Let the length = x
2 lengths are 2x.
Then you have 400 - 2x for both widths, so the width is 200 - x.
The are if the rectangle is

y = x(200 - x)

y = 200x - x^2

y = -x^2 + 200x

Take the first derivative ans set equal to zero to find a maximum value.

y' = -2x + 200

-2x + 200 = 0

-2x = -200

x = 100

Since the side of the rectangle is 100, all sides measure 100 ft, and you have a square.
The maximum area is 100 ft * 100 ft = 10,000 ft.

3 0

4 years ago

Complete these sentences

GenaCL600 [577]

Where’s the sentences?

3 0

2 years ago

according to a salad recipe each serving requires 4 teaspoons of vegetable oil and 12 teaspoons of vinegar. if 14 teaspoons of v

Citrus2011 [14]

Answer:

42 teaspoons of vinegar

Step-by-step explanation:

Given

$x \to vegertable$

$y \to vinegar$

$x : y = 4 :12$

Required

Find y when $x = 14$

$x : y = 4 :12$ implies that:

$14 : y = 4 : 12$

Express as fraction

$\frac{y}{14} = \frac{12}{4}$

$\frac{y}{14} = 3$

Multiply by 3

$y = 14* 3$

$y = 42$

7 0

3 years ago

In sunlight, a vertical stick has a height of 4 ft and casts a shadow 2 ft long at the same time that a nearby tree casts a shad

marshall27 [118]

Remark
Make up a proportion that relates the tree and its properties to the stick and its properties.

Givens
Stick height (s_h) = 4
Stick shadow(s_s) = 2
Tree shadow = t_s = 18
Tree height = x

Formula
s_h / s_s = x / t_s

Substitute and solve.
4/2 = x / 18 Cross multiply
4*18 = 2 * x
72 = 2x Divide by 2
72/2 = x
x = 36

The height of the tree is 36 feet.

6 0

3 years ago