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SOVA2 [1]
3 years ago
10

A farmer wants to fence a rectangular area of 128 square feet next to a river. Find the length and width of the rectangle which

uses the least amount of fencing if no fencing is needed along the river. Assume the length of the fence runs parallel to the river.
Mathematics
1 answer:
Delicious77 [7]3 years ago
7 0

Answer:

Length=16 ft

Width=8 ft

Step-by-step explanation:

Let width be w and length will be 128/w since area is product of length and width

Perimeter will be w+w+128/w. Note that along the river, fencing isn't needed that is why perimeter equals 2w+128/w

Getting the first differential of perimeter with respect to w then

2-\frac {128}{w^{2}}

At critical point

2-\frac {128}{w^{2}}=0

2=\frac {128}{w^{2}}

w^{2}=64\\w=8

Therefore, since length is 128/w, length is 128/8=16 ft

Therefore, maximum length and width are 16 ft and 8ft respectively

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A lumber yard has five different lengths of 2 by 4 boards. Based on cost per linear foot, which is the best deal available on 2
ExtremeBDS [4]

Complete Question:

Here is the complete question:

<em>A lumber yard has five different lengths of 2 by 4 boards. Based on cost per linear foot, which is the best deal available on 2 by 4 boards at this lumber yard?</em>

<em>2 × 4 BOARD PRICES </em>

<em>8 foot board for $2.95 </em>

<em>10 foot board for $3.15 </em>

<em>12 foot board for $4.10 </em>

<em>16 foot board for $5.80 </em>

<em>20 foot board for $6.95</em>

Step-by-step explanation:

  • 8 foot board for $2.95

         \frac{2.95}{8}= 0.36875

  • 10 foot board for $3.15

        \:\frac{3.15}{10}=0.315

  • 12 foot board for $4.10

        \frac{4.1}{12}=0.341

  • 16 foot board for $5.80

        \frac{5.8}{16}= 0.3625

  • 20 foot board for $6.95

        \frac{6.95}{20}= 0.3475

Therefore, <em>10 foot board for $3.15</em><em>  </em>is the best deal available on 2 by 4 boards at this lumber yard. It means  you should be able to get 1 board for $0.315 when you buy 10 boards.

3 0
3 years ago
12.) (5pts) Sarah wants to fence her garden, as shown below. Determine how much fencing to the nearst foot hd
Maksim231197 [3]

Answer:

If those are the sides of the garden then it should be 86ft to fence around her garden.

Step-by-step explanation:

Add them together and then multi ply it by two.

4 0
3 years ago
What is the sum of 10000+101010
vredina [299]

Answer:

111010

Step-by-step explanation:

it is the correct answer

6 0
2 years ago
Read 2 more answers
Please HELP!!!!
Karolina [17]

Answer:


Step-by-step explanation:

Firstly, note that -2i really is just z = 0 + (-2)i, so we see that Re(z) = 0 and Im(z) = -2.

When we're going from Cartesian to polar coordinates, we need to be aware of a few things! With Cartesian coordinates, we are dealing explicitly with x = blah and y = blah. With polar coordinates, we are looking at the same plane but with angle and magnitude in consideration.

Graphing z = -2i on the Argand diagram will look like a segment of the y axis. So we ask ourselves "What angle does this make with the positive x axis? One answer you could ask yourself is -90°! But at the same time, it's 270°! Why do you think this is the case?

What about the magnitude? How far is "-2i" stretched from the typical "i". And the answer is -2! Well... really it gets stretched by a factor of 2 but in the negative direction!

Putting all of this together gives us:

z = |mag|*(cos(angle) + isin(angle))

= 2*cos(270°) + isin(270°)).

To verify, let's consider what cos(270°) and sin(270°) are.

If you graph cos(x) and look at 270°, you get 0.

If you graph sin(x) and look at 270°, you get -1.

So 2*(cos(270°) + isin(270°)) = 2(0 + -1*i) = -2i as expected.

3 0
3 years ago
PLEEEEASE PLAZE HELP ME WITH THIS! ITS A REALLY LATE ASSIGNMENT I FORGOT ABOUT AND ITS DUE TODAY AT 12:00! I WILL MARK AS BRINLI
Drupady [299]
1,800 is your answer because 1,200/72=16.6666667 and 1,800/108=16.6666667.


Hoped I helped!
7 0
2 years ago
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