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VladimirAG [237]
3 years ago
11

A rectangular area adjacent to a river is fenced​ in; no fence is needed on the river side. The enclosed area is 1000 square fee

t. Fencing for the side parallel to the river is $ 8 per​ foot, and fencing for the other two sides is $ 4 per foot. The four corner posts are $ 20 each. Let x be the length of one of the sides perpendicular to the river.
(a) Write a function C(x) that describes the cost of the project.
(b) What is the domain of C?
Mathematics
1 answer:
user100 [1]3 years ago
5 0

Answer:

C(x)  =  8*x  +  8* (1000)/x  + 80

C(x)  Domain  x > 0

Step-by-step explanation:

enclosed area     1000 ft²

let   x be side perpendicular to the river

and  y  parallel to the river

Then:

A = x*y               y  =  A / x           y  =  1000/x

Cost of one side (x)    4*x  $   then two sides     cost = 4*2*x    cost = 8*x

Cost of one side (y)    8*y  $      8* (1000/x)

Cost of four cornes posts   4*20 = 80 $

Total cost  C(x)

C(x)  =  8*x  +  8* (1000)/x  + 80

R {   x > 0}

Taking derivatives both sides of the equation

C´(x) = 8  - 8000/x²       C´(x) = 0        8  - 8000/x² = 0

8x² -8000 = 0     x²  = 1000

x = 100

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Answer:

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Step-by-step explanation:

These are corresponding angles. When a transversal crosses 2 parallel lines, 4 angles are created at each intersection, and each pair of corresponding angles between those are congruent.

These angles are congruent, so you can set them equal to each other:

2x+20=3x-15

Then, just solve for x:

20=x-15\\35=x\\x=35

You can check that by plugging it back into both:

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(15.2*0.25-48.51/14.7)/x=(13/44-2/11-5/66/2.50)1.2/(3.2+0.8(5.5-3.25)
goldfiish [28.3K]

Answer:

x = 41.67

Step-by-step explanation:

The above equation, would be simplified or divided into parts;

Therefore, the given equation becomes;

A/x = B/C

Where;

A = (15.2*0.25-48.51/14.7)

B = (13/44-2/11-5/66/2.50)1.2

C = 3.2+0.8(5.5-3.25)

x = unknown variable.

<u>Part A</u>

(15.2*0.25-48.51/14.7) = (15.2*0.25 - 3.3)

A = (3.8 - 3.3)

A = 0.5

<u>Part B</u>

(13/44-2/11-5/66/2.50)1.2 = (0.3 - 0.18 - 0.030) * 1.2

B = 0.09 * 1.2

B = 0.108

<u>Part C</u>

(3.2+0.8(5.5-3.25)

C = 4*(2.25)

C = 9

<em>Substituting the values into the equation, we have;</em>

0.5/x = 0.108/9

<em>Cross-multiplying, we have;</em>

9 * 0.5 = 0.108x

4.5 = 0.108x

x = 4.5/0.108

x = 41.67

6 0
2 years ago
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