Find the length of a diagonal of a square enclosure with a perimeter of 16 feet. Round your answer to the nearest tenth

Answers

Answer 1
Answer:

Answer:

Step-by-step explanation:

A square enclosure would have all sides of equal length.  Thus, a perimeter of 16 feet would have 4 sides (16/4) or 4 feet in length.  The diagonal would form a right triangle with two sides of 4 feet each.  

The diagonal, the hypotenuse, is determined by:

4^2 + 4^2 = x^2

32 = x^2

x = 5.6569 feet

Answer 2
Answer:

Final answer:

The length of the diagonal of the square enclosure is approximately 5.7 feet.

Explanation:

The perimeter of a square is the sum of all its sides. In this case, the square enclosure has a perimeter of 16 feet. Since all the sides of a square are equal in length, we can divide the perimeter by 4 to find the length of one side.

The length of one side of the square is 16/4 = 4 feet.

To find the length of the diagonal of a square, we can use the Pythagorean theorem. The diagonal, the side, and the side form a right triangle, where the diagonal is the hypotenuse. The formula for the length of the diagonal is d = sqrt(2)s, where s is the length of one side of the square.

Substituting the value for s, we have d = sqrt(2) * 4.

Calculating this using a calculator, we get d ≈ 5.7 feet.

Learn more about Finding the length of the diagonal of a square enclosure here:

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In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 21% of your total grade, each major test is worth 25%, and the final exam is worth 29%. Compute the weighted average for the following scores: 60 on the lab, 81 on the first major test, 69 on the second major test, and 79 on the final exam. Enter your answer as a whole number.

Answers

Answer:

Weighted\ Average =  73

Step-by-step explanation:

Given

Lab = 21\%

Tests = 25\%

Exam = 29\%

Lab\ Score = 60

First\ Test = 81

Second\ Test = 69

Exam = 79

Required

The weighted average

To do this, we simply multiply each score by the corresponding worth.

i.e.

Weighted\ Average =  Lab\ worth * Lab\ score + Tests\ worth * Tests\ score.....

So, we have:

Weighted\ Average =  21\% * 60 + 25\% * 81 + 25\% * 69 + 29\% * 79

Using a calculator, we have:

Weighted\ Average =  73.01

Weighted\ Average =  73 --- approximated

Whart is 1 divided by 1/2

Answers

Answer:

The answer is 2

Step-by-step explanation:

Use a calculator.

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Answers

Answer:

It may look simple to the owner because he is not the one losing a job. For the three machinists it represents a major event with major consequences

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Write the complex number 4(cos 60 + i sin 60) in standard form 10. Use DeMoivre's Theorem to find (2+3i)6

Answers

Answer:

a) The standard form of z = 4\cdot (\cos 60^(\circ)+i\cdot \sin 60^(\circ)) is z = 2 + i\cdot 2√(3), b)z = (2+i\cdot 3)^(6) = 1219.585 + i \cdot 1829.381.

Step-by-step explanation:

a) The standard form of the complex number is z = a + i\cdot b, \forall \,a,b \in \mathbb{R}. If we get that z = 4\cdot (\cos 60^(\circ)+i\cdot \sin 60^(\circ)), whose standard form is obtained by algebraic means:

1)z = 4\cdot (\cos 60^(\circ)+i\cdot \sin 60^(\circ)) Given

2)z = (4\cdot \cos 60^(\circ))+i\cdot (4\cdot \sin 60^(\circ)) Distributive and Associative properties.

3)z = 2 + i\cdot 2√(3) Multiplication/Result.

The standard form of z = 4\cdot (\cos 60^(\circ)+i\cdot \sin 60^(\circ)) is z = 2 + i\cdot 2√(3).

b) The De Moivre's Theorem states that:

z = (a+i\cdot b)^(n)= r^(n)\cdot (\cos \theta + i\cdot \sin \theta)

Where:

r =\sqrt{a^(2)+b^(2)} and \theta = \tan^(-1) \left((b)/(a)\right).

If we know that z = (2+i\cdot 3)^(6), then:

r = \sqrt{2^(2)+3^(2)}

r =√(13)

r \approx 3.606

\theta = \tan^(-1)\left((3)/(2) \right)

\theta \approx 56.310^(\circ)

The resulting expression is:

z = 3.606^(6)\cdot (\cos 56.310^(\circ)+i\cdot \sin 56.310^(\circ))

z = 1219.585+i\cdot 1829.381

Therefore, z = (2+i\cdot 3)^(6) = 1219.585 + i \cdot 1829.381.