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Is f(x)=7-2x a polynomial function

Answers

Answer 1

Answer:

Answer:

Yes

Step-by-step explanation:

Yes, this F(x) is a polynomial function involving the first and null integer powers of x: x^0 and x^1.

Answer 2

Answer:

Final answer:

Yes, f(x) = 7 - 2x is a polynomial function because it satisfies the general form of a polynomial, which requires that every term is in the form ax^n for nonnegative integer n.

Explanation:

Yes, the function f(x) = 7-2x is indeed a polynomial function. A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on, for which the function is of the form f(x) = ax^n, where n is a nonnegative integer. In this case, f(x) = 7-2x can be more comprehensively written as f(x) = -2x^1 + 7x^0, which reflects the general form of a polynomial function.

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A researcher examines 27 sedimentary samples for bromide concentration. The mean bromide concentration for the sample data is 0.383 cc/cubic meter with a standard deviation of 0.0209. Determine the 90% confidence interval for the population mean bromide concentration. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

Answer:

Critical value: $z = 1.645$

The 90% confidence interval for the population mean bromide concentration is (0.376, 0.39).

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = (1-0.9)/(2) = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.05 = 0.95$ , so $z = 1.645$ . This value of z is the critical value

Now, find M as such

$M = z*(\sigma)/(√(n))$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.645*(0.0209)/(√(27)) = 0.0066$

The lower end of the interval is the mean subtracted by M. So it is 0.383 - 0.0066 = 0.376 cc/cubic meter

The upper end of the interval is the mean added to M. So it is 0.383 + 0.0066 = 0.39 cc/cubic meter

The 90% confidence interval for the population mean bromide concentration is (0.376, 0.39).

Which function is continuous?

Answers

The answer is D. Cost of U.S. postage as a function of the weight of the letter.

Answer:

The answer is B

Step-by-step explanation:

Did the practice on edge.

Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0, y0) in the region. (x2 + y2)y' = y2 1. A unique solution exists in the region y ≥ x.
2. A unique solution exists in the entire xy-plane.
3. A unique solution exists in the region y ≤ x.
4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.
5. A unique solution exists in the region x2 + y2 < 1.

Answers

A unique solution exists in the region consisting of all points in the xy-plane except the origin.

The correct option is 4.

The given differential equation is:

(x² + y²)y' = y²

The equation can be rewritten as:

$x^2 + y^2 (dy)/(dx) = y^2$

We need to determine a region of the xy-plane for which the differential equation would have a unique solution whose graph passes through a point (x₀, y₀) in the region.

To determine the region, we can use the existence and uniqueness theorem for first-order differential equations.

According to the theorem, a unique solution exists in a region if the differential equation is continuous and satisfies the Lipschitz condition in that region.

To check if the differential equation satisfies the Lipschitz condition, we can take the partial derivative of the equation with respect to y:

dy/dx = y / (x² + y²)

The partial derivative is continuous and bounded in the entire xy-plane except at the origin (x=0, y=0).

Therefore, the differential equation satisfies the Lipschitz condition in the entire xy-plane except at the origin.

Since the differential equation is continuous in the entire xy-plane, a unique solution exists in any region that does not contain the origin. Therefore, the correct answer is:

A unique solution exists in the region consisting of all points in the xy-plane except the origin.

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Final answer:

The differential equation will have a unique solution in the entire xy-plane except at the origin, as both the function and its partial derivatives are continuous and well-defined everywhere except at that point.

Explanation:

To determine a region of the xy-plane where the differential equation (x2 + y2)y' = y2 has a unique solution passing through a point (x0, y0), we need to consider where the function and its derivative are continuous and well-defined. According to the existence and uniqueness theorem for differential equations, a necessary condition for a unique solution to exist is that the functions of x and y in the equation, as well as their partial derivatives with respect to y, should be continuous in the region around the point (x0, y0).

We note that both the function (x2 + y2)y' and its partial derivative with respect to y, which is 2y, are continuous and well-defined everywhere except at the origin where x = 0 and y = 0. Therefore, a unique solution exists in the region consisting of all points in the xy-plane except the origin.

From the given options, the correct answer is:

4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.