Answer:
D over 24
Step-by-step explanation:
just had the same question
Formula for perimeter of a rectangle is:
P = 2 * (a+b)
This means that sum of two sides is:
64 = 2* (a+b)
a+b=32
Pairs of numbers that add to 32 are:
1+31
2+30
3+29
4+28
5+27
6+26
7+25
8+24
9+23
10+22
11+21
12+20
13+19
14+18
15+17
16+16
We do not consider last pair as it would represent square. Areas these sides cover are:
1*31=31
2*30=60
3*29=87
4*28=112
5**27=135
6*26=156
7*25=175
8*24=192
9*23=207
10*22=220
11*21=231
12*20=240
13*19=247
14*18=252
15*17=255
Maximum area is 255 and lengths of sides are 15 and 17. This answer makes sense because larger sides give larger area.
<span>1. 10 square units.
2. 16.9 units
1. The area of a triangle is 1/2bh where b is the base and h is the height of the triangle. Any of the 3 sides of the triangle may be the base. So looking at the 3 points, I'll consider the line segment DE to be the base since both D and E have an X value of 3, so the length of the base is 3 - (-1) = 4. Since the base of the triangle is a vertical line with X = 3, the height of the triangle will be the absolute value of the X value of vertex F minus 3. So abs(-2 - 3) = abs(-5) = 5. We now have a base of 4 and height of 5 and using the 0.5bh formula, that gives us 0.5 * 4 * 5 = 10.
2. I'll call the points A(-2,-2), B(3,-3), C(4,-6), D(1,-6), and E(-2,-4). Using the pythagorean theorem, we can calculate the length of each side. SO
length AB = sqrt((-2 - 3)^2 + (-2 - (-3))^2) = sqrt(-5^2 + 1^2) = sqrt(25 + 1) = sqrt(26) = 5.099
length BC = sqrt((3 - 4)^2 + (-3 - (-6))^2) = sqrt(-1^2 + 3^2) = sqrt(1 + 9) = sqrt(10) = 3.162
Do the same for the lengths of CD, DE, and EA getting 3.000, 3.606, and 2 respectively.
Now just add them together. So
5.099 + 3.162 + 3.000 + 3.606 + 2.000 = 16.867, which rounds to 16.9</span>
Answer:
x = 125 ft and y = 250/3 ft
Step-by-step explanation:
Let assume that,
x be the length of the northern part of the fence (parallel to the north wall)
y be the length of the western and eastern pieces of the fence
As well as farmer has $4000 to spend hence we can write,
8x + 8y + 4y = 4000
8x + 12y = 4000
Hence we can say that,
from the above equation we can write
We know that area
A=xy.
we can write
equating it 0 we get
Also,
which is less than zero.
we can see that A''(x) is always less than 0 hence using second derivative test we can say that x = 125 is a maximum point.
now, solving for y we get
Hence we can say that dimensions for the plot that would enclose the most area is,
x = 125 ft and y = 250/3 ft
The slope of a horizontal line =0 not undefined the slope of a vertical line= undefined