1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
hammer [34]
2 years ago
13

55. The sum of an infinite geometric series is five times the value of the first term. What is the common ratio of the series?

Mathematics
1 answer:
myrzilka [38]2 years ago
8 0

Answer:

r = 4/5

Step-by-step explanation:

Formula

Sum of an infinite geometric series = a / (1 - r)

Givens

Sum = 5*a

a = a

r = ?

Solution

5a = a/(1 - r)                   Divide both sides by a

5a/a = a / (a * (1 - r)       The a's on the right cancel

5 = 1 / (1 - r)                    Multiply both sides by 1 - r

5*(1 - r) = 1*(1 - r)/(1 - r)   The 1 - r s on the right cancel

5*(1 - r) = 1                     Remove the brackets.

5 - 5r = 1                        Subtract 5 from both sides

5-5 - 5r = 1 - 5               Combine

-5r = - 4                          Divide by - 5

r = 4/5  

You might be interested in
​Joe's annual income has been increasing each year by the same dollar amount. The first year his income was ​$17 comma 90017,900
Vedmedyk [2.9K]

Answer:

In 17th year, his income was $30,700.

Step-by-step explanation:

It is given that the income has been increasing each year by the same dollar amount. It means it is linear function.

Income in first year = $17,900

Income in 4th year = $20,300

Let y be the income at x year.

It means the line passes through the point (1,17900) and (4,20300).

If a line passes through two points (x_1,y_1) and (x_2,y_2), then the equation of line is

y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)

The equation of line is

y-17900=\frac{20300-17900}{4-1}(x-1)

y-17900=\frac{2400}{3}(x-1)

y-17900=800(x-1)

y-17900=800x-800

Add 17900 on both sides.

y=800x-800+17900

y=800x+17100

The income equation is y=800x+17100.

Substitute y=30,700 in the above equation.

30700=800x+17100

Subtract 17100 from both sides.

30700-17100=800x

13600=800x

Divide both sides by 800.

\frac{13600}{800}=x

17=x

Therefore, in 17th year his income was $30,700.

5 0
3 years ago
Question 1
Phantasy [73]

Answer:

yes

Step-by-step explanation:

5 0
3 years ago
You have 88 grams of a radioactive kind of actinium. How much will be left after 44 years if its half-life is 22 years?
mash [69]

Answer:

22 grams

Step-by-step explanation:

loses 50% of it's mass per 22 years

so after 22 years the mass would be 44 grams

22 years later would leave 50% of 44 grams = 22 grams

3 0
3 years ago
Help me please !!!!!!
PilotLPTM [1.2K]
The correct answer is B. x is greater than -2.

7 0
3 years ago
Add 34+(−212) using the number line. Select the location on the number line to plot the sum.
nexus9112 [7]

Answer:

-1 3/4

Step-by-step explanation:

3/4 + (-2 1/2)

3/4 - 2

-1 3/4

5 0
3 years ago
Other questions:
  • If (x) = -54 - 4 and g(x) = -3x - 2. find (f - g)(x).
    9·1 answer
  • Which is the best approximate solution of the system of linear equations y = 1.5x – 1 and y = 1?
    12·2 answers
  • Use the table to identify the relationship of the second sentence to the first sentence
    15·1 answer
  • In a college of 1250 students, 350 students owned their own car. What fraction of the students owned their own car?
    14·1 answer
  • Paul predicts that n stalks of corn planted together will produce (2n2–2n)(2n2–2n) ears of corn. If Paul plants three corn plant
    5·1 answer
  • I have two proof questions and I don't really know how to do them.
    12·1 answer
  • I need help with this.
    12·1 answer
  • Solve the equation 4x +30 = 2(x-10)
    12·1 answer
  • Please help meeeeeeeeeeeee
    15·1 answer
  • What IS the value of z?<br> Enter your answer In the box.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!