Using the profit concept, we have that:
- The expression is: P(x) = -0.5x² + 40x - 300.
- A profit of $300 is found with x = 20 and x = 60.
<h3>What is the profit concept?</h3>
Profit is given by <u>revenue subtracted by costs</u>.
In this problem, we have that:
- The revenue is: R(x) = 90x - 0.5x².
- The costs are: C(x) = 50x + 300.
Hence the expression for the profit is given as follows:
P(x) = R(x) - C(x)
P(x) = 90x - 0.5x² - 50x - 300
P(x) = -0.5x² + 40x - 300.
A profit of $300 is found when P(x) = 300, hence:
300 = -0.5x² + 40x - 300
0.5x² - 40x + 600 = 0.
x² - 80x + 1200 = 0.
(x - 60)(x - 20) = 0.
Hence the values are:
More can be learned about the profit concept at brainly.com/question/4001746
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The initial length of the blue ribbon = 1.6 meters
Step-by-step explanation:
Here, according to the question:
The initial length of orange ribbon = 2 meters
Let us assume the initial length of blue ribbon = S meters
Now, the length of blue ribbon = (4/5) times the length of orange ribbon
x Length of Orange ribbon
or S = 1.6 meters
Hence, the initial length of the blue ribbon is 1.6 meters.
Round pan volume is:
3.14•r^2•h
D=7 so r=3.5 in
3.14• (3.5^2)•2 = 76.97 in^3
Rec. pan vol. is :
9•6•2= 108 in^3
Rec. Pan is larger because 108 in^3 is > 76.97 in^3 :) .
The icing that will be needed to frost the round cake pan is:
We need to find the surface area:
S.A= 3.14r^2 + 2 • 3.14•r • h .... 3.14 is the value of PI
So, S.A= 3.14• 3.5^2 + 6.28• 3.5• 2= 82.47 in^2 the icing that'll be needed to frost the round cake pan.
Icing that will be needed for the rec. cake pan is:
2•9•2=36 in^2
6•9•2= 108in^2
6•2= 12 in^2
S.A= 156 in^2 the icing needed to frost the rec. cake pan .... the S.A of all sides except the bottom one :).
Good luck ;-)
