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maw [93]
3 years ago
12

A particle starts at the point P=(−5,−1,3) when t=0 and moves along a straight line toward Q=(−6,−6,8) at a speed of 9 cm/sec. L

et x, y, and z be measured in cm, and t in seconds. Find a parametric vector equation for the position of the object.
Mathematics
1 answer:
navik [9.2K]3 years ago
6 0

Answer:

Step-by-step explanation:

Given

Particle moves from P\ (-5,-1,3)\ to\ Q\ (-6,-6,8)

speed of particle is v=9\ cm/s

Unit vector in the direction of vector \vec{PQ} is given by

\hat{n}=\frac{\vec{Q}-\vec{P}}{|\vec{Q}-\vec{P}|}

\hat{n}=\frac{-}{\sqrt{(-1)^2+(-5)^2+(5)^2}}

\hat{n}=\frac{}{\sqrt{1+25+25}}

Now Position of Particle at any time is given by

\vec{r(t)}=velocity\cdot time\cdot direction

\vec{r(t)}=9\cdot t\cdot \frac{}{\sqrt{1+25+25}}

Parametric vector equation is given by

x=\frac{-9t}{\sqrt{51}}

y=\frac{-45t}{\sqrt{51}}

z=\frac{45t}{\sqrt{51}}

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Answer:

Correct option: (a) 0.1452

Step-by-step explanation:

The new test designed for detecting TB is being analysed.

Denote the events as follows:

<em>D</em> = a person has the disease

<em>X</em> = the test is positive.

The information provided is:

P(D)=0.88\\P(X|D)=0.97\\P(X^{c}|D^{c})=0.99

Compute the probability that a person does not have the disease as follows:

P(D^{c})=1-P(D)=1-0.88=0.12

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Compute the probability that a randomly selected person is tested negative but does have the disease as follows:

P(X^{c}\cap D)=P(X^{c}|D)P(D)\\=[1-P(X|D)]\times P(D)\\=[1-0.97]\times 0.88\\=0.03\times 0.88\\=0.0264

Compute the probability that a randomly selected person is tested negative but does not have the disease as follows:

P(X^{c}\cap D^{c})=P(X^{c}|D^{c})P(D^{c})\\=[1-P(X|D)]\times{1- P(D)]\\=0.99\times 0.12\\=0.1188

Compute the probability that a randomly selected person is tested negative  as follows:

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Thus, the probability of the test indicating that the person does not have the disease is 0.1452.

4 0
3 years ago
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astraxan [27]
<span>The individual factors for each integer along with the common factors and greatest common factor will be shown. Factors of 18 are 1, 2, 3, 6, 9, 18. Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.</span>
6 0
2 years ago
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Fiesta28 [93]
If we  draw a perpendicular line from one of the vertices of the triangle we get  2 right angled triangles  each with  altitude 9 ins  and vertex angle = 30 degrees.   So:-

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5 0
3 years ago
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Answer:

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The percentage of people that are actively looking for job is called active job seekers. The active job seekers can be people that are unemployed, but also people that re employed but want to work something or somewhere else. While some people struggle to find jobs and would accept almost anything, other people want to constantly progress, thus they are not satisfying with a job where they do not progress, so they seek for new challenges and opportunities.

7 0
2 years ago
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