Need help on writing an equation. the question is let H represent the stack height. Write an equation that represents the height of a stack of medium lampshades in terms of the number of lampshades, s, in the stack.
# of lamp shades stack height med
1 8
2 10.5
3 13
4 15.5
5 18
Thanks...
note that H increases by 2.5 for each shade. So, since H starts at 8 when s=1,
H(s) = 5.5 + 2.5s
To write an equation that represents the height of a stack of medium lampshades in terms of the number of lampshades, you need to identify the pattern or relationship between the number of lampshades and the corresponding stack height.
Looking at the given data:
Number of lampshades (s) Stack height (H)
1 8
2 10.5
3 13
4 15.5
5 18
We can observe that for each additional lampshade added to the stack, the stack height increases by 2.5 units. This means that the stack height is increasing linearly with respect to the number of lampshades.
To write the equation, we can use the concept of slope-intercept form, which is y = mx + b, where y represents the dependent variable, x represents the independent variable, m represents the slope, and b represents the y-intercept.
In this case, the number of lampshades (s) is the independent variable, and the stack height (H) is the dependent variable. So, we can rewrite the equation as:
H = ms + b
Now, let's find the values of m and b.
Using the given data, we can calculate the slope (m). The change in stack height (ΔH) for each additional lampshade (Δs) is:
ΔH = 10.5 - 8 = 2.5
Δs = 2 - 1 = 1
m (slope) = ΔH / Δs = 2.5 / 1 = 2.5
Next, we need to find the y-intercept (b). From the data, we can see that when there are no lampshades (s = 0), the stack height is 8 units. Therefore, b = 8.
Now we have the values of m and b, we can write the equation:
H = 2.5s + 8
This equation represents the height of a stack of medium lampshades (H) in terms of the number of lampshades (s) in the stack. To find the stack height for any given number of lampshades, substitute the value of s into the equation and solve for H.