Electric power for an island 200 m offshore must come from a town 500 m away along the shore. If it costs $35/m to lay cable underwater and $21/m to lay cable underground, what path
should be chosen to minimize the total cost?

For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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The purpose of truth tables is to represent the possible values of a logical expression or a combination of expressions based on different input values. Truth tables help in determining the output of a particular statement, given a specific set of inputs. They are a vital tool in digital logic design and Boolean algebra.

Number systems, such as binary, relate to truth tables as binary digits (0 and 1) represent the two possible truth values (False and True) in Boolean logic. For example, when working with logical operators like AND, OR, and NOT, the inputs and outputs are represented by binary digits in truth tables.

Set Theory relates to truth tables as both are used to analyze and represent relationships between different elements or values. In set theory, you work with sets, which are collections of elements. The relationships between sets can be represented using Venn diagrams, which can be compared to truth tables in terms of visualizing relationships between elements.

To give an example, consider the logical AND operator:

1. Write down the possible input values: A and B can be either 0 (False) or 1 (True), leading to four possible input combinations.
2. Create a table with columns for each input and one for the output.
3. Fill in the table with the possible input combinations.
4. Determine the output for each combination based on the logical operator (AND).

The truth table for the AND operator would look like this:

| A | B | Output (A AND B) |
|---|---|------------------|
| 0 | 0 |        0         |
| 0 | 1 |        0         |
| 1 | 0 |        0         |
| 1 | 1 |        1         |

In this example, the truth table demonstrates that the AND operator only returns a 1 (True) when both input values A and B are 1 (True).

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1 pie is cut into eighths or 1/8 a slice. 3 are taken out.

8/8-3/8=5/8 is left.

Answer:

7/8

Step-by-step explanation:

8/8-1/8=7/8

The change in temperature from morning to night is ₋18°F which means the temperature decreased from morning to night.

Given the temperature in the morning is ₋10°F

and temperature in the night is 8°F

To calculate the difference, subtraction is used between the starting and final temperatures. In other words, if something starts at 50 degrees Celsius and ends up at 75 degrees C, the temperature difference is 25 degrees C, or 75 degrees C minus 50 degrees C. The outcome is adverse for drops in temperature.

change in temperature from morning to night  = ₋10°F ₋ 8°F

= ₋18°F

the result is negative, hence the temperature decreases from morning to night.

Hence we get the temperature change as ₋18°F.

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Answer:

35=3.5s =40 4.5s

Step-by-step explanation:

tell me if I'm wrong.

To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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Answer:

Next term is 31

Step-by-step explanation:

The numbers keep going up by 7.

If this has helped you please mark as brainliest

The required GCF is 8.

The greatest common factor is that greatest number from the factors which divides the number completely.

For example take numbers 12 and 16.

The factors of 12 are 2×2×3.

And the factors of 16 are 2×2×2×2.

We can clearly see that the common factors are 2×2 which gives 4. So, 4 is the greatest common factor which divides both 12 and 16.

Here it is given to find the greatest common factor of 16 and 40.

Factors of 16 = 2×2×2×2

Factors of 40 = 2×2×2×5

We can see clearly the common factors are 2×2×2 which gives 8.

So, 8 is the greatest common factor.

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Answer:

P = 1

Explanation:

The first two numbers in the form will be the numbers related to the month. Since there is no month 00, the probability that the number made up is greater than 0 is 1.

It means that in all forms, the number made up of the first two digits will be greater than 0.

So, the answer is:

P = 1

Answer:

87

Step-by-step explanation:

The median of a data set is the value that is exactly in the middle of all other values.

To find the median of a data set, we typically list the values in order of greatest to least, and we look for the number in the middle.

Here, the list-maker has already provided the list in this order!

78, 78, 83, 85, 89, 91, 95, 98

we can see two numbers exactly in the middle here--when this happens, we take the mean/average of the two:

85 + 89 = 174

174 / 2 = 87

So, the median of this data set is 87

hope this helps! have a lovely day :)

The train will take 3hour 7.5min to travel a distance of 250 km

Given that,

Distance of 250 km with a speed of 80 kmh

To find: Time taken by train to travel a distance of 250 km with a speed of 80 kmh

Distance = 250km

Speed of the train =80km/h

Speed is calculated as distance times speed. You need to be aware of the units for distance and time in order to calculate the units for speed. The units in this example will be metres per second (m/s), since the distance is measured in metres (m) and the time is measured in seconds (s).

Time = Distance /speed

=250km /80km/h

=25/8 h

= 3⅛h

= 3hour ⅛*60

= 3hour 7.5min.

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Answer:

3 hours 7.5 mim

Step-by-step explanation:

The train will take 3hour 7.5min to travel a distance of 250 km

Given that,

Distance of 250 km with a speed of 80 kmh

To find: Time taken by train to travel a distance of 250 km with a speed of 80 kmh

Distance = 250km

Speed of the train =80km/h

Speed is calculated as distance times speed. You need to be aware of the units for distance and time in order to calculate the units for speed. The units in this example will be metres per second (m/s), since the distance is measured in metres (m) and the time is measured in seconds (s).

Time = Distance /speed

=250km /80km/h

=25/8 h

= 3⅛h

= 3hour ⅛*60

= 3hour 7.5min.

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The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

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Answer:

The answer is 44x^15

Step-by-step explanation:

Simplify the expression.

Hoped this helped!

brainly, please?

Answer:

Greater :D

hope this helped (i may not be right)

Step-by-step explanation:

okay only the sy is replaced with xy

hope it helps:)

Answer:

Step-by-step explanation: 3(z-4)= -6

                                        3z-12=-6

                                        3z=6

                                           z=2

The perimeter of square ABCD is 28 units.

The perimeter of a square is the sum of all its sides. In this case, we need to find the perimeter of square ABCD.

The question provides two possible answers: 28 units and 37 units. However, we can only choose one correct answer. To determine the correct answer, let's think step by step.

A square has all four sides equal in length. Therefore, if we know the length of one side, we can find the perimeter.

If the perimeter of the square is 28 units, that would mean each side is 28/4 = 7 units long. However, if the perimeter is 37 units, that would mean each side is 37/4 = 9.25 units long.

Since a side length of 9.25 units is not a whole number, it is unlikely to be the correct answer. Hence, the perimeter of square ABCD is most likely 28 units.

In conclusion, the perimeter of square ABCD is 28 units.

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False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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Answer:

C

Step-by-step explanation:

Answer:

AAS

Step-by-step explanation:

2 angles and one included side

The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

In the Social Exchange Theory of interpersonal relationship satisfaction, you would feel happiest in relationships when you feel that the rewards of the relationship equal or exceed its costs.

The Social Exchange Theory states that people evaluate their relationships in economic terms, with rewards being the benefits of the relationship and costs being the negatives. Rewards can include affection, attention, emotional support, sex, and companionship. Costs can include time, effort, money, and negative emotions such as stress, anxiety, and sadness.

According to the theory, individuals will be motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

The opposite is also true; if individuals feel that the costs of the relationship are greater than the rewards, they will be motivated to leave the relationship.

Therefore, people are constantly evaluating their relationships to determine whether they are getting what they need from the relationship and whether it is worth continuing.

The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

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The sum of all the perfect squares between $15$ and $25$, inclusive, minus the sum of all the other integers between $15$ and $25$, inclusive, is \($-164$\).

To find the sum of all the perfect squares between $15$ and $25$, we need to list them out: $16$, $25$. The sum of these perfect squares is $16+25=41$.

To find the sum of all the other integers between $15$ and $25$, we can use the formula for the sum of an arithmetic series. The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms. In this case, the first term is $16$ and the last term is $25$, so there are $10$ terms. The average of the first and last term is \($\frac{16+25}{2}=20.5$\). Therefore, the sum of all the other integers between $15$ and $25$ is $20.5\times 10 = 205$.

Now we can subtract the sum of all the other integers from the sum of the perfect squares to get our final answer: $41-205 = -164$.

Therefore, the sum of all the perfect squares between $15$ and $25$, inclusive, minus the sum of all the other integers between $15$ and $25$, inclusive, is $-164$.

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If pipes A and B can fill a storage tank in 8 h and 12 h and pipe A was turned on at noon, and  pipe B was turned on at 1:30 P.M, then the water tank will be full at 5:24 pm

Another type of time- and work-based inquiry is called "pipes and cistern." You could ask questions like how long it takes to fill or empty a tank, how much effort is involved, and other similar inquiries. There are two important points that a candidate should understand about such questions:

An inlet is a conduit that is linked to a tank to allow water to be added to it. This kind of work has been accomplished.

An exit is a conduit that is attached to empty the water from the tank. This shows that the task was done in an unfavourable manner. In the query, it may also be referred to as "leak."

How to solve?

Let t = the "on" time duration of pipe A

(t-1.5) = the "on" time of pipe B

Let the completed job = 1; (a full tank)

3t + 2(t-1.5) = 24(1)

3t + 2t - 3 = 24

5t = 24 + 3

t = 27/5

t = 5.4 hrs, which is 5 hrs + (.4*60) = 5 hrs, 24 min

Therefore, the tank will be full at 5:24 pm

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The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

Given that,

We have to find for the marginal revenue function, locate the demand function.

Remember that the income is zero if no things are sold:

R'(x) = 0.06x² - 0.05x + 152

p(x) is what.

We know that,

MR = dTR/dx = 0.06x² - 0.05x + 152

Integrating the marginal revenue function , we get total revenue function,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 152x

= (0.06x³)/3 - (0.05x²)/2 + 152 x

TR  = 0.02 x³ - 0.025 x² + 152 x

TR = (P)(Q) = (P)(x) =  0.02 x³ - 0.025 x² + 152 x

P = ( 0.02 x³ - 0.025 x² + 152 x)/x

P = 0.02x² -0.025x + 152

Therefore, The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

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\(g(x)=a f(b(x-h))+c\)

We're given:

\(f(x)=x^3\)

\(f'(x)=x^3-3\)

f'(x) is equal to f(x) + 3.

This is the same as the "c" value mentioned above, which is a vertical translation.

If c is positive, the function translates up.

Therefore, it moves 3 units upward.

It moves 3 units upward.

The earnings per share can be calculated as $0.066 per share (rounded to the nearest cent).

a. The earnings per share for Company XYZ can be calculated by dividing the closing price by the P/E ratio. In this case, the closing price is $100.76 and the P/E ratio is 1525. Therefore, the earnings per share can be calculated as $0.066 per share (rounded to the nearest cent).

b. Based on the historical P/E ratio range of 12-14, the stock price of Company XYZ seems overpriced. The P/E ratio indicates the price investors are willing to pay for each dollar of earnings generated by the company. A higher P/E ratio suggests that investors have higher expectations for future earnings growth. In this case, the P/E ratio of 1525 is significantly higher than the historical range of 12-14, indicating that the stock is being valued at a much higher premium relative to its earnings. This suggests that the stock price may be inflated and not in line with the company's historical valuation metrics, indicating an overpriced condition.

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Answer:

a.

Step-by-step explanation:

by elimanation,cimparison or substitution you wull get the value of x=-60/17 and y=6/17

The smallest angle is 70 degrees, the angle that is 10 degrees greater is 80 degrees, and the angle that is 10 degrees less than twice the smallest is 130 degrees.

Let x be the smallest angle in the rectangle. Then:

One angle is 10 degrees greater than the smallest, so it is x + 10 degrees.

Another angle is opposite to the smallest angle and has the same measure, so it is also x degrees.

The third angle is 10 degrees less than twice the smallest, so it is 2x - 10 degrees.

We know that the sum of the angles in a rectangle is 360 degrees, so we can set up an equation:

x + (x + 10) + x + (2x - 10) = 360

Simplifying and solving for x, we get:

5x = 360 - 10

5x = 350

x = 70

Therefore, the smallest angle is 70 degrees, the angle that is 10 degrees greater is 80 degrees, and the angle that is 10 degrees less than twice the smallest is 130 degrees.

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Answer:

75°

Step-by-step explanation:

we can form a triangle to help us understand how to solve this problem:

                                                    puppy

∠ Leslie = 35°                                                   ∠ Surekha = 70°

If Leslie's angle is 35° and Surekha's angle is 70°, that gives us a total of 105°. Since the sum of the triangle's three angles is 180°, then the angle at which they will meet is 180° - 105° = 75°

In this exercise, we have to calculate the angle of the path that they met, so we will have:

75°

We know that the geometric figure in question is a triangle and that the sum of its internal angles must be equal to 180 degrees, thus:

\(180-105=X\\180-105=75\\\)

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