A steel plate has the form of one-fourth of a circle with a radius of 42 centimeters. Two two-centimeter holes are to be drilled in the plate positioned as shown in the figure in the website. Find the coordinates of the center of each hole.
www.webassign.net/waplots/a/3/5408bf697d56f65296201c59e1cdcf.gif
(x1, y1)=
(x2, y2)=
I AM IN THE PROCESS OF FINDING THIS ANSWER
top hole
x = 38 cos 60
y = 38 sin 60
bottom hole
x = 38 cos 30
y = 38 sin 30
thanks damon
Well, just between you and me, drilling holes in steel plates sounds like a hole lot of fun! Anyway, let's get to the coordinates of those holes.
In the given figure, the center of the steel plate (the center of the circle) is already provided as (0, 0). Now, let's find the coordinates for each hole:
For the first hole, we need to calculate its x-coordinate. Since it is located two centimeters to the left of the center, the x-coordinate would be -2.
For the y-coordinate, we can use the Pythagorean theorem. The radius of the plate is 42 centimeters, and the hole is 2 centimeters above the center. So, we have a right-angled triangle with the radius as the hypotenuse. Using the theorem, we can find the height of the triangle:
r^2 = a^2 + b^2
42^2 = a^2 + 2^2
a^2 = 42^2 - 2^2
a^2 = 1764 - 4
a^2 = 1760
Taking the square root of both sides, we find:
a = sqrt(1760) ≈ 41.96
The y-coordinate of the first hole would then be approximately 41.96.
For the second hole, the x-coordinate would also be -2 as it is also located 2 centimeters to the left of the center.
For the y-coordinate, the hole is 2 centimeters below the center. Using the same calculations as before, we find that the y-coordinate of the second hole is approximately -41.96.
So, the coordinates of the first hole would be (-2, 41.96), and the coordinates of the second hole would be (-2, -41.96).
Hope that helps, and remember, be careful not to fall into any holes while drilling!
To find the coordinates of the center of each hole, we can use the properties of circles and triangles. Here's how you can approach this problem:
1. First, let's identify the relevant points on the diagram. The center of the circle is also the origin (0,0). The center of the first hole will be denoted as (x1, y1), and the center of the second hole will be denoted as (x2, y2).
2. Since the steel plate is one-fourth of a circle, we know that the angle between the x-axis and the line connecting the center of the circle to the first hole is 90 degrees. Therefore, the x-coordinate of the first hole will be the radius (42) minus the horizontal distance from the origin to the hole. The horizontal distance is given as 8 centimeters (2 centimeters for the hole and 6 centimeters for the remaining part of the plate). Thus, x1 = 42 - 8 = 34.
3. Similarly, the y-coordinate of the first hole will be the radius (42) minus the vertical distance from the origin to the hole. The vertical distance is given as 8 centimeters (2 centimeters for the hole and 6 centimeters for the remaining part of the plate). Thus, y1 = 42 - 8 = 34.
4. For the second hole, we have to consider the angle between the x-axis and the line connecting the center of the circle to the second hole. This angle can be calculated as the complement of the known angle (90 degrees) minus the angle of the quarter-circle (90 degrees). Therefore, the angle is 0 degrees in this case. As a result, the x-coordinate and y-coordinate of the second hole will be the same as the x-coordinate and y-coordinate of the first hole, respectively. Hence, x2 = x1 = 34 and y2 = y1 = 34.
Therefore, the coordinates of the center of each hole are:
(x1, y1) = (34, 34)
(x2, y2) = (34, 34)