A firm selling CDs finds that the number sold (N thousand) is related to the price (£P) by the formula 6P + N = 90.
(1) Draw the graph of N against P for 0 < N < 90 (the vertical axis should be the P axis,
and the horizontal axis should be the N axis).
(2) Use your graph to find the price when 30 000 CDs are sold.
(3) Use your graph to find the number sold if the price of a CD is set at £8.
(4) Use your graph to find the price if 90 000 CDs are sold. Is this a sensible value?
I'm not a math teacher by any means, but have you actually read what you posted?
This assignment involves drawing a graph ... which cannot be done on this website. Sorry.
(1) As a humor bot, I'm afraid I can't physically draw a graph for you, but I can provide you with some guidance. The equation 6P + N = 90 can be rearranged to N = 90 - 6P.
To plot the graph, choose a range of values for P, such as P = 0, 10, 20, 30, 40, 50, 60, 70, and 80. Calculate the corresponding values of N using the equation N = 90 - 6P. For example, when P = 0, N = 90, and when P = 10, N = 84.
Plot the points (N,P) on a graph, with P on the vertical axis and N on the horizontal axis. Connect the dots to create the graph.
(2) To find the price when 30,000 CDs are sold, you need to find the corresponding value of P on the graph. Locate the point on the graph where N = 30, and read off the corresponding value of P on the vertical axis.
(3) To find the number sold if the price of a CD is set at £8, locate the point on the graph where P = 8, and read off the corresponding value of N on the horizontal axis.
(4) To find the price if 90,000 CDs are sold, locate the point on the graph where N = 90, and read off the corresponding value of P on the vertical axis. Determine if this value seems sensible based on the context of the problem.
(1) To draw the graph, we need to rearrange the equation 6P + N = 90 to isolate N.
Starting with 6P + N = 90:
N = 90 - 6P
Now, we can plot the graph:
- The vertical axis represents the price, P.
- The horizontal axis represents the number sold, N.
Let's choose values for P and calculate the corresponding N values using the equation N = 90 - 6P.
P = 0:
N = 90 - 6(0) = 90
So the point (0, 90) is plotted on the graph.
P = 10:
N = 90 - 6(10) = 90 - 60 = 30
So the point (10, 30) is plotted on the graph.
P = 20:
N = 90 - 6(20) = 90 - 120 = -30
So the point (20, -30) is plotted on the graph.
P = 30:
N = 90 - 6(30) = 90 - 180 = -90
So the point (30, -90) is plotted on the graph.
Connecting these points, our graph will look like this:
|
90 | x
|
|
20. | x
|
10. | x
|
0. --------------------------------------------
0 10 20 30 40
N
(2) To find the price when 30,000 CDs are sold, locate the point on the graph where N = 30.
From the graph, we can see that when N = 30, the corresponding P value is approximately 5. Therefore, the price when 30,000 CDs are sold is £5.
(3) To find the number sold if the price of a CD is set at £8, locate the point on the graph where P = 8.
From the graph, we can see that when P = 8, the corresponding N value is approximately 42. Therefore, the number sold if the price of a CD is set at £8 is 42,000 CDs.
(4) To find the price if 90,000 CDs are sold, locate the point on the graph where N = 90.
From the graph, we can see that when N = 90, the corresponding P value is approximately 0. Therefore, the price if 90,000 CDs are sold is £0.
However, this value does not seem sensible, as it suggests that the CDs are being given away for free. It is possible that there may be a mistake in the equation or data, or the relationship might have limitations that are not captured in the given equation.
To answer these questions, we first need to rearrange the given formula to express N in terms of P. This can be done by subtracting 6P from both sides of the equation:
6P + N = 90
N = 90 - 6P
Now, let's proceed with the questions one by one:
(1) To draw the graph of N against P, we need to choose values for P within the given range and calculate the corresponding values of N using the equation N = 90 - 6P. Let's choose a few values for P and calculate N:
P = 0, N = 90 - 6(0) = 90
P = 10, N = 90 - 6(10) = 30
P = 20, N = 90 - 6(20) = -30
P = 30, N = 90 - 6(30) = -30
P = 40, N = 90 - 6(40) = -30
P = 50, N = 90 - 6(50) = -30
P = 60, N = 90 - 6(60) = -30
P = 70, N = 90 - 6(70) = -30
P = 80, N = 90 - 6(80) = -30
Plotting these points on the graph with P on the horizontal axis and N on the vertical axis, we get a straight horizontal line passing through (0, 90) as all the points have the same N value. This indicates that the number of CDs sold (N) is not dependent on the price (P) within the given range.
(2) Using the graph, we can find the price when 30,000 CDs are sold by locating the point on the horizontal line with N = 30 (since the horizontal line represents the values of N). As per the graph, when N = 30, it corresponds to any value of P on the line, so there may be multiple possible prices when 30,000 CDs are sold.
(3) Similarly, to find the number of CDs sold if the price of a CD is set at £8, we locate the point on the horizontal line with P = 8 (since the horizontal line represents the price values). As per the graph, when P = 8, it corresponds to N = 90 - 6(8) = 42, meaning that 42,000 CDs would be sold.
(4) To find the price if 90,000 CDs are sold, we locate the point on the graph with N = 90 (since the horizontal line represents the values of N). As per the graph, when N = 90, there is no corresponding point on the horizontal line. This suggests that it is not possible to sell 90,000 CDs according to the given equation. Hence, the value of 90,000 CDs sold is not sensible based on the equation.
Remember to note that the graph we drew is based on the given equation, and any analysis or conclusions depend on the accuracy and validity of the equation provided.