Ask question

Ask question

All categories

3 years ago

8

The owner of the Rancho Grande has 3,044 yd of fencing with which to enclose a rectangular piece of grazing land situated along

the straight portion of a river. If fencing is not required along the river, what are the dimensions (in yd) of the largest area he can enclose? shorter side? longer side? what is the area?

1 answer:

inysia [295]3 years ago

7 0

Answer:

Step-by-step explanation:

Area of the rectangular piece A = xy

x is the length

y is the width

Perimeter =2x+2y

Given

Perimeter = 3044yds

3044 = 2x+2y

1522 = x+y

x = 1522-y

Substitute into the formula for area

A = xy

A = (1522-y)y

A = 1522y-y²

To maximize the area, dA/dy must be zero

dA/dy = 1522-2y

0 = 1522-2y

2y = 1522

y = 1522/2

y = 761

Since x+y = 1522

X+761 = 1522

X = 761

Dimension is 761yd by 761yd

Area = 761×761 = 579121yd²

You might be interested in

How many solutions does the system of equations below have?

soldier1979 [14.2K]

Answer:

One solution

Step-by-step explanation:

5x + y = 8

15x + 15y = 14

Lets solve using substitution, first we need to turn "5x + = 8" into "y = mx + b" or slope - intercept form

So we solve for "y" in the equation "5x + y = 8"

5x + y = 8

Step 1: Subtract 5x from both sides.

5x + y − 5x = 8 − 5x

Step 2: 5x subtracted by 5x cancel out and "8 - 5x" are flipped

y = −5x + 8

Now we can solve using substitution:

We substitute "-5x + 8" into the equation "15x + 15y = 14" for y

So it would look like this:

15x + 15(-5x + 8) = 14

Now we just solve for x

15x + (15)(−5x) + (15)(8) = 14(Distribute)

15x − 75x + 120 = 14

(15x − 75x) + (120) = 14(Combine Like Terms)

−60x + 120 = 14

Step 2: Subtract 120 from both sides.

−60x + 120 − 120 = 14 − 120

−60x = −106

Divide both sides by -60

$\dfrac{ -60x }{ -60 } = \dfrac{ -106 }{ -60 }$

Simplify

$x = \dfrac{ 53 }{ 30 }$

Now that we know the value of x, we can solve for y in any of the equations, but let's use the equation "y = −5x + 8"

$\mathrm{So\:it\:would\:look\:like\:this:\ y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}$

$\mathrm{Now\:lets\:solve\:for\:"y"\:then}$

$y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}$

$\mathrm{Express\: -5 \times \dfrac{ 53 }{ 30 }\:as\:a\:single\:fraction}$

$y = \dfrac{ -5 \times 53 }{ 30 } +8$

$\mathrm{Multiply\:-5 \:and\:53\:to\:get\:-265 }$

$y = \dfrac{ -265 }{ 30 } +8$

$\mathrm{Simplify\: \dfrac{ -265 }{ 30 } \:,by\:dividing\:both\:-265\:and\:30\:by\:5} }$

$y = \dfrac{ -265 \div 5 }{ 30 \div 5 } +8$

$\mathrm{Simplify}$

$y = - \dfrac{ 53 }{ 6 } +8$

$\mathrm{Turn\:8\:into\:a\:fraction\:that\:has\:the\:same\:denominator\:as\: - \dfrac{ 53 }{ 6 }}$

$\mathrm{Multiples\:of\:1: \:1,2,3,4,5,6}$

$\mathrm{Multiples\:of\:6: \:6,12,18,24,30,36,42,48}$

$\mathrm{Convert\:8\:to\:fraction\:\dfrac{ 48 }{ 6 }}$

$y = - \dfrac{ 53 }{ 6 } + \dfrac{ 48 }{ 6 }$

$\mathrm{Since\: - \dfrac{ 53 }{ 6 }\:have\:the\:same\:denominator\:,\:add\:them\:by\:adding\:their\:numerators}$

$y = \dfrac{ -53+48 }{ 6 }$

$\mathrm{Add\: -53 \: and\: 48\: to\: get\: -5}$

$y = - \dfrac{ 5 }{ 6 }$

$\mathrm{The\:solution\:is\:the\:ordered\:pair\:(\dfrac{ 53 }{ 30 }, - \dfrac{ 5 }{ 6 })}$

So there is only one solution to the equation.

5 0

2 years ago

PLEASE ANSWER ASAP!!! THANK YOU!!! ONLY 3 QUESTIONS!!

d1i1m1o1n [39]

For the each of them simply substitute for x in each equation to see if you get the corresponding y , it doesnt really get any more straightforward than this

4 0

3 years ago

In the figure, solve for x and y.

evablogger [386]

Answer:

y=124°

x=67°

Step-by-step explanation:

For the triangle on the right

180-74-50=56°

then y= 180-56=124°

For the triangle on the middle (that small triangle)

180-85(Head opposite angles)-50=45°

So

x=180-45-68=67°

5 0

3 years ago

NEED HELP IN THREE MATH QUESTIONS

RUDIKE [14]

I can'r see the problem

6 0

3 years ago

-x + 1/2 = x + 41/2<br> *PLEASE SHOW WORK*

ollegr [7]

-x + 1/2 = x + 4 1/2
  +x           +x
         1/2 = 2x + 4 1/2
       -4 1/2       - 4 1/2
        -4 = 2x
         x = -2

6 0

3 years ago