what is the square root of 64 multiplied by 72 divided by the sum of 43 plus 0

The approximation sin (x) = x - x^3/6 has an absolute error below 0.000001 for the interval [-0.164375,+0.164375].

In mathematics, the alternating series is an infinite series of a term in the form of

[tex]{\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}}{\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}} \\{\displaystyle \sum _{n=0}^{\infty }(-1)^{n+1}a_{n}}{\displaystyle \sum _{n=0}^{\infty }(-1)^{n+1}a_{n}}[/tex]

The expansion series of sin(x)

[tex]\rm sin (x) = \frac{x}{1!} -\frac{x^{3} }{3!} +\frac{x^{5} }{5!} -\frac{x^{7} }{7!} +..[/tex]  (a)

the given approximation [tex]\rm sin (x) = \frac{x}{1!} -\frac{x^{3} }{3!}[/tex]     (b)

So, the approximation error term =(b)-(a)

       [tex]\rm = -[ +\frac{x^{5} }{5!} -\frac{x^{7} }{7!} +\frac{x^{9} }{9!}-....]\\\rm = -\frac{x^{5} }{5!} +\frac{x^{7} }{7!} -\frac{x^{9} }{9!}+....[/tex]

The alternative series theorem states that we need to ensure that the absolute value of the first term [tex]\rm \frac{x^{5} }{5!}[/tex]less than the error limit, For that the sum will be below the error limit, which means

[tex]\rm \frac{x^{5} }{5!}[/tex] <  0.000001

Solving for x, we get

x [tex]\rm x^{5} = 5! \times 0.000001\\ = 0.000120\\\rm = 0.000120^{1/5} \\ = 0.164375[/tex]

Therefore, the approximation   [tex]\rm sin (x) = \frac{x}{1!} -\frac{x^{3} }{3!}[/tex] has an absolute error below 0.000001 for the interval [-0.164375,+0.164375].

by checking

[tex]\rm sin(0.164375)-(0.164375)^{3/3!} \\= 9.993513\times10^{-7} < 0.000001[/tex]

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Answer:

Step-by-step explanation:

A geometric sequence or geometric progression is a sequence where each term after the first one can be found by multiplying a certain factor.

So, basically, to find the geometric sequence, we just need to divide the second term by the first term and observe if it results a constant factor.

By doing that, we observe that the second equence is a geometric sequence with a reasonf of 1/2, let's demonstrate it

[tex]8\times \frac{1}{2}= 4 (second \ term)\\4 \times \frac{1}{2}=2 (third \ term)\\ 2 \times \frac{1}{2}= 1 (fourth \ term)\\ 1 \times \frac{1}{2}= \frac{1}{2} (fiftg \ term)\\ \frac{1}{2} \times \frac{1}{2}= \frac{1}{4} (sixth \ term)[/tex]

As you can observe, we perfectly built the sequence is its ratio or factor.

Therefore, choice B is a geometric sequence.

Answer:

The correct answer is a triangle will be formed.

Step-by-step explanation:

If a cross section of the paperweight is cut perpendicular to the base and passes through the top vertex, the resulting figure will have 3 sides or vertices. Hence, this shape will be a triangle. The triangle only forms if it does pass through the top vertex.

So, triangle is the answer.

The element with 35 protons is bromine (Br). Its isotopes with 44 and 46 neutrons have the symbols ^79Br and ^81Br, respectively, with the mass numbers derived from adding the number of neutrons to the atomic number 35.

To address Exercise 1.8.2, we first need to identify the element with 35 protons. In the periodic table, the element with 35 protons is bromine (Br). This element is defined by the number of protons in its nucleus, which is also known as its atomic number. Therefore, bromine is the element we are looking for.

Next, we need to write the symbols for bromine's isotopes with 44 and 46 neutrons. The total number of nucleons (protons plus neutrons) gives us the mass number of an isotope. For bromine with 44 neutrons, the mass number is 35 (protons) + 44 (neutrons) = 79. Therefore, the symbol for this isotope of bromine is ^79Br.

For the isotope with 46 neutrons, the mass number is 35 (protons) + 46 (neutrons) = 81. So, the symbol for this isotope of bromine is ^81Br. Each isotope differs in the number of neutrons, and therefore, in the mass number, while the number of protons (the atomic number) remains constant.

The element with 35 protons is bromine (Br). Its isotopes with 44 and 46 neutrons are written as ^79Br and ^81Br, respectively, where the numbers represent the mass numbers of each isotope.

To answer Exercise 1.8.2, we must first identify the element with 35 protons. The element with 35 protons is bromine, which is represented by the chemical symbol Br. To write the symbols for its isotopes with 44 and 46 neutrons, we must add the atomic number (protons) and the number of neutrons to get the mass number for each isotope.

For the isotope with 44 neutrons:

For the isotope with 46 neutrons:

Isotopes of an element have the same number of protons but different numbers of neutrons, hence different mass numbers. The isotopes of bromine are thus ^79Br and ^81Br, referring to the atomic mass which is composed of the protons and neutrons together.

Answer:

Answers are

Y

2+s

4x^3+y

Step-by-step explanation:

I did the quiz

The first, second, and third are the polynomials.

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable

Given

1.  y

2.  x² - x +√2

3.  2 + s

4.  4x³ + y

To find

Which expressions are polynomials?

1.  y is a polynomial with variable y.

2.  x² - x +√2 is a polynomial with variable x.

3.  2 + s is a polynomial with variable s.

4.  4x³ + y is not a polynomial because the polynomial has only one variable in it.

Thus, the first, second, and third are the polynomials.

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A diameter is a line segment that has endpoints on a circle and passes through the center of the circle. The correct option is: diameter

A diameter is a line segment that has endpoints on a circle and passes through the center of the circle. It is a crucial geometric element in the study of circles and plays a fundamental role in various geometric properties.

Key points about the diameter:

Definition: As mentioned, a diameter is a line segment that connects any two points on the circle's circumference and passes through the center of the circle. It is the longest chord of the circle.

Length: The length of the diameter is exactly twice the length of the radius. If "r" represents the radius, then the length of the diameter is "2r."

Properties: The diameter divides the circle into two equal halves, each known as a semicircle. It is also the largest possible chord of a circle.

In summary, a diameter is a significant geometric concept related to circles, and it is characterized by its property of passing through the center of the circle and being twice the length of the radius.

The correct option is: diameter

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To calculate the cash option payout, we need to discount the annual payment at a rate of 44% over 2222 years using the present value formula. The cash option payout would be approximately $2,938,624.13.

To determine the cash option payout, we need to calculate the present value of the annuity. The annual payment is the total amount of the lottery prize divided by the number of years, which is $33 million / 2222 = $14,808.81. To discount this amount at a rate of 44% over 2222 years, we can use the formula:

PV = Payment / ((1 + r)^n - 1) * (1 - (1 / (1 + r))^n)

where PV is the present value, Payment is the annual payment, r is the discount rate (0.44), and n is the number of years (2222). Plugging in the values, we get:

PV = $14,808.81 / ((1 + 0.44)^2222 - 1) * (1 - (1 / (1 + 0.44))^2222)

Solving this equation gives us the cash option payout, which is approximately $2,938,624.13.

To determine the affected area by an asteroid impact, calculate the radius from the circumference of the crater and then the area of the circle. The estimated crater area from a 79.5-mile circumference is approximately 506.7 square miles, indicating the surface area affected.

To estimate how much of the Earth's surface has been affected by the asteroid impact that resulted in a crater with a measured circumference of 79.5 miles, we need to recognize that this measurement refers to the circumference of a circle (the crater). We use the circumference to find the radius of that circle, and then calculate the area of the circle to understand the extent of the impact.

First, we calculate the radius (r) of the crater using the circumference (C): C = 2πr. Plugging in the known circumference, r = C / (2π), so r = 79.5 miles / (2 × 3.14), which approximates to 12.7 miles. Moving forward, we can now find the area (A) of the crater using A = πr². Squaring the radius gives us [tex](12.7)^2[/tex] and then multiplying by π gives us approximately 506.7 square miles.

The actual crater area accounting for the circular shape is approximately 506.7 square miles, which roughly indicates the immediate surface area affected by the impact. It's noteworthy that the surrounding ecosystem and earth's surface may also experience indirect effects extending beyond this area.

Answer:

12 and 5

Step-by-step explanation:

The standard deviation for the given binomial distribution is 1.449.

A binomial random variable is the number of successes x in n repeated trials of a binomial experiment. The probability distribution of a binomial random variable is called a binomial distribution.

σ = [tex]\sqrt{nP(1 -P)}[/tex]

where,

σ is the standard deviation

n is the number of trials in the binomial experiment.

P is the probability of success on an individual.

According to the given question we have,

The number of trials in the binomial experiment, n = 10

The probability of success on an individual, p = 0.70

Therefore, the standard deviation is given by

σ = [tex]\sqrt{10(0.70)(1 -0.70)} = \sqrt{7(0.3)}=\sqrt{2.1} =1.449[/tex]

Hence, the standard deviation for the given binomial distribution is 1.449.

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The equation for the plane that contains the given line and is perpendicular to the provided plane is 8x + 5y - 7z + 17 = 0.

To find an equation for the plane that contains the line given by v = (−1, 1, 2) + t(7, 6, 2) and is perpendicular to the plane described by 8x + 5y − 7z + 8 = 0, we first need to understand that the normal vector of this plane will be parallel to the normal vector (8, 5, -7) of the given plane since both planes are perpendicular to each other.

Knowing that the line lies on the required plane, we can use the point (−1, 1, 2) that the line passes through, along with the parallel normal vector, to write the equation of our plane. The general form of the equation of a plane is Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane. Substituting our point into the equation, we calculate the constant D.

Thus, the equation of our plane will be 8x + 5y − 7z + D = 0. Inserting the point (−1, 1, 2) into this equation gives us 8(-1) + 5(1) - 7(2) + D = 0, which simplifies to -8 + 5 - 14 + D = 0. Solving for D yields D = 17. Hence, the final equation of the plane is 8x + 5y − 7z + 17 = 0.

Using Cramer's Rule, the value of x in the given system of linear equations is 1.

We can solve the given system of equations using Cramer's Rule. Cramer's Rule states that in a system of linear equations, if the determinant of the coefficient matrix is non-zero, then the system has a unique solution.

First, let's find the determinant of the coefficient matrix:

| 1   3 |

| 3   1 |

Det = (1*1) - (3*3) = -8

Since the determinant is non-zero (-8 ≠ 0), the system has a unique solution.

Next, let's find the determinant of the x-column matrix:

| 16   3 |

|  8   1 |

Det(x) = (16*1) - (3*8) = -8

Finally, we can find the value of x by dividing the determinant of the x-column matrix by the determinant of the coefficient matrix: x = Det(x) / Det = (-8) / (-8) = 1.