A beach has to enclose a rectangular area, because some endangered species are nesting there. They have 200 feet of rope to rope off the area with. What is the maximum area that they can rope off?
Answers
A = l * w
200 = 2l + 2w
solve for either l or w
l = 100 - w
plug into the area equation to get one equation with two variables
A = w(100 - w)
A = -w^2 + 100w
take the derivative
A' = -2w + 100
set the derivative equal to zero
0 = -2w + 100
2w = 100
w = 50
This is the width that maximizes the area
with a width of 50, the length must also be 50 to have a perimeter of 200
therefore, they can rope up to 50 * 50 = 2500 ft^2
Final answer:
The maximum area that can be roped off with 200 feet of rope is 2500 square feet by making the roped off area a square.
Explanation:
The question deals with the optimization of area given a fixed perimeter, which involves the principles of geometry and algebra. Since the area needs to be roped off is a rectangle, and you have 200 feet of rope, your rectangle will have dimensions length (L) and width (W) such that 2L + 2W = 200.
To maximize the area of a rectangle given a fixed perimeter, the rectangle should be a square. So, for a maximum area, the length and width should be equal. Thus, each dimension (length and width) would be 200/4 = 50 feet.
Finally, to find the maximum area, we multiply the length by the width: 50 feet * 50 feet = 2500 square feet. So, the maximum area that they can rope off with 200 feet of rope is 2500 square feet.
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B. An oblique solid with a base of 6 cm2 and a slant height of 12cm
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D. An oblique solid with a base of 6 cm2 and a height of 12 cm
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The two solid figures with the same volume are a rectangular solid with a base of 6 cm² and a height of 12 cm and an oblique solid with a base of 6 cm² and a height of 12 cm
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An equation is an expression that shows the relationship between two or more numbers and variables.
The volume of a rectangular solid with a base of 6 cm² and a height of 12 cm is:
Volume = 6 cm² * 12 cm = 72 cm³
The volume of an oblique solid with a base of 6 cm² and a height of 12 cm is:
Volume = 6 cm² * 12 cm = 72 cm³
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Answers
First, expand your problem. / Your problem should look like:
Second, simplify 5x - 32x + 56. / Your problem should look like:
Third, subtract 56 from both sides. / Your problem should look like:
Fourth, subtract 2 - 56 to get -54. / Your problem should look like:
Fifth, divide both sides by -27. / Your problem should look like:
Sixth, simplify the fraction to
Seventh, simplify. / Your problem should look like:
Answer: x = 2
Yes
or
No
Answers
Answer:
Yes
Step-by-step explanation:
f(x) = x^3 + x^2 −4x − 4
Factor by grouping taking x^2 out of the first group and -4 out of the second
0 = x^3 + x^2 −4x − 4
x^2(x+1) -4(x+1)
Factor out (x+1)
0=(x+1)(x^2-4)
Now we have the difference of squares
0=(x+1) (x-2)(x+2)
x+1 is a factor
Answer:
Yes
Step-by-step explanation:
( x^3 + x^2) (-4x - 4)
x^2 ( x+1) -4 (x+1)
(x^2 - 4) (x+1)
(x-2) (x+2) (x+1)
X= 2 x=-2 x=-1
Answers
25%=25/100=1/4
ratio is 1:4 or 2:8 or 6:12
Answers
Answer:
x=30
2x=60
3x=90
Step-by-step explanation:
in total there is 6x
180/6=30
x=30
2x=60
3x=90
Answer:30°
Step-by-step explanation:
Thera are 3 angles in a triangel. The sum of all angles is 180°
x+2x+3x=180
6x=180
x=180/6=30