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

Answer 1

Answer: Given:
rectangular area
200 feet of rope to rope off the area with.

200 feet is the perimeter of the rectangle. Since its a rectangle its length should be greater than its width.

Perimeter = 2(L + W)
200 ft = 2 (L + W)
200 ft / 2 = (L + W)
100 ft = L + W

100 ft can be distributed as follows:
Length Width Area = Length * Width
90 10 900
85 15 1,275
80 20 1,600
75 25 1,875
70 30 2,100
65 35 2,275
60 40 2,400
55 45 2,475

The maximum area that can be roped off is 2,475 ft².

Answer 2

Answer:

Answer:

2500

Step-by-step explanation:

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The sum of two numbers is 30. Their difference is 6. What are the numbers?6 and 24
12 and 18
10 and 20
8 and 14

Answers

Answer:

Find out the numbers .

To prove

Let us assume that one number be x.

Let us assume that second number be y.

As given

The sum of two numbers is 30.

Than the equation becomes

x + y = 30

Their difference is 6.

x - y = 6

Thus two equation are .

x + y = 30 and x - y = 6

Subtracted x - y = 6 from x + y = 30

x - x + y - (-y) = 30 - 6

y + y = 24

2y = 24

$y = (24)/(2)$

y = 12

Put in the x - y = 6

x - 12 = 6

x = 6 + 12

x = 18

Therefore the two numbers are 12 and 18 .

Okay lets start by getting rid of the ones that don't have a difference of 6. We are now left with '12 and 18' and '6 and 14'. If we take a look we can see that '6 and 14' add up to 20. So it is clear that only '12 and 18' add up to 30 and have a difference of 6.

Let R be the region in the first quadrant bounded by the graph of y=sqrt{x-2} and the line y=2.(a). Find the volume of the solid generated when R is revolved about the x-axis.
(b). Find the volume of the solid generated when R is revolved about the line y=-2.

Answers

Volume of the solid generated when R is revolved about the x-axis is 10π and the volume of the solid generated when R is revolved about the line y = -2 is 40π/3.

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The volume of the solid generated when R is revolved about the x-axis,

$V=\int\limits^a_b\pi {y^(2) } \, dx$

where a and b are the x-coordinates of the points of intersection of the curve y = √(x-2) and the line y = 2.

Solving y = √(x-2) and y = 2 for x, we get:

x = 6 and x = 2

Limits of integration are a = 2 and b = 6. Substituting y = √(x-2) into the formula for the volume, we get:

V = $\int\limits^6_2\pi\sqrt{(x-2)^(2) } \, dx$

V= π [(6²/2 - 2(6)) - (2²/2 - 2(2))]

=10π

Volume of the solid generated when R is revolved about the x-axis is 10π.

b. The volume of the solid generated when R is revolved about the line y = -2

$V=\int\limits^a_b\pi {(y+2)^(2) } \, dx$

Substituting y = √(x-2) into the formula for the volume, we get:

$V=\int\limits^2_6\pi (√(x-2)+2)^(2) \, dx$

We can simplify this by using the identity:

V =40π/3

Therefore, the volume of the solid generated when R is revolved about the line y = -2 is 40π/3.

Hence, Volume of the solid generated when R is revolved about the x-axis is 10π and the volume of the solid generated when R is revolved about the line y = -2 is 40π/3.

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A.) Find the volume of the solid generated when R is revolved about the x-axis.

What is the average (mean) of the following numbers: 2, 5, 8, and 1? Options: 4 3 5 4.5

Answers

Answer:

mean = 4

Step-by-step explanation:

the average ( or mean ) of a data set is calculated as

mean = $(sum)/(count)$

sum = 2 + 5 + 8 + 1 = 16

count = 4 ( number of values in data set )

substitute these values into the formula for mean

mean = $(16)/(4)$ = 4

Final answer:

The mean (average) of the numbers 2, 5, 8, and 1 is calculated by adding the numbers together (which gives 16), and then dividing this sum by the total number of numbers (4). So, the mean of these numbers is 4.

Explanation:

The subject of this question is Mathematics and it relates to the concept of statistical mean (average). To find the mean of the numbers 2, 5, 8, and 1, you add them all up and then divide by the number of numbers.

First, add the numbers together: 2 + 5 + 8 + 1 = 16.
Then, divide by the total number of numbers, which in this case is 4. 16 divided by 4 is 4.

So, the mean (average) of 2, 5, 8, and 1 is 4.

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Mauritius island is 2 km due south of its closest point along a straight coastline. Gibril is staying at a private room on the shore that is 6 km east of that point. Gibril is planning to go from the room to the island. Suppose Gibril runs at a rate of 8 kmph and swims at a rate of 3 kmph. How far should Gibril run before swimming to minimize the time it takes to reach the island?