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Ksju [112]
2 years ago
11

A square has a perimeter of 16 units and an area of 16 square units. What is the side length of the square? Show your work.

Mathematics
2 answers:
Free_Kalibri [48]2 years ago
6 0

Step-by-step explanation:

that r = P/(2π) so A = π(P/(2π))2 = P2/(4π). Any positive area less than this is also possible. So in this problem the largest area possible is (16 in.)2/(4π) = 64/π sq.

defon2 years ago
5 0

Answer:

4 units

Step-by-step explanation:

according to question:

perimeter of square = 16 units

4a = 16

where a is the side length

a = 16/4

= 4 units

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Read 2 more answers
Dana has 800 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed are
grin007 [14]

Answer:

Perimeter of rectangle states that total distance around the outside, which can be found by adding together the length of each side.

As per the given statement, Dana has 800 yards of fencing to enclose a rectangular area.

Therefore, perimeter of rectangle = 800 yards.

Perimeter(P) of rectangle is given by :

P = 2(x+y) where x is the length and y is the width of the rectangles respectively.

Then,

2(x+y) = 800

Divide both sides by 2 we get;

x+y =400

or

y = 400 -x            .....[1]

We know, the area(A) of rectangle is given by

A = xy                   .....[2]

Substitute equation [1] into [2] we get;l

A = x(400-x)

using distributive property a\cdot (b+c) = a\cdot b+ a\cdot c

A = 400x -x^2            

or

A =-x^2+400x    ......[3]

To maximize the enclosed area.

For a quadratic function in standard form y =ax^2+bx+c , the axis of symmetry is a vertical line given by;  

x = -\frac{b}{2a}

Then; we have from equation [3]

a = -1 and b = 400

By axis of symmetry;

x = -\frac{b}{2a} = -\frac{400}{2 \cdot -1} =\frac{400}{2} = 200

Substitute in equation [1] to solve for y:

y = 400 - 200 = 200

The dimensions of the rectangle that maximize enclosed area are:

x = 200 units and y = 200 units.

Maximum area = 200 \times 200 = 40,000 square units.

We can say that maximum area of rectangle will always be a square



4 0
3 years ago
Question 1 (1 point)
kykrilka [37]

Answer:

The description for the problem is listed throughout the section below on explanations.

Step-by-step explanation:

The given values are:

The amount of bank loan = $22,000

Interest rate = 7.99%

Pays monthly = $700

So, the principal amount decreases by 700 per month.

Now,

The principal amount at the end of the m^{th} month = (22000 - 700 m)

Then,

The interest paid at the end of 1 year:

⇒ (22000)0.0799+(22000-700)0.0799+...+(22000-700(11))0.0799

On simplifying the above equation, we get

⇒ 0.0799[12(22000)-\frac{11\times 12}{2}\times 700]

⇒ 0.0799[264000-11\times 6\times 700]

⇒ 0.0799[264000-46200]

⇒ $17402.22

Therefore interest could be measured correctly at the end of each year, likewise.

⇒ (2200-700m)R+(22000-700(m+1))R+...+(22000-700(m+11))R

⇒ R[12\times 22000-700[12m+\frac{11\times 12}{2}]]

⇒ R[264000-700[12m+\frac{11\times 12}{2}]]

⇒ R[263300(12m+66)]

R : interest rate

7 0
3 years ago
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