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The circumference of the ellipse approximate. Which equation is the result of solving the formula of the circumference for b?

Serhud [2]

Answer:

$b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}$

Step-by-step explanation:

Given - The circumference of the ellipse approximated by $C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }$ where 2a and 2b are the lengths of 2 the axes of the ellipse.

To find - Which equation is the result of solving the formula of the circumference for b ?

Solution -

$C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }\\\frac{C}{2\pi } = \sqrt{\frac{a^{2} + b^{2} }{2} }$

Squaring Both sides, we get

$[\frac{C}{2\pi }]^{2} = [\sqrt{\frac{a^{2} + b^{2} }{2} }]^{2} \\\frac{C^{2} }{(2\pi)^{2} } = {\frac{a^{2} + b^{2} }{2} }\\2\frac{C^{2} }{4(\pi)^{2} } = {{a^{2} + b^{2} }$

$\frac{C^{2} }{2(\pi )^{2} } = a^{2} + b^{2} \\\frac{C^{2} }{2(\pi )^{2} } - a^{2} = b^{2} \\\sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}} = b$

∴ we get

$b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}$

8 0

2 years ago

Plz hurry I will give 17 points

UNO [17]

Your answer should be organize, correct me if I’m wrong !

6 0

3 years ago

Read 2 more answers

Find the slope for each of the order pair. (-2,-1) and (8,-3)

kondaur [170]

Answer:

-0.2

Step-by-step explanation:

Slope (m) =ΔY/ΔX= 8-(-2)/-3-(-1)

= -1/5

= -0.2

4 0

2 years ago

Which of the following best represents the highest potential for nonresponse bias in a sampling strategy? Describe why this opti

natta225 [31]

Answer:

c. Asking people leaving a local election to take part in an exit poll

Step-by-step explanation:

Asking people leaving a local election to take part in an exit poll best represents the highest potential for nonresponse bias in a sampling strategy because of the importance of the local election compared to the exit polls.

It is worthy of note that nonresponse bias occurs when some respondents included in the sample do not respond to the survey. The major difference here is that the error comes from an absence of respondents not the collection of erroneous data. ...

Oftentimes, this form of bias is created by refusals to participate for one reason or another or the inability to reach some respondents.

7 0

3 years ago

The world population is estimated to be 7.8 billion in 2020, and growing at an instantaneous rate of 1.05%. (a) Estimate the pop

REY [17]

Answer:

Population in 2100 is 17.99 billion.

Step-by-step explanation:

The population of the world in 2020 = 7.8 billion.

The growth rate = 1.05%

Now find the population after 2100. Use the below formula to find the population.

Population in 2100 = Population of 2020 (1 + growth rate)^n

Population in 2100 = 7.8 (1 + 0.0105)^80

Population in 2100 = 17.99 billions.

Now, find the growth rate in 2100.

dN/dt = [r N (K – N) ] / K

r = Malthusian parameter

K = carrying capacity.

Now divide both sides by K, now x = N/K then do the differential equation.

dx/dt = r x ( 1- x)

Now integrate, x(t) = 1/ [ 1 + (1/x – 1) c^-rt

From the first equation = dN/dt = (13 – 7.8) / 80 = (r × 7.8×(13 – 7.8) / 12

0.065 = (r × 7.8× 5.2) / 12

0.065 = r × 3.38

r = 1.92%

3 0

2 years ago