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Answer:
The angle it turns through if it sweeps an area of 48 cm² is 448.8°
Step-by-step explanation:
If the length of a minute hand of a clock is 3.5cm, to find the angle it turns through if it sweeps an area of 48 cm, we will follow the steps below;
area of a sector = Ф/360 × πr²
where Ф is the angle, r is the radius π is a constant
from the question given, the length of the minute hand is 3.5 cm, this implies that radius r = 3.5
Ф =? area of the sector= 48 cm² π =
we can now go ahead to substitute the values into the formula and solve Ф
area of a sector = Ф/360 × πr²
48 = Ф/360 × × (3.5)²
48 = Ф/360 × ×12.25
48 = 269.5Ф / 2520
multiply both-side of the equation by 2520
48×2520 = 269.5Ф
120960 = 269.5Ф
divide both-side of the equation by 269.5
448.8≈Ф
Ф = 448.8°
The angle it turns through if it sweeps an area of 48 cm² is 448.8°
Answer:
(x + 6)² + 16 = 0
Step-by-step explanation:
To complete the square we will first need to get our equation to look like: x² + bx = c
Here we have x² + bx + c = 0 → x² + 12x + 52 = 0
- First we need to subtract our c, in this case 52, from both sides to get x² + 12x = -52
- We then need to add
to both sides of the equation
- Here our b value is 12, so plugging this into our formula we get
- Adding 36 to both sides our equation becomes: x² + 12x + 36 = -52 + 36
- Then combining like terms on the right side we get x² + 12x + 36 = -16
- Now making our left side of the equation into a perfect square we get: (x + 6)² = -16
- Finally adding the 16 to both sides of the equation we get: (x + 6)² + 16 = 0