Ask question

Ask question

All categories

3 years ago

9

One side of a rectangular field is adjacent to a river. There are 160 yards of fencing available for the other three sides. What

dimensions of the field will result in the maximum area?

1 answer:

kupik [55]3 years ago

6 0

Answer:

The dimensions of 40 yards by 80 yards of the field will result in maximum area of 3200 yards squared.

Step-by-step explanation:

Let "x" and "y" be the lengths of the sides of rectangle.

So, the perimeters of three sides is:

2x + y = 160 yards

y = 160 - 2x ______ eqn (1)

Area = A = xy = x(160 - 2x)

A(x) = 160x - 2x² [in terms of x]

Taking 1st and setting value to zero:

A'(x) = 0 = 160 - 4x

4x = 160

x = 40 yards

Now, taking 2nd derivative to check whether value is minimum or maximum.

A"(x) = -4

since, A"(x) < 0

therefore, it means the value x = 40 yards is maximum.

Thus, from eqn (1):

y = 160 - 2(40 yards)

y = 80 yards

and maximum area will be:

Amax = (40 yards)(80 yards)

<u>Amax = 3200 yards squared</u>

You might be interested in

What is the inverse of the function f(x) = 2x + 1?

tiny-mole [99]

F(X) = 2x + 1

Replace f(x) with y:

Y = 2x+ 1

Switch variables:

X = 2y + 1

Solve for Y:

Subtract 1 from both sides:

X- 1 = 2y

Divide both sides by 2:

X-1 / 2 = y

Rewrite so y is in the left side:

Y = x-1 / 2

Replace y with f^-1(x):

F^-1(x) = x-1 / 2

This can also be written as x/2 - 1/2

8 0

3 years ago

What do the arrows and coefficients in equations communicate.

jok3333 [9.3K]

Step-by-step explanation:

arrows mean

an example:

6>5

what ever the arrows pointing at is smaller than the othernumber

8 0

2 years ago

1,325,468.097 what is the value of the underline digit?

8_murik_8 [283]

Answer:

a

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A quadrilateral has vertices at A(–5, 5), B(1, 8), C(4, 2), D(–2, –2). Use slope to determine if the quadrilateral is a rectangl

lianna [129]

With the properties of rectangle in mind we must perform two verification. Verify to see if opposite sides are parallel and adjacent sides are perpendicular.

We need to determine the slope of each side, using the formula,

$m=\frac{y_2-y_1}{x_2-x_1 }$

<u>Slope of AB</u>

$m_{AB}=\frac{8-5}{1--5}$

$\Rightarrow m_{AB}=\frac{8-5}{1+5}$

$\Rightarrow m_{AB}=\frac{3}{6}$

$\Rightarrow m_{AB}=\frac{1}{2}$

<u>Slope of BC</u>

$m_{BC}=\frac{2-8}{4-1}$

$\Rightarrow m_{BC}=\frac{-6}{3}$

$\Rightarrow m_{BC}=-2$

<u>Slope of CD</u>

$m_{CD}=\frac{-2-2}{-2-4}$

$\Rightarrow m_{CD}=\frac{-2-2}{-2-4}$

$\Rightarrow m_{CD}=\frac{-4}{-6}$

$\Rightarrow m_{CD}=\frac{2}{3}$

<u>Slope of AD</u>

$m_{AD}=\frac{-2-5}{-2--5}$

$\Rightarrow m_{AD}=\frac{-2-5}{-2+5}$

$\Rightarrow m_{AD}=\frac{-7}{3}$

<u>Verify Parallel sides</u>

If the quadrilateral is a rectangle, then opposite sides should have the same slope. But

$m_{AD} = \frac{-7}{3} \neq m_{BC}=-2$

$m_{AB}=\frac{1}{2} \neq m_{CD}=\frac{2}{3}$

<u>Verify Perpendicularity</u>

And also the product of slopes of all sides with a common vertex should be -1. But

$m_{AB} \times m_{BC}=\frac{1}{2} \times -2=-1$

$m_{AB} \times m_{AD}=\frac{1}{2} \times -\frac{7}{3} \neq -1$

$\Rightarrow m_{CD} \times m_{AD}=\frac{2}{3} \times -\frac{7}{3} \neq -1$

$\Rightarrow m_{CD} \times m_{BC}=\frac{2}{3} \times -2 \neq -1$

Since the quadrilateral fails to satisfy all these conditions, the quadrilateral is not a rectangle

6 0

3 years ago

What is the 25% discount of $120 dollars?

Varvara68 [4.7K]

25% discount of $120
=100*0.25
=$25

3 0

3 years ago