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Roman55 [17]
3 years ago
15

a farmer wants to fence in three sides of a rectangular field shown below with 960 feet of fencing. The other side of the rectan

gle will be a river. If the enclosed area is to be a maximum, find the dimensions of the field. ​

Mathematics
1 answer:
Alika [10]3 years ago
3 0

9514 1404 393

Answer:

  240 ft by 480 ft

Step-by-step explanation:

Area is maximized when the long side is half the total length of the fence. That makes the short side (out from the river) be half the length of the long side.

The fenced field dimensions are 240 feet by 480 feet.

__

You can let x represent the length of the long side. Then the length of the short side is half the remaining fence: (960 -x)/2.

The total area is the product of these dimensions:

  A = x(960 -x)/2

We note that this is the equation of a parabola with zeros at x=0 and x=960. The maximum will be found on the line of symmetry, halfway between the zeros. That is at x = (0 +960)/2 = 480.

The area is maximized for a long-side dimension of 480 feet. The short sides are 240 feet.

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At 82°F, a certain insect chirps at a rate of 61 times per minute, and at 91°F, they chirp 124 times per minute. Write an equati
Ganezh [65]

Answer:

y=7x-513

Step-by-step explanation:

Let

x----> the temperature in degrees Fahrenheit

y ---->insect chirping rate in times per minute

we have the ordered pairs

(82,61) and (91,124)

step 1

Find the slope

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{124-61}{91-82}

m=\frac{63}{9}=7

step 2

Find the equation of the line

we know that

The equation in slope intercept form is equal to

y=mx+b

where

m is the slope

b is the y-intercept

we have

m=7  ---> the units are chirps per minute/degree F

take the point (82,61)

substitute and solve for b

61=7(82)+b

61=574+b

b=-513

substitute

y=7x-513

4 0
3 years ago
The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water is the
SOVA2 [1]

Answer:

The height of the water increases 2 inches per minute. Or A

Step-by-step explanation:

Edge

6 0
3 years ago
Solve: x^4-34x^2=-225
dangina [55]
X
4
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2 Factor
x
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x
4
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2
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(
x
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−
25
)
(
x
2
−
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=
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(x
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8 0
3 years ago
Free 50 points hurry up and i will mark brainliest
svetlana [45]
Yes please merry Christmas
8 0
2 years ago
Read 2 more answers
Find the equation of the line shown.
vladimir1956 [14]

Answer:

y = - x + 9

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (0, 9) and (x₂, y₂ ) = (9, 0) ← 2 points on the line

m = \frac{0-9}{9-0} = \frac{-9}{9} = - 1

the line crosses the y- axis at (0, 9 ) ⇒ c = 9

y = - x + 9 ← equation of line

4 0
2 years ago
Read 2 more answers
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