Answer:
12πx⁴, 15x⁷, 16x⁹
Step-by-step explanation:
Volume of a cylinder: πr²h
Volume of a rectangular prism: whl
Plugging in variables for the volume of a cylinder, we get: 3x²·(2x)²·π
3x²·(2x)² = 3·2·2·x·x·x·x
= 12·x⁴
=12x⁴
Now, we just multiply that by π.
12x⁴·π = 12x⁴π
A monomial is a 1-term polynomial, so 12x⁴π is a monomial.
Plugging in variables for the volume of a rectangular prism, we get: 5x³·3x²·x²
5x³·3x² = 5·3·x·x·x·x·x
= 15·x⁵
= 15x⁵
Now, we just multiply that by x².
15x⁵·x²
= 15·x·x·x·x·x·x·x
= 15·x⁷
=15x⁷
A monomial is a 1-term polynomial, so 15x⁷ is a monomial.
Same steps for the last shape, another rectangular prism:
2x²·2x³·4x⁴
2x²·2x³
= 2·2·x·x·x·x·x
= 4·x⁵
= 4x⁵
Now, we just multiply that by 4x⁴.
4x⁵·4x⁴
= 4·4·x·x·x·x·x·x·x·x·x·
= 16·x⁹
= 16x⁹
A monomial is a 1-term polynomial, so 16x⁹ is a monomial.
Answer:
- The solution that optimizes the profit is producing 0 small lifts and 50 large lifts.
- Below are all the steps explained in detail.
Explanation:
<u />
<u>1. Name the variables:</u>
- x: number of smaller lifts
- y: number of larger lifts
<u></u>
<u>2. Build a table to determine the number of hours each lift requires from each department:</u>
<u></u>
Number of hours
small lift large lift total per department
Welding department 1x 3y x + 3y
Packaging department 2x 1y 2x + y
<u></u>
<u>3. Constraints</u>
- 150 hours available in welding: x + 3y ≤ 150
- 120 hours available in packaging: 2x + y ≤ 120
- The variables cannot be negative: x ≥ 0, and y ≥ 0
Then you must:
- draw the lines and regions defined by each constraint
- determine the region of solution that satisfies all the constraints
- determine the vertices of the solution region
- test the profit function for each of the vertices. The vertex that gives the greatest profit is the solution (the number of each tupe that should be produced to maximize profits)
<u></u>
<u>4. Graph</u>
See the graph attached.
Here is how you draw it.
- x + 3y ≤ 150
- draw the line x + 3y = 150 (a solid line because it is included in the solution set)
- shade the region below and to the left of the line
- 2x + y ≤ 120
- draw the line 2x + y ≤ 120 (a solid line because it is included in the solution set)
- shade the region below and to the left of the line
- x ≥ 0 and y ≥ 0: means that only the first quadrant is considered
- the solution region is the intersection of the regions described above.
- take the points that are vertices inside the solutoin region.
<u>5. Test the profit function for each vertex</u>
The profit function is P(x,y) = 25x + 90y
The vertices shown in the graph are:
The profits with the vertices are:
- P(0,0) = 0
- P(0,50) = 25(0) + 90(50) = 4,500
- P(42,36) = 25(42) + 90(36) = 4,290
- P(60,0) = 25(60) + 90(0) = 1,500
Thus, the solution that optimizes the profit is producing 0 smaller lifts and 90 larger lifts.
Answer:
4.55294117. If you want it rounded look below.
Step-by-step explanation:
-Rounded-
Hundredths:4.55
Tenth: 4.6
Thousandth: 4.553
Whole Number: 5
Hope this helps. :D