If a number is a whole number, then it cannot be

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

3 years ago

The manager of a supermarket wants to obtain information about the proportion of customers who dislike a new policy on cashing c

alex41 [277]

Answer:

n = 61 costumers

Step-by-step explanation:

For calculating the number of costumers he should sample we use the next equation:

$n = \frac{z_{1-\alpha/2}^{2}p(1-p)}{E^{2} }$

Where E is the error that we are prepared to accept, in this case E = 0.15

How we don't know the value of p, we can estimate it like p = 0.5

∝ = 1-0.98 = 0.02

1-∝/2 = 0.99

$z_{0.99} = 2.33$

$n = \frac{(2.33^{2})(0.5)(1-0.5)}{0.15^{2} }$

n = 60.32 costumers

n ≈ 61 costumers

4 0

3 years ago

How to solve<br> -7(-3r+2)=3r-6

Ymorist [56]

Step-by-step explanation:

-7(-3r+2)=3r-6

Distribute the - 7

21r-14=3r-6

Add 14

21r=3r+8

Subtract 3r

18r=8

Divide 18r by 8

2.25 should be the answer to r.

8 0

3 years ago

A triangle has 2 sides that equal 6 inches. The other side equals 4 inches. What kind of triangle is this

Tom [10]

Ισοσκελες τρίγωνο
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7 0

3 years ago

Read 2 more answers

Aliyah interviewed 20 people who have just one sibling. She asked them what the difference in age, in years, is between them and

Gnoma [55]

The correct answer will be option C. Mode.

Mode is the most frequently occurring value of the data. From the above line plot we can see that the most frequently occurring value is 3. Even if 10 is removed from the line plot, 3 will still be the most frequently occurring value and will be the mode of the data. Thus removing 10 does not changes the mode of the data at all.

The mean will obviously be changed. The range is difference of maximum and minimum value. 10 was initially the maximum value. If 10 is removed, the maximum value will change and so does the Range of the data. Removing 10 changes the total number of data values, so the position of median also changes which changes the value of Median.

Therefore, the correct answer to this question is option C

4 0

3 years ago