Evaluate (12.78 × 10⁻³)/9 × 10⁻¹ and find angles ACB and ADB.

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Here are the solutions to the remaining questions. 4. Evaluate ((12.78 × 10⁻³))/(9 × 10⁻¹) expressing your answer in: Step 1: Evaluate the expression. (12.78 × 10⁻³)/(9 × 10⁻¹) = (12.78/9) × ((10⁻³)/(10⁻¹)); = 1.42 × 10⁻³⁻⁽⁻¹⁾; = 1.42 × 10⁻³⁺¹; = 1.42 × 10⁻² a) Standard form The number is already in standard form. 1.42 × 10⁻² b) Convert to 3 significant figures The number 1.42 × 10⁻² has three significant figures (1, 4, 2). 1.42 × 10⁻² c) In three decimal places First, convert to decimal form: 1.42 × 10⁻² = 0.0142 Now, round to three decimal places. The fourth decimal place is 2, so we round down. 0.014 5. Find angle ACB and angle ADB The image shows a circle with center O. The angle ∠ AOB = 50° is the central angle subtended by the arc AB. Angles ∠ ACB and ∠ ADB are angles subtended by the same arc AB at the circumference. Step 1: Apply the circle theorem for angles subtended by the same arc. The angle subtended by an arc at the center is twice the angle subtended by the same arc at any point on the remaining part of the circle. Therefore, ∠ ACB = 1/2 ∠ AOB. Step 2: Calculate ∠ ACB. ∠ ACB = 1/2 × 50°; ∠ ACB = 25° Step 3: Calculate ∠ ADB. Angles subtended by the same arc in the same segment are equal. Since ∠ ADB is also subtended by arc AB in the same segment as ∠ ACB, they are equal. ∠ ADB = ∠ ACB; ∠ ADB = 25° The value of ∠ ACB is 25° and the value of ∠ ADB is 25°.

Evaluate (12.78 x 10⁻³)/9 x 10⁻¹ and find angles ACB and ADB.

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Step-by-step solution

Part a

Part b
$1.42 \times 10^{-2}$

Part c· 3 steps0.014

Apply the circle theorem for angles subtended by the same arc.

Calculate $\angle ACB$ .

Calculate $\angle ADB$ .

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