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Inga [223]
3 years ago
15

Find all the points having an x coordinate of 1 whose distance from the point (-2,-3) is 5

Mathematics
1 answer:
Vikki [24]3 years ago
6 0
The\ distance\ between\ A(x_A;\ y_A)\ and\ B(x_B;\ y_B):\\\\d=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\\------------------------------\\\\A(1;\ y);\ B(-2;-3);\ d=5\\\\subtitute\\\\\sqrt{(-2-1)^2+(-3-y)^2}=5\\\sqrt{(-3)^2+(-3-y)^2}=5\\\sqrt{9+(-3-y)^2}=5\Rightarrow9+(-3-y)^2=5^2\\9+(-3-y)^2=25\ \ \ \ |subtract\ 9\ from\ both\ sides\\(-3-y)^2=16\iff-3-y=-\sqrt{16}\ or\ -3-y=\sqrt{16}\\-3-y=-4\ or\ -3-y=4\ \ \ \ |add\ 3\ to\ both\ sides\\-y=-1\ or\ -y=7\ \ \ \ |change\ the\ signs\\y=1\ or\ y=-7

Answer:\boxed{(1;\ 1)\ and\ (1;-7).}
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Significance level : \alpha= 1-0.95=0.05

Critical value : z_{\alpha/2}=1.96

Confidence level for population proportion:-

\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.1628\pm (1.96)\sqrt{\dfrac{0.1628(1-0.1628)}{559}}\\\\=0.1628\pm0.030604971367\\\\\approx 0.1628\pm0.0306=(0.1322,\ 0.1934)=(13.22\%,\ 19.34\%)

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