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Juliette [100K]
3 years ago
14

Calculate the distance between (−3 + 4i) and (3 −3i) on the coordinate plane.

Mathematics
1 answer:
Nikitich [7]3 years ago
7 0
Another one for my "impossible math problems" file.

The distance between real parts of these numbers is 3-(-3) = 6.
The distance between imaginary parts of these numbers is (4-(-3)) = 7.
The straight-line distance on the complex plane between these numbers is given by the Pythagorean theorem as
  distance = √(6² + 7²)
  distance = √85 ≈ 9.2195

_____
If your answer choices are supposed to have radical signs, then the best choice is ...
  D) √85

Otherwise, no offered choice is correct.
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The population of a community is known to increase at a rate proportional to the number of people present at time t. If the popu
Lady bird [3.3K]

Answer:

P(t) = P(0)e^{0.0693t}

Step-by-step explanation:

The population of a community is known to increase at a rate proportional to the number of people present at time t.

This means that the population growth is modeled by the following differential equation:

\frac{dP(t)}{dt} = rP(t)

Which has the following solution:

P(t) = P(0)e^{rt}

In which P(t) is the population after t years, P(0) is the initial population and r is the growth rate.

The population has doubled in 10 years

This means that P(10) = 2P(0). We use this to find r.

P(t) = P(0)e^{rt}

2P(0) = P(0)e^{10r}

e^{10r} = 2

\ln{e^{10r}} = \ln{2}

10r = \ln{2}

r = \frac{\ln{2}}{10}

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So the equation that will estimate the population of the community in t years is:

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6 0
3 years ago
For 300 trading​ days, the daily closing price of a stock​ (in $) is well modeled by a Normal model with mean ​$196.99 and stand
KATRIN_1 [288]

Answer:

a) 2.5% b) 84% c) 95% d) D. The more unusual day is if the stock closed below $185 because it has the largest absolute z-score.

Step-by-step explanation:

For a) b) and c) we will use the empirical rule, so, we can observe the image shown below

a) 211.23 is exactly two standard deviation above the mean, so, the probability that on a randomly selected day in this period the stock price closed above 211.23 is 2.35% + 0.15% = 2.5%  

b) 204.11 represents exactly one standard deviation above the mean, so, the probability of being below 204.11 is 50% + 34% = 84%

c) The probability of getting a value between 182.75 and 211.23 is 95%, this because 182.75 is exactly two standard deviations below the mean and 211.23 is exactly two standard deviations above the mean.

d) The z-score related to 208 is z_{1} = (208-196.99)/7.12 = 1.5 and the z-score related to 185 is  z_{2} = (185-196.99)/7.12 = -1.7, therefore, the more unusual day is if the stock closed below $185 because it has the largest absolute z-score.

5 0
3 years ago
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