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Olin [163]
2 years ago
11

Find an equation of the sphere through the point (4,3,-1) and has center (3,8,1).

Mathematics
1 answer:
sleet_krkn [62]2 years ago
6 0

Answer:

(x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = 30

Step-by-step explanation:

The general equation of a sphere is as follows:

(x - x_{c})^{2} + (y - y_{c})^{2} + (z - z_{c})^{2} = r^{2}

In which the center is (x_{c}, y_{c}, z_{c}, and r is the radius.

In this problem, we have that:

x_{c} = 3, y_{c} = 8, z_{c} = 1

So

(x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = r^{2}

through the point (4,3,-1)

This leads us to find the radius.

(4 - 3)^{2} + (3 - 8)^{2} + (-1 - 1)^{2} = r^{2}

r^{2} = 1 + 25 + 4

r^{2} = 30

So the equation of the sphere is:

(x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = 30

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kakasveta [241]

Answer:

Following are the responses to the given choices:

Step-by-step explanation:

In step 1:

State the zero and alternate test hypotheses. Insert underneath.

H_0 : \mu = 24: H_a : \mu < 24

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In step 2:

Each test statistics meaning is calculated. Around two decimal places for your reply.

z=\frac{\bar{X}-\mu_{0}}{\frac{\sigma}{\sqrt{n}}}=\frac{23.2-24}{\frac{4.2}{\sqrt{88}}}=-1.787

In step 3:

Draw a start and write the decision.

Since it is observed that z=-1.787 < z_c=-1.64 it is then concluded that the null hypothesis is rejected.

Consequently we consider that small companies in their field may not expand, as they spend or less 24 hours per week on marketing.

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I think its saying find the mixed numbers but keep the denominator

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Step-by-step explanation:

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