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Stells [14]
3 years ago
12

Preston wants to create a garden that backs up to an existing fence in his yard. He won't need to enclose the garden with fencin

g and he only has 85 feet of fencing available. What was the largest dimensions of the garden be if you could encloses the three sides of the garden and use the existing fence as the fourth side? If necessary, round answer to the nearest tenth.
Mathematics
1 answer:
Daniel [21]3 years ago
8 0

Answer:

  42.5 ft by 21.3 ft

Step-by-step explanation:

The largest area is obtained when half the available fence is used parallel to the existing fence, and the other half is used to fence the two ends of the rectangle. Here, that means the dimension parallel to the existing fence is ...

  (85 ft)/2 = 42.5 ft

and the ends of the rectangular garden are ...

  (42.5 ft)/2 = 21.25 ft ≈ 21.3 ft

_____

You can figure this as follows:

Let x represent the length of fence parallel to the existing fence. Then the other dimension of the fenced area is (85 -x)/2 and the fenced area is the product of these dimensions.

  area = x(85-x)/2

This expression describes a downward-opening parabola with zeros at x=0 and at x=85. The vertex (maximum) will be found where x is halfway between these values, at x = (0 +85)/2 = 42.5.

Area is maximized when 42.5 ft of fencing is used parallel to the existing fence, and the other half of the fencing is used for the other two sides of the enclosure.

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A plumber charges $130 2 hours of work and $235 for 5 hours of workWhat is the of change in dollars per hour
kogti [31]

Answer:

235

Step-by-step explanation:

Figure the rates per hr.

110/3 = 36 2/3

160/5 = 32.

So, the rates are not the same.

Knowing a bit about plumbers, they normally charge a basic fee to just show up, and then they charge per hr.

In cases like these, where we're asked to project to a new data point (in this case an 8-hr job), you should immediately think of a graph. The x-axis would be the hours worked. The y-axis would be the charge for the work (the cost of the job).

We're given two pairs of values:

(3,110) and (5,160).

The next step is to fit a line to them.

y = mx+b is the general equation for a line.

m = the slope = rise/run = change in y / change in x

Call the change in y, dy (for delta y).

Call the change in x, dx (for delta x).

m = dy/dx = 50/2 = 25

The slope is thus 25, which means for each hour, the price goes up by $25. That means the plumber charges $25/hr.

We also know the plumber charges $110 for a 3-hr job. 3*25 = $75. So the base charge would be $110-75 = $35.

y = 25x + 35

Checking this formula at x=3, we know it is 110.

Checking it at x=5, we obtain:

y = 25*5 + 35 = 125 + 35 = 160.

That checks.

Now to figure an 8-hr job, set x=8 and use the equation"

y = 25*8 + 35.

y = 200 + 35.

y = 235.

That means an 8-hr job costs $235.

3 0
3 years ago
Who feels to talk
zubka84 [21]

Answer:

I gotcu

The answer is 30.25

Step-by-step explanation:

5.5 divided by 4 equals 1.375

22 times 1.375 equals 30.25

8 0
3 years ago
What is the sqrt{-38} in the simplest form
mixas84 [53]

Answer: 6.164 √38

Step-by-step explanation: hope this is what your looking for :)

3 0
3 years ago
Read 2 more answers
$8000.00,r=12.5%,t=3months
victus00 [196]
P times r times t is wwhat you need to do
8 0
4 years ago
What percent of 480 is 160?<br> A. 0.3%<br> B. 3%<br> C. 30%<br> D. 33.3%<br> E. 300%
Kaylis [27]
Answer: E

Explanation: If you are using a calculator, simply enter 480÷160×100 which will give you 300 as the answer.
4 0
3 years ago
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