An appliance manufacturer estimates that the profit y (in dolars) generated by producing x cooktops per month is given by the equation
y= 10x + 0.5x^2 - 0.001x^3 - 5000
where 0 ¡Ü x ¡Ü 450.
Graph the equation.
I punched in the equation and I didn't get anything. I don't know what I should do with 0 ¡Ü x ¡Ü 450
First, the inequality converted to Western encoding is:
where 0 ≤ x ≤ 450.
Then you need to understand that not all calculators have the same features. So it would help if you identify the make and model of your graphics calculators if you are looking into the operation of the calculator. In general, graphing software allow the limits of the independent variable to graph, which is precisely the "0 ≤ x ≤ 450" requirement.
oops the 0 <or= x <or= 450
I don't know how to make the less than equal sign on my keyboard.
my calculator is TI - 83 Plus
Unfortunately I don't have a TI-83plus. I hope someone who has one will be able to help you.
To type ≤ or ≥ you would type "& l e ;" and "& g e ;" respectively, without the double quotes and without the intevening spaces. Try it on your next post.
Don't forget to change the encoding back to Western-8859-1 before you do so. You probably have a default with another coding.
To graph the equation, you need to plot the points on a graph representing the relationship between x (the number of cooktops produced per month) and y (the profit generated). The given equation is:
y = 10x + 0.5x^2 - 0.001x^3 - 5000
The range of x values is given as 0 ≤ x ≤ 450. This means you need to consider values of x ranging from 0 to 450. For each value of x, you can calculate the corresponding y value using the given equation. The resulting points can then be plotted on a graph.
Here's an example:
Let's select a few values of x within the given range and calculate their corresponding y values:
For x = 0:
y = 10(0) + 0.5(0)^2 - 0.001(0)^3 - 5000
y = 0 - 0 - 0 - 5000
y = -5000
For x = 100:
y = 10(100) + 0.5(100)^2 - 0.001(100)^3 - 5000
y = 1000 + 5000 - 1000000 - 5000
y = -999000
For x = 200:
y = 10(200) + 0.5(200)^2 - 0.001(200)^3 - 5000
y = 2000 + 20000 - 16000000 - 5000
y = -15960000
Once you have these points, you can plot them on a graph with x on the x-axis and y on the y-axis. Connect the points with a smooth curve to get a visual representation of the equation.
Remember to label the axes and indicate the range of x values (0 to 450 in this case) to make the graph clear and accurate.
Note: You might need to use graphing software or a graphing calculator to plot the graph accurately since the equation involves cubic terms.