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Shalnov [3]
3 years ago
6

A rectangle has one side on the x-axis and two vertices on the curve, = 1/1+x^2. find the coordinates of the vertices of the rec

tangle with the maximum area
Mathematics
2 answers:
Readme [11.4K]3 years ago
8 0
I believe that you have issues with the function for the curve. Because if that function is correct, the rectangle with the maximum area will have the two coordinates off the X-axis of (-infinity, infinity) and (infinity, infinity) and the area of the rectangle will be infinite.

Assuming correct expression is
y = 1/1 + x^2 = 1 + x^2.
Then you need to find 2 x values that have the same y value. You'll quickly realize that the values X and -X will work and give you the same Y value. And as you use large absolute values of X, the Y value will also increase. And carried to the logical limit, the largest possible rectangle will happen with X values of -infinity and +infinity.

Assuming correct expression is
1 = 1 + x^2, which simplifies to 0 = x^2, which has the exact same argument. The coordinates of the 2 points are (-infinity, infinity) and (infinity, infinity). So once again, the area of the rectangle increases without limit.

Tcecarenko [31]3 years ago
5 0
<span>The dimension of the rectangle would be length=#4/sqrt3# and width =4-#4/3= 8/3# Explanation: Let one vertex on the x axis be x, then the other vertex would be -x. Length of the rectangle would be thus 2x and width would be #4-x^2# Area of the rectangle would be A=#2x(4-x^2)= 8x-2x^3# For maximum area #(dA)/dx=0=8-6x^2#, which gives x=#2/sqrt3# The dimension of the rectangle would be length=#4/sqrt3# and width =4-#4/3= 8/3# Was this helpful? Let the contributor know!</span>
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Answer:

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

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Step-by-step explanation:

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