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2 years ago

Find the value of b for which 1+e^b+e^2b+e^3b+...=9

1 answer:

5 0

This is a geometric series, let r=e^b then we have
1+r+r^2+r^3+....=9 
1/(1-r)=9 
1-r=(1/9) 
r=1-(1/9) 
r=8/9 
e^b=8/9 take ln of both sides 
ln(e^b)=8/9 ln(x^y)=y*ln(x) and ln(e)=1 so 
b*ln(e)=b=ln(8/9) 
thus 
b=ln(8/9)

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Seth’s father is thinking of buying his son a six-month movie pass for $40. With the pass, matinees cost $1.00. If matinees are

Ymorist [56]

Answer:

In order for it to benefit his father to buy the pass Seth have to attend the movies for 11 times.

Step-by-step explanation:

Given:

Cost of movie pass = $40

Cost per matinees with pass = $1.00

Cost per matinees without pass = $3.50

To Find:

Number of times must Seth attend in order for it to benefit his father to buy the pass = ?

Solution:

Let x be the number of times he wants to visit

To profit his father

The number of visits without pass = the number of visits with passin the cost of $3.50

Then, without pass if he visits for x times then the cost will be = 3.50x

Also with pass, the number of times he can visit the pass = $\frac{40}{3.50}$

then

$\frac{350 x}{3.50} = \frac{40}{3.50}$

$3.50x = 40$

$x = \frac{40}{3.50}$

x = 11.42

x = 11 (approx)

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2 years ago

How many solutions does the equation and 4x+8=0.1x+3+3.9x have? Explain.

iogann1982 [59]

Reduces to 8=-3. no solutions

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2 years ago

A central purple circle labeled O has 2 concentric rings around it. The inner ring has 2 small green spheres. The outer ring has

natulia [17]

Answer:

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Step-by-step explanation:

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Maru [420]

Answer:

Step-by-step explanation:

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2 years ago

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Adam is using the equation (x)(x + 2) = 255 to find two consecutive odd integers with a product of 255. When Adam solves the pro

kondaur [170]

$\bf (x)(x+2)=255\implies x^2+2x=255\implies x^2+2x-255=y
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\textit{setting y=0}\implies x^2+2x-255=0
\\\\
\textit{now, factoring that}
\\\\
(x+17)(x-15)=0\implies 
\begin{cases}
x=-17\\
x=15
\end{cases}$

notice the picture of the graph added here
low and behold, x = -17, y is 0, and x= 15, y is 0
the graph is touching the x-axis, an x-intercept
or so-called, a "solution"

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2 years ago

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