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3 years ago

Find the the sum for the shown infinite geometric series? 2,2/3, 2/9, ...

Mathematics

1 answer:

Marta_Voda [28]3 years ago

6 0

Answer:

Step-by-step explanation:

The formula for the sum of an infinite geometric series is

$\frac{a}{1-r}$

Where a is the first term and r is the common ratio. We can see that the first term is 2, and to find the common ratio, we can divide a term by the one before it. We can get:

$\frac{\frac{2}{3}}{2} =\frac{2}{3} *\frac{1}{2}=\frac{1}{3}$

Now, we have all the values need to evaluate the formula. We can plug them in:

$\frac{2}{1-\frac{1}{3} } \\\frac{2}{\frac{2}{3} } \\2*\frac{3}{2}\\3$

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Develop an estimate for each of the following situations.(at) The cost of a 500-mile automobile trip, if gaso-line is $4 per gal

Olin [163]

Answer:

The answer is below

Step-by-step explanation:

develop an estimate for each of the following situations.

(a) The cost of a 500- mile automobile trip, if gasoline is $4.00 per gallon, vehicle wear and tear is $0.65 per mile, and our vehicle gets 25 miles per gallon.

(b) The total number of hours in the average human life, if the average life is 75 years.

(c) The number of days it takes to travel around the equator using a hot air balloon, if the balloon averages 100 miles per day, the diameter of the earth is ~4,000 miles.

Solution:

a) The total trip = 500 mile

Cost of wear and tear = $0.65 per mile = $0.65 * 500 mile = $325

25 miles takes 1 gallon of gasoline at a cost of $4 per gallon

Cost of gasoline = $4 per gallon * 500 miles / 25 miles per gallon = $80

cost of a 500-mile automobile trip = Cost of wear and tear + Cost of gasoline = $325 + $80 = $405

b) Average life of human = 75 years.

1 year = 365 days, 1 day = 24 hours

Average life of human in hours = 75 years * 365 days * 24 hours =657000 hours

c) Diameter of earth = 4000 miles

Distance of equator = diameter of earth = 4000 miles

100 mile per day

number of days for the balloon to travel round the earth = 4000 miles / (100 mile per day) = 40 days

5 0

3 years ago

The Height of a ramp is 11 inches and the length of its slanted side it 61 inches. What is the length of the base of the ramp?

o-na [289]

Triangle:

39 degrees, 33 degrees, 108 degrees

Side opposite the 108 degrees is 360 feet.

length asked for is d

Hope this helped you! Brainliest? :)

5 0

3 years ago

A bag has 2 blue marbles 3 red marbles and 5 white marbles. Which event has a probability greater than 1/5 select three options

Evgesh-ka [11]

Answer:

all

Step-by-step explanation:

all of them has the probability

4 0

3 years ago

Rationalize the denominator of square root of negative 9 over open parentheses 4 minus 7 i close parentheses minus open parenthe

AlekseyPX

The answer is
$\frac{-6i-3}{5}$ .

Before we rationalize the denominator, we must simplify the numerator and denominator. We evaluate the square root on the top, and combine like terms on the bottom:
$\frac{\sqrt{-9}}{(4-7i)-(6-6i)}
\\
\\=\frac{\sqrt{9i^2}}{4-6-7i--6i}
\\
\\=\frac{3i}{-2-i}$

To rationalize the denominator, we multiply by the conjugate. The conjugate is found by making the imaginary term of the complex number, the i part, the opposite sign. The conjugate of -2-i is -2+i:

$\frac{3i}{-2-i}\times \frac{-2+i}{-2+i}
\\
\\=\frac{3i(-2+i)}{(-2-i)(-2+i)}
\\
\\=\frac{3i\times -2 + 3i\times i}{-2\times -2 + -2\times i + -2\times -i + -i\times i}
\\
\\=\frac{-6i+3i^2}{4-2i+2i-i^2}
\\
\\=\frac{-6i+3(-1)}{4-i^2}=\frac{-6i-3}{4-(-1)}=\frac{-6i-3}{5}$

7 0

3 years ago

Use the quadratic formula to solve x2 – 3x - 2 = 0.

r-ruslan [8.4K]

Answer:

x = 2 , 1

Step-by-step explanation:

6 0

3 years ago

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