A circle has a center at #(1 ,2 )# and passes through #(4 ,2 )#. What is the length of an arc covering #pi /4 # radians on the circle?

Answer 1

I found #28.3# units but have a look at my method.

I would first find the radius #r# as the distance between the center and your given point: #r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)=sqrt((4-1)^2+(2-2)^2)=sqrt(3^2+0^2)=3#
Then I would consider that the length #s# of an arc of angle #theta# (in radians) will be: #s=r*theta# so that: #s=3*pi/4=3/4*3.14=28.27~~28.3# units
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Answer 2

To find the length of an arc covering (\frac{\pi}{4}) radians on the circle with a center at ((1, 2)) and passing through ((4, 2)), follow these steps:

  1. Find the radius of the circle using the distance formula between the center ((1, 2)) and a point on the circle ((4, 2)).
  2. Use the formula for the circumference of a circle to find the total circumference.
  3. Calculate the length of the arc by multiplying the fraction of the circumference corresponding to (\frac{\pi}{4}) radians.

Let's go through the calculations:

  1. Radius = (\sqrt{(4 - 1)^2 + (2 - 2)^2} = \sqrt{3^2 + 0^2} = 3).
  2. Circumference = (2\pi \times \text{radius} = 2\pi \times 3 = 6\pi).
  3. Length of arc (= \frac{\text{arc angle}}{2\pi} \times \text{circumference}). Length of arc (= \frac{\frac{\pi}{4}}{2\pi} \times 6\pi = \frac{1}{8} \times 6\pi = \frac{3\pi}{4}).

Therefore, the length of the arc covering (\frac{\pi}{4}) radians on the circle is (\frac{3\pi}{4}) units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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