A landscape architect used the entire length of an 80-foot rope to lay out a flower bed in the shape of a square. In another area, he used the entire
length of the same rope to lay out a second flower bed in the shape of a circle. (Drawings not to scale.)
Exhit
Perimeter 80 feet
Circumference - 80 feet
What is the area of the circle?
A 125.6 ft2
B. 2,041.8 ft2
c. 215.2 ft
D. 506.5 ft2

Answers

Answer 1

A square has 4 sides so 80/4= 20ft
area= 20^2
area=400 square ft

2*3.14*r = 80
r = 80/6.28
r=12.74 ft

area= A = 3.14*12.74^2
A = 509.6 sq/ft

if you wanted to find the difference:

509.6 - 400 = 109.6 sq/ft more in the circle

Answer 2

The area of the circle with a perimeter of 80 feet is 509.31 square feet.

The entire length of the rope = 80 feet

So, the perimeter of the flower bed = 80 feet

Since the flower bed is in a square shape

So, the perimeter of the square = The entire length of the rope

The perimeter of the square = 80 feet

Suppose the side of the square is a

So, 4a = 80

a =20

So, the area of the square = 20² = 400 square feet.

What is the area of a circle?

The area of a circle with a radius r is πr².

Similarly, when the flower bed is in a circular shape

The perimeter of the circle = 80

Suppose the radius of the circle is r

So, [tex]2\pi r =80\\\\[/tex]

[tex]r= 12.73 feet[/tex]

Area of circle = [tex]\pi r^{2}[/tex]

Area of circle = 509.31 square feet.

Therefore, the area of the circle with a perimeter of 80 feet is 509.31 square feet.

To get more about circles visit:

https://brainly.com/question/24375372

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Express each of these system specifications using predicates, quantifiers, and logical connectives, if necessary.

a. At least one console must be accessible during every fault condition.
b. The e-mail address of every user can be retrieved whenever the archive contains at least one message sent by every user on the system.
c. For every security breach there is at least one mecha- nism that can detect that breach if and only if there is a process that has not been compromised.
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Answers

The system specification with predicates, quantifiers, and logical connectives are:

a. ∃C(x) ∀F(y) such that if F(y) is true, C(x) is true.

b. ∀U(x) (∃M(y) if ∀U(z), ∃M(w) is true, then E(x) is true).

c. ∀B(x) (∃D(y) D(y) can detect B(x) ↔ (∃P(z) ¬P(z) is true)).

d. ∀E(x, y) (∃P(z, w) and ∃P(u, v) such that P(z, w) and P(u, v) connect

E(x, y)).

e. ∀U(x) (¬P(x) is true, except for the system administrator who knows all passwords: ∀U(y) P(y) if y is the system administrator).

We have,

Let C(x) be the predicate "x is a console" and F(x) be the predicate "x is a fault condition".