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Murrr4er [49]
3 years ago
15

A rectangular bird sanctuary is being created with one side along a straight riverbank. The remaining three sides are to be encl

osed with a protective fence. If there are 12 km of fence available, find the dimension of the rectangle to maximize the area of the sanctuary.
Mathematics
1 answer:
shusha [124]3 years ago
6 0

Answer:

For a rectangle of length L and width W, the perimeter is:

P = 2*L + 2*W

And the area is:

A = L*W.

Now, we know that the sanctuary has one side along a straight riverbank, then we will not fence that side. if L > W, then makes sense to put one of the "length" sides in the riverbank, in that way, we are saving more fence for the other 3 sides.

Then we will have that, the total length of fence used is:

12km = 2*W + L (two times the width and only one time the length are fenced).

From this, we can isolate one of the variables:

L = 12km - 2*W

And replace that in the area equation:

A(W) = (12km - 2*W)*W = 12km*W - 2*W^2.

To maximize this function, we must see when the first derivate is equal to zero:

A'(W) = 12km - 4*W = 0

            12km = 4*W

             12km/4 = 3km = W

Then the width that maximizes the area is W = 3km.

And the maximum area will be:

A'(3km) = 12km*3km - 2*(3km)^2 = 18km^2

And the length can be computed with the equation:

L = 12km - 2*W = 12km - 2*3km = 6km

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Eloise's rabbit cage is shape like a rectangular prism. The cage has a height of 28 inches and a volume of 8,680 cubic inches. E
Tems11 [23]

Answer:

310 inches²

Step-by-step explanation:

Given: A rectangular prism cage has a height of 28 inches.

           Volume of prism is 8680 cubic inches.

           

We know the area of base of rectangular prism is equal to the area of rectangle.

∴ Lets find out the lenght and width of rectangular prism.

Volume of rectangular prism= w\times l\times h

Where, w is width

             l is length

             h is height.

Now, putting the value in the formula of volume.

⇒ 8,680= w\times l\times 28

cross multiplying

⇒ wl= \frac{8680}{28}

∴ wl= 310 inches²

As we need to find the area of the plastic mat on the bottom of the cage, which is rectangle in shape.

Area of rectangle= wl

∴ Area of rectangle= 310 inches²

Hence,  310 inches² is the area of the plastic mat on the bottom of the cage.

4 0
3 years ago
The circumference of a circle is 18.84 yards. What is the circle's diameter?
zhannawk [14.2K]

Answer:

The diameter is 6 yards.

Step-by-step explanation:

2pir=18.84

pir=9.42

r=3(nearest whole number)

d=2r

d=2*3

d=6

Therefore, the diameter is 6 yards.

5 0
3 years ago
Read 2 more answers
Naruto ran 634 miles today, and Sakura Ran412 miles. How many times the length of Sakura's distance was Naruto's distance? Selec
dezoksy [38]

Answer:

Step-by-step explanation:

The question reads much more complicatedly than the actual equation.

Sakura * x = Nanuto

412 x = 634     Divide by 412

x = 634/412

x = 1.54 times

The closest answer is 3/2 as far. 1.54 is just about 3/2.

6 0
2 years ago
Graph the line that has a slope of 6 and includes the point (0,4).
faust18 [17]

Answer:

The equation of the line with slope 6 and containing the point (0, 4) will be:

y = 6x+4

The graph of the line y = 6x+4 is attached below.

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

Given

  • The slope m = 6
  • The point (0, 4)

The y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

The point (0, 4) indicates that:

at x = 0, y = 4

Thus, the y-intercept b = 4

now substituting b = 4 and m = 6 in the slope-intercept form of the line equation

y = mx+b

y = 6x+4

Thus, the equation of the line with slope 6 and containing the point (0, 4) will be:

y = 6x+4

The graph of the line y = 6x+4 is attached below.

3 0
3 years ago
The sum of five consecutive multiples of 4 is 20.Find the smallest integer.
Aloiza [94]

Answer:

The smallest integer is -4.

Step-by-step explanation:

Let the smallest integer be x.

Since the integers are all multiples of 4, they are

=> x, x+4, x+8, x+12 and x+16

=> x + x+4 + x+8 + x+12 + x+16 = 20

=> 5x + 40 = 20

Subtract 40 from both sides of the equation

5x +40 - 40 = 20 - 40

5x = -20

Divide both sides by the coefficient of x(which is 5)

\frac{5x}{5} = \frac{-20}{5}

x = -4

∴ the smallest integer is -4.

Hope this helps!!!

6 0
2 years ago
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