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
Answer:
B
Step-by-step explanation:
Getting info from multiple places is better
Answer:
the answer would basically be 720 smoothies in total from Jul.-Dec.
Step-by-step explanation:
YWW :)
Answer:
Step-by-step explanation:
1. Area of base
The radius given is that of the circumcircle.
The general formula for the edge length a of a regular polygon is
a = 2Rsin(π/n)
So,
a = 2 × 5 × sin(π/5) = 10sin0.6283 = 10 × 0.5878 = 5.878 in
The general formula for the area of a regular polygon is
A = ¼na²cot(π/n)
So,
A = ¼ × 5 × 5.878²cot(π/5) = ¼ × 5 × 5.878² × 1.376 = 59.44 in²
2. Lateral area
The general formula for the lateral area L of regular prism is
L = nah
So,
L = 5 × 5.878 × 12 = 352.7 in²
3. Total area
Total surface area = lateral area + 2×base area
S = L + 2B = 352.7 + 2 × 59.44 = 471.6 in²
Answer:
a. 20,579.52 cubic inches
b.10,289.76 cubic inches.
c. 13.49 inches
Step-by-step explanation:
Hi, to answer this question we have to calculate the volume of a sphere:
Volume of a sphere: 4/3 π r³
Since diameter (d) = 2 radius (r)
Replacing with the value given:
34 =2r
34/2=r
r= 17 in
Back with the volume formula:
V = 4/3 π r³
V =4/3 π (17)³
V = 20,579.52 cubic inches
The volume of the half-inflated balloon is equal to the volume of the sphere divided by 2.
20,579.52/2 = 10,289.76 cubic inches.
To find the radius of the half-inflated balloon we have to apply again the volume formula and substitute v=10,289.76
10,289.76= 4/3 π r³
Solving for r
10,289.76/ (4/3 π)= r³
2,456.5 = r³
∛2,456.5 = r
r = 13.49 inches
