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laila [671]
3 years ago
9

What is the sum of the infinite geometric series?

Mathematics
2 answers:
grandymaker [24]3 years ago
8 0
<h2>Answer:</h2>

The sum of the  infinite geometric series is:

                                 -288

<h2>Step-by-step explanation:</h2>

We know that the sum of the infinite geometric series:

\sum_{n=1}^{\infty} ar^{n-1}

is given by the formula:

Sum=\dfrac{a}{1-r}

The series is given by:

     \sum_{n=1}^{\infty} (-144)\cdot (\dfrac{1}{2})^{n-1}

By looking at the series we observe that the first term of the series is:

            a=-144

and the common ratio of the series is:

r=\dfrac{1}{2}

Hence, the sum of the series is:

Sum=\dfrac{-144}{1-\dfrac{1}{2}}\\\\Sum=\dfrac{-144}{\dfrac{1}{2}}\\\\Sum=-144\times 2\\\\Sum=-288

Alexandra [31]3 years ago
3 0

Answer:

-288

Step-by-step explanation:

n=1/2 divided by -144. You then just plug that number which is .00347 into n in the equation and use a scientific calculator to find the answer.

You might be interested in
Explain how you can use the distributive property and mental math to find 5 x 198
viktelen [127]
Answer is 990
I hope It is the right answer
7 0
2 years ago
The local radio tower is located 20 miles east and 12 miles north of Pamela's cabin. The radio tower has a 25 mile broadcast rad
pychu [463]

Answer:

x^2 +y^2 -40x -24y  -81 =0

Step-by-step explanation:

We can write the equation of a circle in the form

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center and r is the radius

Assuming that Pamela's cabin is the center

( x-20)^2 + (y- 12)^2 = 25^2

We want to get to general form

x^2 + y^2 + Dx + Ey + F = 0,

Distributing

x^2 -40x +400 + y^2 -24y +144 = 625

x^2 +y^2 -40x -24y +544 -625 =0

x^2 +y^2 -40x -24y  -81 =0

3 0
3 years ago
Use the model below to estimate the average annual growth rate of a certain country's population for 1950, 1988, and 2010, where
Morgarella [4.7K]

Answer:

The average annual growth rate of a certain country's population for 1950, 1988, and 2010 are 2.398, 0.9985 and 0.2236 respectively.

Step-by-step explanation:

The given equation is

Y=-0.0000084x^3+0.00211x^2-0.205x+8.423

Where Y is the annual growth rate of  a certain country's population and x is the number of years after 1900.

Difference between 1950 and 1900 is 50.

Put x=50 in the given equation.

Y=-0.0000084(50)^3+0.00211(50)^2-0.205(50)+8.423

Y=2.398

Therefore the estimated average annual growth rate of the country's population for 1950 is 2.398.

Difference between 1988 and 1900 is 88.

Put x=88 in the given equation.

Y=-0.0000084(88)^3+0.00211(88)^2-0.205(88)+8.423

Y=0.9984752\approx 0.9985

Therefore the estimated average annual growth rate of the country's population for 1988 is 0.9985.

Difference between 2010 and 1900 is 110.

Put x=110 in the given equation.

Y=-0.0000084(110)^3+0.00211(110)^2-0.205(110)+8.423

Y=0.2236

Therefore the estimated average annual growth rate of the country's population for 2010 is 0.2236.

8 0
2 years ago
PLS HELP ITS A MAJOR GRADE AND DUE TOMORROW
Alexus [3.1K]

Answer:

*See below*

Step-by-step explanation:

<u>Identify and Explain Error</u>

The method shown is using fractions to compare costs. This strategy does not work due to the fact that they have not factored in the $55 he pays for the car before hand. Also, 150 divided by 0.5 does not equal 30, it equals 300 so, even if he did not pay $55 beforehand, the equation is still incorrect.

<u>Correct Work/Solution</u>

$55 to rent

$0.50 per mile

Let's start by removing $55 from $150 to see how many dollars is left over for gas.

150 - 55 = 95

Then, divide 95 by 0.5

95 ÷ 0.5 = 190

He can drive at least 190 miles.

<u>Share Strategy</u>

Since he starts off paying $55 dollars out of $150, we need to subtract $55 by $150 to see how much cash he has left over for mileage. $150 minus $55 equals $95 so, he has $95 left over for mileage. $95 will then be divided by $0.50 to find out how many miles he can drive. We are dividing by $0.50 because that's the cost per mile. $95 divided by $0.50 equals 190 so he can drive at least 190 miles.

Note:

Hope this helps :)

Have a great day!

7 0
2 years ago
Teresa needs to save $25.50 to go to the movies this weekend. She currently has $3. If Teresa makes $7.50 an hour babysitting, h
seraphim [82]

Answer:she need to do at least 3 hours of babysitting.

Step-by-step explanation:

you subtract how much she already has, 3$ from 25.50 and then you divide how much she makes in one hour of babysitting by how much money she needs so 22.50/7.50=3

3 0
3 years ago
Read 2 more answers
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