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3 years ago

The endpoints of a diameter of a circle are A(3,1) and B(8,13). Find the area of the circle in terms of pi.

Mathematics

1 answer:

Talja [164]3 years ago

7 0

Answer:

A = 169π/4

Step-by-step explanation:

From these two given points we find the length of the diameter of this circle, using the Pythagorean Theorem:

d^2 = (8 - 3)^2 + (13 - 1)^2, or

d^2 = 25 + 144 = 169

Thus, the diameter, d, of this circle is √169, or 13.

The radius is thus 13/2 units.

The area formula is A = πr^2. Here the area is

A = π(169/4), or A = 169π/4

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2 years ago

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Answer:

$t=\frac{8.19-9.02}{\frac{0.8}{\sqrt{17}}}=-4.28$

The degrees of freedom are given by

$df=n-1=17-1=16$

The p value would be given by this probability:

$p_v =P(t_{(16)}$

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Step-by-step explanation:

Information given

$\bar X=8.19 cm^3$ represent the sample mean

$s=0.8 cm^3$ represent the sample deviation

$n=17$ sample size

$\mu_o =9.02$ represent the value to verify

$\alpha=0.01$ represent the significance level for the hypothesis test.

t would represent the statistic

$p_v$ represent the p value

System of hypothesis to check

We want to check if the true mean is less than the normal value of 9.02 cm^3, the system of hypothesis would be:

Null hypothesis: $\mu \geq 9.02$

Alternative hypothesis: $\mu < 9.02$

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info given we got:

$t=\frac{8.19-9.02}{\frac{0.8}{\sqrt{17}}}=-4.28$

The degrees of freedom are given by

$df=n-1=17-1=16$

The p value would be given by this probability:

$p_v =P(t_{(16)}$

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3 years ago

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3 years ago

The endpoints of a diameter of a circle are ​A(3​,​1) and ​B(8​,13​). Find the area of the circle in terms of pi.

The endpoints of a diameter of a circle are A(3,1) and B(8,13). Find the area of the circle in terms of pi.