In circle T with m∠STU=54 and ST=18 units find area of sector STU. Round to the nearest hundredth.
2 answers:
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Answer:
The length of DC in meters is ⇒ A
Step-by-step explanation:
In the circle O
∵ AB passing through O
∴ AB is a diameter
∵ D is on the circle
∴ ∠ADB is an inscribed angle subtended by arc AB
∵ Arc AB is half the circle
→ That means its measure is 180°
∴ m∠ADB = × 180° = 90°
In ΔADB
∵ m∠ADB = 90°
∵ AD = 5 m
∵ BD = 12 m
→ By using Pythagorase Theorem
∵ (AB)² = (AD)² + (DB)²
∴ (AB)² = (5)² + (12)²
∴ (AB)² = 25 + 144 = 169
→ Take square root for both sides
∴ AB = 13 m
∵ ∠ADB is a right angle
∵ DC ⊥ AB
∴ DC × AB = AD × DB
→ Substitute the lengths of AB, AD, and DB
∵ DC × 13 = 5 × 12
∴ 13 DC = 60
→ Divide both sides by 13
∴ DC = m
∴ The length of DC in meters is
Answer:
Complete the square on x by adding <u>49</u> to both sides.
Complete the square on y by adding <u>81</u> to both sides.
Step-by-step explanation:
We have been given an equation . We are asked to complete the squares for both x and y.
We know to complete a square, we add the half the square of coefficient of x or y term.
Upon looking at our given equation, we can see that coefficient of x is 14 and coefficient of y is 18.
Now, we will add 49 to complete the x term square and 81 to complete y term square on both sides of our given equation as:
Applying the perfect square formula , we will get:
Therefore, We can complete the square on x by adding <u>49</u> to both sides and the square on y by adding <u>81</u> to both sides.