Given:
l = length of the rectangle
w = width of the rectangle
P = 4 ft, constant perimeter

Because the given perimeter is constant,
2(w + l) = 4
w + l = 2
w = 2 - l (1)

Part A.
The area is
A = w*l
= (2 - l)*l
A = 2l - l²
This is a quadratic function or a parabola.

Part B.
Write the parabola in standard form.
A = -[l² - 2l]
= -[ (l -1)² - 1]
= -(l -1)² + 1
This is a parabola with vertex at (1, 1). Because the leading coefficient is negative the curve is downward, as shown below.

The maximum value occurs at the vertex, so the maximum value of A = 1.
From equation (1), obtain
w = 2 - l = 2 - 1 = 1.
The maximum value of the area occurs when w=1 and l=1 (a square).

Answer:
The area is maximum when l=1 and w=1.
The geometric argument is based on the vertex of the parabola denoting maximum area.

4 0

4 years ago

Find the slope of the line that contains the points (-5, 3) and (-1,-5).

Nutka1998 [239]

Look at the attached picture⤴

Hope this will help u....

8 0

3 years ago

Donald bought a box of golf balls for $9.27. There were 18 golf balls in the box.

wlad13 [49]

Answer:

Each golf ball costs about $2.

Step-by-step explanation:

Given:

Donald bought a box of golf balls for $9.27. There were 18 golf balls in the box.

Rename the decimal dividend as a whole number that is compatible with the divisor to estimate the quotient.

Now, to find the cost of each golf ball.

As given:

Rename the decimal dividend as a whole number that is compatible with the divisor to estimate the quotient.

As, the cost of golf ball box = $9.27.

So, 9.27 nearest to whole number is 9.

Thus to get the cost of each ball:

18 golf balls cost = $9.

So, 1 golf ball cost = $18\div 9=2.$

Therefore, each golf ball costs about $2.

3 0

3 years ago