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3 years ago

Determine whether the geometric series 19.2 + 9.6 + 4.8 + ... converges or diverges, and identify the sum if it exists.

Mathematics

1 answer:

zloy xaker [14]3 years ago

6 0

Answer: The infinite geometric series converges to 38.4

====================================================

Explanation:

Divide each term by its previous term

term2/term1 = 9.6/19.2 = 0.5

term3/term2 = 4.8/9.6 = 0.5

The common ratio is r = 0.5

Since -1 < r < 1 is true, this means the infinite geometric series converges.

It converges to...

S = a/(1-r)

S = 19.2/(1-0.5)

S = 38.4

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Answer:

This is a long answer. I got 82.5

Step-by-step explanation:

Area of isoceles triangle is

$\frac{1}{2} (b)(h)$

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Let draw a altuide going through Point D that split side FE into 2 equal lines. Let call that point that is equidistant from FE, H.

Since it is a altitude,it forms a right angle. So angle H=90.

Angle H is equidistant from F and E so

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EH=11.

The height is still unknown.

We can use pythagorean theorem to find side h but we need to know the slanted side or side DF to use the theorem.

Using triangle DFH, we know that angle H is 90 and angle F is 34. So using triangle interior rule,Angle D equal 56.

We know side FH=11
We know Angle D equal 56
We are trying to find side DF
We know angle H equal 90

We can use law of sines to find side DF

$\frac{fh}{ \sin(d) } = \frac{df}{ \sin(h) }$

Plug in the numbers

$\frac{11}{ \sin(56) } = \frac{df}{ \sin(90) }$

sin of 90 =1 so

$\frac{11}{ \sin(56) } = df$

Side df is about 13.3 inches.

Since we know our slanted side is 13.3 we can set up our pythagorean theorem equation,

$(fh) {}^{2} + (dh) {}^{2} = df {}^{2}$

$(11) {}^{2} +( dh) {}^{2} = (13.3) {}^{2}$

$121 + dh {}^{2} = 176.89$

$(dh) {}^{2} = 55.89$

$\sqrt{55.89} = 7.5$

is approximately 7.5 so dh=7.5 approximately.

Now using base times height times 1/2 multiply them out

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3 years ago

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strojnjashka [21]

Answer:

The value of the parameter is λ is 0.03692

Step-by-step explanation:

Consider the provided function.

$f(x) = 0.5\lambda e^{-\lambda |x|}$ for −∞ < x < ∞.

It is given that standard deviation is given as 38.3 km.

Now we need to calculate the value of parameter λ.

The general formula for the probability density function of the double exponential distribution is: $f(x)=\frac{e^{-|\frac{x-\mu}{\beta}|}}{2\beta}$

Where μ is the location parameter and β is the scale parameter.

Compare the provided equation with the above formula we get.

$\lambda=\frac{1}{\beta}$ and μ = 0.

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Now substitute the value of β in $\lambda=\frac{1}{\beta}$ .

$\lambda=\frac{1}{27.08219}=0.03692$

Hence, the value of the parameter is λ is 0.03692

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3 years ago

Determine whether the geometric series 19.2 + 9.6 + 4.8 + ... converges or diverges, and identify the sum if it exists.​

Determine whether the geometric series 19.2 + 9.6 + 4.8 + ... converges or diverges, and identify the sum if it exists.