Answer:
The value of r to have maximum profit is 3/25 ft
Step-by-step explanation:
To find:
The size of the sphere so that the profit can be maximized.
Manufacturing cost of the solid sphere = $500/ ft^3
Selling price of sphere (on surface area) = $30 / ft^2
We see that the manufacturing cost dealt with he volume of the sphere where as the selling price dealt with the surface area.
So,
To maximize the profit (P) .
We can say that:
⇒
⇒
⇒
⇒
Differentiate "" and find the "" value then double differentiate "", plug the "" values from to find the minimum and maximum values.
⇒
⇒
Finding r values :
⇒
Dividing both sides with 240π .
⇒ ⇒
⇒ and
To find maxima value the double differentiation is :
⇒ ...first derivative
Double differentiating :
⇒ ...second derivative
⇒
Test the value r = 3/25 dividing both sides with 240π
⇒
⇒
⇒
It passed the double differentiation test.
Extra work :
Thus:
⇒
⇒
⇒
Finally r =3/25 ft that will maximize the profit of the manufacturing company.
Answer:
6
Step-by-step explanation:
6.9 - 5 = 1.9
1.9 + 4.1 = 6
Here are the completed tables
Gallons Quart
1 4
2 8
5 20
7 28
Quart Pint
1 2
3 6
6 12
8 16
Pint Cup
1 2
3 6
5 10
9 18
The capacity of the objects are:
Swimming pool - 5000 gallons
Watering can - 8 quarts
Juice box - 2 pints
Soup bowl - 2 cups
The measurement from least to greatest is: 6 pints, 2 galloons, 18 cups, 6 quart.
<h3>How would the tables be filled?</h3>
In order to fill the tables, the unit of conversion has to be known:
1 gallon = 4 quart
- 2 gallon = 2 x 4 = 8 quarts
- 5 gallons : 5 x 4 = 20 quarts
- 7 gallons: 7 x 4 = 28 quarts
1 quart = 2 pints
6 pint / 2 = 3 quarts
12 / 2 = 6 quarts
8 x 2 = 16 pints
<h3>
How to order the measurment from least to largest?</h3>
In order to order the measurement, all the measurements have to be in the same units. All the units would be converted to cups
1 quart = 4 cups
4 x 6 = 24 cups
1 galloon = 16 cups
16 x 2 = 32 cups
1 pint = 2 cups
6 x 2 = 12 cups
To learn how to convert units, please check: brainly.com/question/25993533
the line would be at x=15 and you would shade all to the left of the line and a point in that zone or on the line would work in the equation