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
dmitriy555 [2]
2 years ago
12

An infinite geometric series has a first term ai = 15 and a sum of 45. Explain how you

Mathematics
1 answer:
oee [108]2 years ago
8 0

Answer:

r= \frac{2}{3}

Step-by-step explanation:

The sum to infinity of a geometric series is calculated as

S∞ = \frac{a_{1} }{1-r} ; | r | < 1

where a₁ is the first term and r the common ratio

here a₁ = 15 and S∞ = 45 , then

45 = \frac{15}{1-r} ( multiply both sides by (1 - r ) )

45(1 - r) = 15 ( divide both sides by 45 )

1 - r = \frac{15}{45} = \frac{1}{3} ( subtract 1 from both sides )

- r = \frac{1}{3} - 1 = - \frac{2}{3} ( multiply both sides by - 1 )

r = \frac{2}{3}

You might be interested in
Can someone help me with this
katrin [286]

Half  the length of the curve which separates the 2 halves = 1/2 circumference of a circle with diameter 6 mm.  = 1/2 * pi * d = 3pi mm

So the length of the line = 6pi =  18.85 mm to nearest hundredth. answer

The area of shaded region = 1/2 area of the circle = 1/2 pi r^2

= 1/2 * pi * 6^2

=  56.55 mm^2  to nearest hundredth  answer


8 0
3 years ago
What type of angle is each angle in this figure?
Naya [18.7K]
J= obtuse
K=right
L=acute
M=acute
8 0
2 years ago
<img src="https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B4%7D%20%20-%206%20%7Bx%7D%5E%7B3%7D%20%20%2B%2022%20%7Bx%7D%5E%7B2%7D%20%20-%2
alexira [117]

Answer:

x = 2, 1 + 3i, 1 − 3i

Step-by-step explanation:

Find the Roots (Zeros)

x^4 − 6x^3 + 22x^2 − 48x + 40

Set x^4 − 6x^3 + 22x^2 − 48x + 40 equal to 0. x^4 − 6x^3 + 22x^2 − 48x + 40 = 0

Solve for x.

Factor the left side of the equation.

Factor x^4 − 6x^3 + 22x^2 − 48x + 40 using the rational roots test.

(x − 2) (x^3 − 4x^2 + 14x − 20) = 0

 Factor x^3 − 4x^2 + 14x − 20 using the rational roots test.

(x − 2) (x − 2) (x2 − 2x + 10) = 0

 Combine like factors.

(x − 2)2 (x^2 − 2x + 10) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

(x − 2)^2 = 0

x^2 − 2x + 10 = 0

 Set (x − 2)^2 equal to 0 and solve for x.

Set (x − 2)^2 equal to 0.

 (x − 2)^2 = 0

Solve (x − 2)^2 = 0 for x.

x = 2

 Set x^2 − 2x + 10 equal to 0 and solve for x.

Set x^2 − 2x + 10 equal to 0. x^2 − 2x + 10 = 0

Solve x^2 − 2x + 10 = 0 for x.

Use the quadratic formula to find the solutions.

−b ± (√b^2 − 4 (ac) )/2a

Substitute the values a = 1, b = −2, and c = 10 into the quadratic formula and solve for x.

2 ± (√(−2)^2 − 4 ⋅ (1 ⋅ 10))/2 ⋅ 1

Simplify.

Simplify the numerator.

  x =    2 ± 6i/ 2.1

Multiply 2 by 1

 x =  2 ± 6i/2⋅1

 Simplify

  2 ± 6i/2  

   x = 1 ± 3i

The final answer is the combination of both solutions.

x = 1 + 3i, 1 − 3i

The final solution is all the values that make (x − 2)2 (x2 − 2x + 10) = 0 true.

x = 2, 1 + 3i, 1 − 3i

3 0
3 years ago
Use the formula d = rt to find the distance d a long distance runner can run at a rate of 9 1/2 miles per hour for time t or 1 3
LiRa [457]
D = (9 1/2) (1 3/4) D = 11 7/8 miles



7 0
3 years ago
If the equation 3x-5y=-3, what is the value of y when x is 1
pantera1 [17]
The answer is: 6/5

Here is why:
3x - 5y = -3
3(1) - 5y = -3
3 - 5y = -3
3 - 5(6/5) = -3
-3 = -3

6 0
3 years ago
Other questions:
  • How to solve this equation of the missing sides of the triangle
    11·1 answer
  • Find a base length of a shipping box in the shape of a triangle prism.The shipping box has a volume of 276 cubic feet,a height o
    11·1 answer
  • Mika can eat 21 hot dogs in 66 minutes. She wants to know how many minutes it would take her to eat 35 hot dogs if she can keep
    8·1 answer
  • Which one is correct ?
    5·2 answers
  • Jacob ran 2/3 of the length of a football field before he was tackled. if the filled is 100 yards long. how far is did Jacob run
    14·1 answer
  • Your local radio station is having their yearly music player and concert ticket giveaway. For one minute, every ​​ 5th , start s
    8·2 answers
  • Question 18 (4 points)
    9·1 answer
  • Will give Brainlyest answer!
    15·1 answer
  • What is the function of the tentacles of a cnidarian?
    5·1 answer
  • Write the quadratic equation in standard form:<br> -3x^2-16=−3x
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!