one way to resize a ring is to fill a bar into the ring.suppose a ring that is 20 mm in diameter has to be resized to fit a fingure 16 mm n diameter
what is the length of the bar that should be inserted in order to make the ring fit the fingure? ( Hint: write an equation of the ring assuming it is centered at the origin. Determine what the y-coordinate of the bar must be and then substitute this coordinate into the equation to find x
if you are calculating the capacity of material that will fit inside a box, you need to measure the ___ edges of the box.
To resize the ring, we will assume the ring is centered at the origin (0,0) and write an equation for it. Let's call the radius of the ring "r" and the radius of the finger "R".
The equation for the ring assuming it is centered at the origin is:
x^2 + y^2 = r^2
Given that the diameter of the ring is 20 mm, we can determine the radius by dividing the diameter by 2:
r = 20/2 = 10 mm
The diameter of the finger is 16 mm, so the radius of the finger would be:
R = 16/2 = 8 mm
To make the ring fit the finger, we need to find the y-coordinate where the bar needs to be inserted.
Since the ring is centered at the origin, the y-coordinate of the bar must be equal to the radius of the finger (R). Therefore, the y-coordinate is 8 mm.
Substituting this coordinate into the equation of the ring:
x^2 + (8)^2 = 10^2
x^2 + 64 = 100
x^2 = 100 - 64
x^2 = 36
Taking the square root of both sides:
x = sqrt(36)
x = 6 mm
So, the length of the bar that should be inserted in order to make the ring fit the finger is 6 mm.
To resize a ring using a bar, we can use the equation of the ring assuming it is centered at the origin. Let's assume that the equation of the ring is x^2 + y^2 = r^2, where r is the radius of the ring.
In this case, the original ring has a diameter of 20 mm, which means the radius (r) is half of the diameter, so r = 20/2 = 10 mm. Therefore, the equation of the original ring is x^2 + y^2 = 10^2.
Now, let's find the y-coordinate of the bar that must be inserted to make the ring fit a finger with a diameter of 16 mm. Since the finger diameter is smaller than the original ring, we need to find the point on the ring where the y-coordinate is 16/2 = 8 mm.
Substituting y = 8 into the equation x^2 + y^2 = 10^2, we get x^2 + 8^2 = 10^2. Simplifying this equation, we have x^2 + 64 = 100.
Now, solve for x by subtracting 64 from both sides of the equation: x^2 = 100 - 64 = 36.
Taking the square root of both sides, we have x = ±√36. Since the ring is centered at the origin, only the positive root (x = √36) is considered.
Therefore, the length of the bar that should be inserted to make the ring fit the finger is 2x, which is 2 * √36.
Simplifying, we get 2 * √36 = 2 * 6 = 12 mm.
So, the bar that should be inserted into the ring to make it fit the finger would be 12 mm in length.