Answer:
(x,y)=(0,7.333)
Step-by-step explanation:
We are required to:
Maximize p = x + 2y subject to
- x + 3y ≤ 22
- 2x + y ≤ 14
- x ≥ 0, y ≥ 0.
The graph of the lines are plotted and attached below.
From the graph, the vertices of the feasible region are:
At (0,7.333), p=0+2(7.333)=14.666
At (4,6), p=4+2(6)=4+12=16
At (0,0), p=0
At (7,0), p=7+2(0)=7
Since 14.666 is the highest, the maximum point of the feasible region is (0,7.333).
At x=0 and y=7.333, the function p is maximized.
The picture in the attached figure
Part 1) <span>
What is the total area of the swimming pool?</span>
we know that
<span>area of the swimming pool=area rectangle-area semi circle
area rectangle=20*36-----> 720 ft</span>²
area semicircle=pi*r²/2
r=18/2----> 9 ft
area semicircle=pi*9²/2----> 127.17 ft²
area of the swimming pool=720 ft²-127.17 ft²----> 592.83 ft²
the answer Part 1) isThe area of the swimming pool is 592.83 ft²Part 2) <span>What is the perimeter of the swimming pool?
</span>
perimeter of the swimming pool=perimeter of rectangle-18 ft+perimeter semi circle
perimeter of rectangle=2*[20+36]---> 112 ft
perimeter semi circle=2*pi*r/2----> pi*r
r=9 ft
perimeter semi circle=pi*9----> 28.26 ft
so
perimeter of the swimming pool=112 ft-18 ft+28.26 ft----> 122.26 ft
the answer Part 2) is122.26 ft
Add 5 on both sides
Make the denominators the same

Multiply 13 on both sides


Answer: There are 60 different ways that he can arrange the books.
Step-by-step explanation:
Since we have given that
Number of computer science books = 5
Number of math books = 3
Number of books selected = 4
Atleast Number of computer science = 2
Atleast number of math book = 1
According to question, he wants at least two computer science books and at least one math book, and he wants to keep the computer science books and the math books together.
So, Number of different ways that he can arrange the books is given by

Hence, there are 60 different ways that he can arrange the books.
Answer:
37 Degrees
Step-by-step explanation:
arc tan(3/4) = 36.869 degrees