A qulliq [kudlik] is an oil lamp that functions as the main source of heat and light for an igloo in the Inuit culture. It is made of soapstone shaped as a parabolic bowl that contains seal blubber for the oil. It is lined with arctic wool for the wick. If the length of the bowl is 50cm and the height is 15cm, determine the quadratic function that can be used to model the shape of a qulliq.
When the function is written in vertex form, y = a(x - h)2 + k. The values of the parameters a, h and k are as follows:
I guess by length you mean diameter.
so the radius is 25 cm
Since the parabola will be a simple
y = ax^2
You just need to find a such that
a*25^2 = 15
In order to determine the quadratic function that can model the shape of a qulliq, let's identify the values of the parameters a, h, and k in the vertex form equation y = a(x - h)^2 + k.
The vertex form equation represents a parabolic shape, where the vertex (h, k) is the highest or lowest point on the parabola, and a determines the width and direction of the opening.
Given that the length of the bowl is 50cm and the height is 15cm, we can identify the values of h and k:
- The length of the bowl (50cm) represents the x-coordinate of the vertex, which is -h. Since the length is given as 50cm, h = -50/2 = -25.
- The height of the bowl (15cm) represents the y-coordinate of the vertex, which is k. Therefore, k = 15.
So far, we have h = -25 and k = 15.
To determine the value of a, we need more information about the shape and proportions of the qulliq. Unfortunately, the description provided does not include this information.
Without knowing the specific characteristics of the qulliq, such as the width of the opening or the overall shape, we cannot determine the value of a, and therefore are unable to provide the complete quadratic function in vertex form.
To determine the quadratic function that can be used to model the shape of a qulliq, we need to find the values of the parameters a, h, and k in the vertex form equation.
The vertex form of a quadratic equation is given by:
y = a(x - h)^2 + k
In this case, the vertex of the parabolic bowl is at the maximum point, which is the highest point of the qulliq where the seal blubber rests. The x-coordinate of the vertex (h) will be the center of the parabolic bowl, and the y-coordinate (k) will be the height of the parabolic bowl (15 cm).
Now, let's think about the shape of the parabolic bowl. It is described as a parabolic bowl with a length of 50 cm. A parabola is symmetric about its axis, so the length of the bowl will be equal to twice the distance from the center to the x-intercept.
The x-intercept represents the points where the parabolic shape of the qulliq meets the base or the ground. Since we know the length of the bowl is 50 cm, the distance from the center to the x-intercept will be half of that, which is 25 cm.
Therefore, the x-coordinate of the vertex (h) is 25 cm.
Now, let's substitute the known values of h and k into the vertex form equation:
y = a(x - h)^2 + k
y = a(x - 25)^2 + 15
Finally, we need to determine the value of the parameter 'a'. To do this, we need additional information or assumptions about the depth or curvature of the qulliq.
Without further information, it is difficult to determine the exact value of 'a' to accurately model the shape of a qulliq. This parameter would be influenced by factors such as the desired curvature, thickness of the soapstone, and the specific design aesthetics of the qulliq.