MATHEMATICS COLLEGE

Which Number Is Rational?

Answers

Answer 1

Answer:

A. 0.333...

Step-by-step explanation:

Any repeating decimal can be written as a ratio of two integers, hence is rational. 0.333... = 1/3

The last offering appears to be a non-repeating infinite-length decimal, hence is irrational.

Of course π is irrational, as is the square root of any integer that is not the square of an integer.

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Determine whether the geometric series is convergent or divergent. 6 + 5 + 25/6 + 125/36 + ... If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)

Answers

The $n$ -th term in the series is 6 multiplied by the $(n-1)$ -th power of 5/6:

$a_1=6=6\left(\frac56\right)^(1-1)$

$a_2=5=6\left(\frac56\right)^(2-1)$

$a_3=\frac{25}6=6\left(\frac56\right)^(3-1)$

and so on.

$\displaystyle\sum_(n=1)^\infty6\left(\frac56\right)^(n-1)$

Consider the $N$ -th partial sum,

$S_N=\displaystyle\sum_(n=1)^N6\left(\frac56\right)^(n-1)$

$S_N=6\left(1+\frac56+\cdots+(5^(N-2))/(6^(N-2))+(5^(N-1))/(6^(N-1))\right)$

Multiplying both sides by 5/6 gives

$\frac56S_N=6\left(\frac56+(5^2)/(6^2)+\cdots+(5^(N-1))/(6^(N-1))+(5^N)/(6^N)\right)$

and substracting this from $S_N$ gives

$\frac16S_N=6\left(1-(5^N)/(6^N)\right)$

$S_N=36\left(1-\left(\frac56\right)^N}\right)$

As $N\to\infty$ , it's clear that the sum converges to 36.

Final answer:

The geometric series in the question is convergent with a common ratio of 5/6. Using the formula for the sum of an infinite geometric series, the sum of the series is found to be 36.

Explanation:

In mathematics, specifically in series, determining whether a geometric series is convergent or divergent is centered around the common ratio value. In terms of this particular series: 6 + 5 + 25/6 + 125/36 + ..., the common ratio is 5/6. Given this common ratio, it's clear that it falls between -1 and 1. Hence, this geometric series is convergent.

Once we establish it is a convergent series, we can calculate its sum using the formula for the sum of an infinite geometric series: S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio. Inserting the respective values a = 6 and r = 5/6, we get: S = 6 / (1 - 5/6) = 36. Hence, the sum of this infinite geometric series is 36.

Learn more about Geometric Series here:

brainly.com/question/34429025

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If 1 gallon of paint covers 300 square feet, how many gallonsare needed for a room 30' long x 20' wide x 12' high?

Answers

Answer:

can we be friends

Step-by-step explanation:

4(12+3) distributive property

Answers

$\huge\textsf{Hey there!}$

$\large\textsf{4(12 + 3)}$

$\large\textsf{= 4(12) + 4(3)}$

$\large\textsf{4(12) = \bf 48}$

$\large\textsf{4(3) = \bf 12}$

$\large\textsf{= 48 + 12}$

$\large\textsf{= \bf 60}$

$\boxed{\large\textsf{Answer: \huge 60}}\large\checkmark$

$\large\text{OR} \downarrow$

$\large\textsf{4(12 + 3)}$

$\large\textsf{12 + 3 = \bf 15}$

$\large\textsf{= 4(15)}$

$\large\textsf{= \bf 60}$

$\boxed{\large\textsf{Answer: \huge 60}}\large\checkmark$

$\boxed{\boxed{\large\textsf{OVERALL \underline{ANSWER}: \huge \bf 60}}}\huge\checkmark$

$\huge\checkmark\boxed{\boxed{\large\textsf{Or you can say: \huge \bf 48 + 12}}}\huge\checkmark$

$\large\text{Good luck on your assignment and enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

$\huge\boxed{\mathfrak{Answer}}$

$4(12 + 3) \n = 4 * 12 + 4 * 3 \n = 48 + 12 \n = 60$

=> Property used = distributive property.

The club with an occupancy of 100 will sell out at $25 per ticket. If the owner decides to increase the price by $5, then 2 less tickets will be sold. Determine the revenue function if x is the number of $5 increases.

Answers

Answer:

100 + (5X) = -2X

Step-by-step explanation:

Since the club with an occupancy of 100 will sell out at $ 25 per ticket, and if the owner decides to increase the price by $ 5, then 2 less tickets will be sold, to determine the revenue function if X is the number of $ 5 increases the following calculation must be performed:

100 + (5X) = -2X

So, for example, if the price were increased by $ 15, the equation would apply as follows:

15/5 = 3

100 + (5x3) = -2 x 3

100 + 15 = -6

115 = -6

If there are 100 cm in
1 meter, how many
centimeters are in 6
meters?

Answers

Answer:

there are 600 cm in 6 meters

Answer: 600 cm

Step-by-step explanation:

100cm = 1 m

Then ? cm = 6m

Since cm is smaller than m, cm would need more to be equal or equivalent to m. Therefore we say, what multiply by 1m gives you 6m? Because they are asking for 6m. Whatever you do to one side you do to the other.

6(100)cm = 6(1) m

600cm = 6m

A product p and six is wrtten as