A farmer wishes to build a rectangular plot with 800 meters of wire fencing. use calculus to find the maximum area that can be enclosed by the fence

the answer is (6,-3)

When the square sheet of cardboard is cut and folded to create a rectangular box with a lid, the maximum possible volume is achieved when x = 20 inches. All other values will result in a smaller volume for the box.

Here, we have,

1. Calculate the side lengths of the box and lid:

Box: 40 inches - 2x = 40 - 2x

Lid: 2x

2. Calculate the volume of the box with a lid when x = 20 inches:

Box Volume:

(40 - 2x) x (40 - 2x) x (40 - 2x) = (40 - 2*20) x (40 - 2*20) x (40 - 2*20) = (20) x (20) x (20)

= 8000 in^3

Lid Volume: 2x x 2x x 2x = 2*20 x 2*20 x 2*20

= 8000 in^3

Total Volume: 8000 in^3 + 8000 in^3 = 16000 in^3

3. Calculate the volume of the box with a lid when x = 20/3 inches:

Box Volume: (40 - 2x) x (40 - 2x) x (40 - 2x) = (40 - 2*20/3) x (40 - 2*20/3) x (40 - 2*20/3) = (33 1/3) x (33 1/3) x (33 1/3)

= 7157.7 in^3

Lid Volume: 2x x 2x x 2x = 2*20/3 x 2*20/3 x 2*20/3

= 1365.3 in^3

Total Volume: 7157.7 in^3 + 1365.3 in^3

= 8523 in^3

4. Comparison:

When x = 20 inches, the box has a minimum possible volume of 16000 in^3, while when x = 20/3 inches, the box has a volume of 8523 in^3. Therefore, the statement is true.

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Complete question:

The figure above represents a square sheet of cardboard with side length 40 inches. The sheet is cut and pieces are discarded. When the cardboard is folded, it becomes a rectangular box with a lid. The pattern for the rectangular box with a lid is shaded in the figure. Four squares with side length xx and two rectangular regions are discarded from the cardboard. Which of the following statements is true? (The volume V of a rectangular box is given by V=lwh).

A. When x = 20 inches, the box has a minimum possible volume.

B. When x = 20 inches, the box has a maximum possible volume.

C. When x = 20/3 inches, the box has a minimum possible volume.

D. When x = 20/3 inches, the box has a maximum possible volume.

Answer:

The answer is [tex]s^(-1 )(x) = (1)/(2\sqrt(\pi ))\sqrt(x)[/tex] .

Step-by-step explanation:

The input of [tex]s^(-1 )[/tex] is the surface area of a sphere; the output is the length of the radius.

Hence, the Taylor polynomial centered at [tex]x=0[/tex]  for some function [tex]f[/tex] is [tex]p^4(x)=3[/tex].

What is an equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given equation is

[tex]p^4(x)=3-4x+2x^2-3x^3+2x^4 .......(1)[/tex]

Substitute [tex]x=0[/tex] in the equation [tex](1)[/tex], we get

[tex]p^4(x)=3-4(0)+2(0)^2-3(0)^3+2(0)^4 \\p^4(x)=3[/tex]

Hence, the Taylor polynomial centered at [tex]x=0[/tex]  for some function [tex]f[/tex] is [tex]p^4(x)=3[/tex].

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Final answer:

The value of f(0) for the given Taylor polynomial p4(x) = [tex]3 - 4x + 2x^2 - 3x^3 + 2x^4[/tex] is 3, as the constant term in a Taylor polynomial centered at x = 0 represents f(0).

Explanation:

The question asks for the value of f(0) given a degree 4 Taylor polynomial for some function f, centered at x = 0. A Taylor polynomial of a function f centered at x = 0 is given by

f(x) = f(0) + f'(0)x + f''(0)x2/2! + f'''(0)x3/3! + ...

Each coefficient in front of the powers of x represents the derivative of f at 0 divided by the factorial of the order of the derivative. For

p4(x) = [tex]3 - 4x + 2x^2 - 3x^3 + 2x^4[/tex]

the constant term, which is 3, represents f(0), because it corresponds to the value of the function at x = 0 before any derivatives are taken into account.

Answer: B-2.3

Step-by-step explanation:

Just took the test heres the answer and proof

Answer: D) (x+8)2 +( y+5)2 = 13

Step-by-step explanation:

Got this right on USA test prep

Answer:

yes

Step-by-step explanation:

General Idea:

Vertical line test is a test used to determine if a relation is a function. As per vertical line test, a relation is a function if there are no vertical lines that intersect the graph at more than one point.

Applying the concept:

Kelly ask Tyrese to help her use the vertical line test to determine whether or not the curve that she was given it is a function Tyrese informed Kelly that an order for the given curve to be designated as a function of a vertical line drawn through any x value must intersect the Curve [tex] ONE [/tex] time.

The answer to this question is A.

In a box plot, the values outside box are less likely to occur than the values inside the box. The store a person MOST LIKELY pay $18.75 for a pair of shoes from is given by: Option A: Store A

A box plot has 5 data description.

For all the box-plots plotted in the image attached, we can see that only the first box plot is such that the amount $18.75 is falling inside the box's boundaries.

The box is contained with more likely elements than those which are outside of it.  It is because, the box contains those elements which are between first and third quartile. Since the selection was done randomly, so mean, median and mode all lie approximately on the same point due to the distribution tending to normal distribution(sample size is large enough (50 > 30, a needed sample size for consideration of that sample belonging from normal distribution)). Now, for the first graph, the median is closest to $18.75, and the more close a value is to center of a normal distribution, the more probable it is.

That's why, the store a person MOST LIKELY pay $18.75 for a pair of shoes from is given by: Option A: Store A

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To solve this problem you must apply the proccedure shown below:

 1. You have that the data set has SSR=400 and SSE=100

 2. Therefore you have the coefficient of determination is:

 r²=SSR/SSTO

 SSTO=SSR+SSE

 3. Then, when you substitute the values, you obtain:

 SSTO=400+100

 SSTO=500

 r²=400/500

 4. So, you have that the result is:

 r²=0.8

 Therefore, as you can see,  the answer for the exercise shown above is:  the coefficient of determination is 0.8

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i feel like its A but i am dumb

Final answer:

The freight and passenger trains will meet 120 miles from Boston at 2 PM, which is 2 hours after the passenger train departs.

Explanation:

To solve this problem, we need to figure out when the two trains will meet, given their different start times and speeds. Since the freight train leaves at 9 AM and the passenger train leaves at noon, there is a 3-hour difference between their departure times.

In those 3 hours, the freight train will cover a distance of 3 hours  imes 24 miles/hour = 72 miles.

Both trains are now heading towards each other, with the passenger train moving faster. We need to find out how long it will take for the passenger train to catch up to the freight train, starting from the 72-mile head start.

Let's call the time it takes for the passenger train to catch up 't' hours. In 't' hours, the passenger train will cover 60t miles and the freight train will cover 24t miles.

Since the passenger train is trying to cover the lead that the freight train has plus the distance both are covering after noon, we can set up an equation: 60t = 72 + 24t. Solving for 't' gives us 't' = 72 / (60 - 24) = 2 hours. So, in 2 hours after noon, which is at 2 PM, the two trains will meet.

Now we find out how far from Boston they will meet by calculating the distance the passenger train travels in those 2 hours: Distance = 60 miles/hour  imes 2 hours = 120 miles from Boston.

The probability that at most 24 heads occur is; 24/25.

Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true. The probability of all the events occurring need to be 1.

We have been given that a fair coin is tossed 25 times.

So, We need to find the probability:

Favourable outcomes = 24

Total outcomes = 25

The formula of probability = Favourable outcomes/Total outcomes

⇒ 24 /25

Therefore, the probability that at most 24 heads occur is; 24/25.

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The probability of getting at most 24 heads in 25 tosses of a fair coin is approximately 99.999997%

The probability of getting at most 24 heads when a fair coin is tossed 25 times is essentially 100%, because the only other possible outcome is getting exactly 25 heads, which has a very small probability. Since each toss of a fair coin has only two possible outcomes (either head or tail), and each toss is independent, we can use the binomial distribution to find the probability of a certain number of heads occurring.

To calculate the probability of getting exactly 25 heads in 25 tosses, we use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Where:

n is the number of trials (tosses), so n=25,

k is the number of successes (heads) we're calculating the probability for, so k=25,

p is the probability of success on any given trial, which is 0.5 for a fair coin.

Substitute these values into the formula, we get:

P(X = 25) = (25 choose 25) * 0.5^25 * (1-0.5)^(25-25)

This equates to:

P(X = 25) = 1 * 0.5^25 * 1 = 1/33,554,432 ≈ 0.00000003 or 0.000003%.

Therefore, the probability of getting at most 24 heads is 1 - P(X = 25) which is approximately 0.99999997 or 99.999997%.

Answer:

A)ΔXYZ ≅ ΔLMN

B)∠Y ≅ ∠M

C)∠X ≅ ∠L

F)XZ ≅ LN

Step-by-step explanation: correct on edge 2020

A reflected triangle is congruent to the original triangle with corresponding angles and sides being equal. However, the orientation changes such that ∠X corresponds to ∠L, ∠Y to ∠M, and ∠Z to ∠N in the reflected triangle. Similarly, side YZ corresponds to MN, not ML, and XZ corresponds to LN.

In the subject of mathematics, specifically geometry, when you reflect a shape, the original shape and its image are congruent. This means they have the same size and shapes, but their orientation might differ. Therefore, the statement ΔXYZ ≅ ΔLMN is indeed true.

In terms of the specific angles, a reflection does not change their measures; it simply changes their orientations. Therefore, ∠X is congruent to ∠L, ∠Y is congruent to ∠M, and ∠Z is congruent to ∠N. However, the statement ∠Z ≅ ∠L is incorrect as Z corresponds to N, not L, in the reflected triangle.

Similarly, side lengths also remain the same in a reflection. Thus, XY corresponds to ML, YZ corresponds to MN and XZ corresponds to LN, making the statements YZ ≅ MN and XZ ≅ LN true. But the statement YZ ≅ ML is incorrect as YZ corresponds to MN, not ML, in the reflected triangle.

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