Answer:
9!=362880 ways
Step-by-step explanation:
It is given that there are 4 different mathematics books and 5 different science books.
So basically there are 9 different books. So we have 9 choices for the first book, 8 choices for the second book, since we have placed the first one. We have 7 choices for the third book and so on. Therefore, we can arrange 9 different books in,
!9 ways, on solving !9 we get,
So there are 362,880 ways to arrange 9 different books if there are no restrictions.
Answer:
14,062.5ft^2
Step-by-step explanation:
A farmer has a given length of fencing. Since this fencing is used to enclose a rectangular area, before it is then divided it into four pens using the same provided fencing material. This will definitely lead to five lengths of fencing which come along one side of the rectangle to form four pens.
Let us assume that the length of the each of the five sides be xft.
Then let the length of each of the two sides in the be yft.
Since the total length of fencing available is 750 feet.
Then we can have an equation of such:
5x+2y=750
Making y the subject
2y = 750-5x
y = 750-5x/2. ........1
The area of the rectangular region is given by:
A = xy. ......... 2
Combining (1) in (2) to find the area
A(x)= x. (750−5x)/2
=750x−5x^2/2 ........... (*)
Going by the means of first diffential calculus.
A(x)=750x−5x^2/2
A'(x) = 750-10x/2
Setting A'(x) = 0
750-10x/2 = 0
750-10x = 2×0
750-10x = 0
750= 10x
x = 750/10
x = 75
Now that we have x = 75
We can now substitute into equation (*)
A(x) = 750×75-5×75^2/2
= (56250-28125)/2
= 28126/2
= 14062.5
Hence the rectangular region of maximum area is
14062.5ft^2
Detailed Answer:
Diameter = Radius * 2
Radius = Diameter/2
a) 64cm
r = 32 cm
Diameter = 32 * 2 = 64cm
b) 25.2 m
r = 12.6 m
Diameter = 12.6 * 2 = 25.2 m
c) 29.5 in
r = 14 3/4 = 14.75
Diameter = 14.75 * 2 = 29.5 in
d) 64 cm
r = √32 cm^2 = 32 cm
Diameter = 32 * 2 = 64 cm
e) 49.32 ft
r = 24.66 ft
Diameter = 24.66 * 2 = 49.32 ft
Answer: 11/10 or 1 1/10 pages
Step-by-step explanation:
3/5 + 1/2 = x
find the LCD so that you can add the fractions.
3/5 (2/2) = 6/10
1/2 (5/5) 5/10
6/10 + 5/10 = 11/10 or 1 1/10
