCD (diamètre) :

CD=2×7 cm=14 cm.CD = 2 \times 7 \, \rm cm = 14 \, \rm cm.

Step 3: Angle central mineur ∠MOD=360∘−(270∘−30∘)=120∘\angle MOD = 360^\circ - (270^\circ - 30^\circ) = 120^\circ.

Longueur MDMD :

MD=2×7 cm×sin⁡(120∘2)=14 cm×sin⁡60∘=14×32=73 cm.MD = 2 \times 7 \, \rm cm \times \sin\left(\frac{120^\circ}{2}\right) = 14 \, \rm cm \times \sin 60^\circ = 14 \times \frac{\sqrt{3}}{2} = 7\sqrt{3} \, \rm cm.

Step 4: Théorème des cosinus dans △MCD\triangle MCD (angle au CC) :

cos⁡(∠MCD)=MC2+CD2−MD22⋅MC⋅CD.\cos(\angle MCD) = \frac{MC^2 + CD^2 - MD^2}{2 \cdot MC \cdot CD}.

Numérateur :

MC2=72=49 cm2,CD2=142=196 cm2,MD2=(73)2=147 cm2,MC^2 = 7^2 = 49 \, \rm cm^2, \quad CD^2 = 14^2 = 196 \, \rm cm^2, \quad MD^2 = (7\sqrt{3})^2 = 147 \, \rm cm^2, 49+196−147=98 cm2.49 + 196 - 147 = 98 \, \rm cm^2.

Dénominateur :

2×7 cm×14 cm=196 cm2.2 \times 7 \, \rm cm \times 14 \, \rm cm = 196 \, \rm cm^2. cos⁡(∠MCD)=98196=12.\cos(\angle MCD) = \frac{98}{196} = \frac{1}{2}. ∠MCD=cos⁡−1(12)=60∘.\angle MCD = \cos^{-1}\left(\frac{1}{2}\right) = 60^\circ.

∠MCD=60∘\angle MCD = 60^\circ.

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1. Mesure de l'angle AOB Step 1: Le point B est le symétrique de M par rapport à la droite (OA).

Read the passage below and fill in each blank space with the most appropriate word.
Biology

This biology question covers important biological concepts and processes. The step-by-step explanation below helps you understand the underlying mechanisms and reasoning.

ScanSolve AI Answer
1. Mesure de l'angle AOB Step 1: Le point B est le symétrique de M par rapport à la droite (OA). Par symétrie axiale, AOB = 2 × AOM = 2 × 30^ = 60^. Step 2: Conversion en radians. Formule : _ rad = _ deg × ()/(180). 60^ × ()/(180) = (60)/(180) = ()/(3) \, rad. AOB = 60^ ou ()/(3) \, rad. 2. Longueur de l'arc AM Step 1: Angle central AOM = 30^. Conversion en radians : 30^ × ()/(180) = ()/(6) \, rad. Step 2: Formule de la longueur d'arc : l = r ( en radians). l = 7 \, cm × ()/(6) = (7)/(6) \, cm. 3. Mesure de l'angle MCD Step 1: Positions angulaires (par rapport à OA) : M à 30^, C à 90^, D à 270^. Angle central MOC = 90^ - 30^ = 60^. Longueur MC (formule des cordes : 2r (()/(2))) : MC = 2 × 7 \, cm × ((60^)/(2)) = 14 \, cm × 30^ = 14 × 0.5 = 7 \, cm. Step 2: Longueur CD (diamètre) : CD = 2 × 7 \, cm = 14 \, cm. Step 3: Angle central mineur MOD = 360^ - (270^ - 30^) = 120^. Longueur MD : MD = 2 × 7 \, cm × ((120^)/(2)) = 14 \, cm × 60^ = 14 × sqrt(3)2 = 7sqrt(3) \, cm. Step 4: Théorème des cosinus dans MCD (angle au C) : ( MCD) = (MC^2 + CD^2 - MD^2)/(2 · MC · CD). Numérateur : MC^2 = 7^2 = 49 \, cm^2, CD^2 = 14^2 = 196 \, cm^2, MD^2 = (7sqrt(3))^2 = 147 \, cm^2, 49 + 196 - 147 = 98 \, cm^2. Dénominateur : 2 × 7 \, cm × 14 \, cm = 196 \, cm^2. ( MCD) = (98)/(196) = (1)/(2). MCD = ^-1((1)/(2)) = 60^. MCD = 60^.