A circle has a center at #(3 ,0 )# and passes through #(1 ,1 )#. What is the length of an arc covering #(3pi ) /4 # radians on the circle?

Answer 1

The length of the arc is #=5.27#

The radius of the circle is

#r=sqrt((1-3)^2+(1-0)^2)#
#=sqrt(2^2+1^2)#
#=sqrt(5)#

The length of the arc is

#s=rtheta=sqrt5*3/4pi#
#=3sqrt5/4pi#
#=5.27#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the length of an arc covering ( \frac{3\pi}{4} ) radians on the circle, we use the formula for the length of an arc on a circle:

[ \text{Arc Length} = \text{Radius} \times \text{Angle (in radians)} ]

First, we need to find the radius of the circle. We can use the distance formula to find the distance between the center of the circle at (3, 0) and a point on the circle at (1, 1).

[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]

[ \text{Distance} = \sqrt{(1 - 3)^2 + (1 - 0)^2} ]

[ \text{Distance} = \sqrt{(-2)^2 + (1)^2} ]

[ \text{Distance} = \sqrt{4 + 1} ]

[ \text{Distance} = \sqrt{5} ]

So, the radius of the circle is ( \sqrt{5} ).

Now, we can find the length of the arc covering ( \frac{3\pi}{4} ) radians:

[ \text{Arc Length} = \sqrt{5} \times \frac{3\pi}{4} ]

[ \text{Arc Length} = \frac{3\pi\sqrt{5}}{4} ]

Therefore, the length of the arc covering ( \frac{3\pi}{4} ) radians on the circle is ( \frac{3\pi\sqrt{5}}{4} ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7