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2 years ago

12

Repeated decimals can be written as an infinite geometric series to help convert them to a fraction. Consider the repeating deci

mal below.
0.232323… = 0.23 + 0.23(0.01) + 0.23(0.01)2 + …
What is a1?
What is r?

2 answers:

Oksi-84 [34.3K]2 years ago

7 0

Answer:

a1= 0.23

r=0.01

:)

Step-by-step explanation:

fgiga [73]2 years ago

4 0

Answer:

$a_1=0.23$ and $r=0.1$ .

Step-by-step explanation:

It is given that Repeated decimals can be written as an infinite geometric series to help convert them to a fraction.

Consider the repeating decimal below.

$0.232323…=0.23+0.23(0.01)+0.23(0.01)^2+…$

We need to find the value of $a_1\text{ and }r$ .

$a_1$ is the first term of the series. So,

$a_1=0.23$

$r$ is the common ratio of the series. So,

$r=\dfrac{a_2}{a_1}=\dfrac{0.23(0.1)}{0.23}=0.1$

Therefore, $a_1=0.23$ and $r=0.1$ .

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Cindy is making a fruit juice drink. The recipe calls for 5 parts apple juice and 3 parts pineapple juice. Cindy puts cups of ap

myrzilka [38]

She must mix 1.5 cups of pineapple juice into the pitcher.

Since Cindy is making a fruit juice drink, and the recipe calls for 5 parts apple juice and 3 parts pineapple juice, and Cindy puts 2 1/2 cups of apple juice into a pitcher, and Cindy wants the juice drink in her pitcher to taste the same as the drink in the recipe, to determine how much pineapple juice does she need to mix into the pitcher, the following calculation must be performed, proposing a cross multiplication:

5 = 2 1/2
3 = X
5 = 2.5
3 = X
3 x 2.5 / 5 = X
7.5 / 5 = X
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Therefore, she must mix 1.5 cups of pineapple juice into the pitcher.

Learn more in brainly.com/question/13019339

4 0

2 years ago

Shalnov [3]

Answer:

4.013 units

Step-by-step explanation:

We know that the volume of a cone is given by the following equation:

v = pi / 3 * r ^ 2 * h

we need to know the height, therefore we solve for h:

h = 3 * v / (pi * r ^ 2)

replacing v = 105 and r = 5

h = 3 * 105 / (3.14 * 5 ^ 2)

h = 4.013

Which means that the height measures 4.013 units

4 0

3 years ago

Read 2 more answers

When graphing do you use an open or closed circle for >

meriva

Answer:

open

Step-by-step explanation:

When there is a line under the inequality symbol its a closed circle but if there is not then its an open circle

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2 years ago

Z varies directly as x^3 and inversely as y^3. if z=59 when x=8 and y=8, find Z if x=3 and y=4

marissa [1.9K]

$z=\dfrac{kx^3}{y^3}\\\\\\59=\dfrac{k\cdot 8^3}{8^3}\\k=59\\\\\\z=\dfrac{59x^3}{y^3}\\\\\\z=\dfrac{59\cdot 3^3}{4^3}=\dfrac{1593}{64}$

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1 year ago

Which equation represents a line that passes through (2,-1/2) and has a slope of 3 ?

Anna11 [10]

Answer:

C. $y + \frac{1}{2} = 3(x - 2)$

Step-by-step explanation:

Given

$Point: (2,\frac{-1}{2})$

$Slope: 3$

Required

Equation of line

Let m represents the slope of the line;

m is calculated as thus

$m = \frac{y - y_1}{x - x_1}$

$where (x_1,y_1) = (2,\frac{-1}{2})$

$So; x_1 = 2; y_1 = \frac{-1}{2}$

$m = 3$

By substituting the right values in the formula above;

$m = \frac{y - y_1}{x - x_1}$ becomes

$3 = \frac{y - \frac{-1}{2}}{x - 2}$

Multiply both sides by $(x - 2)$

$3 *(x - 2) = \frac{y - \frac{-1}{2}}{x - 2} *(x - 2)$

$3 *(x - 2) = (y - \frac{-1}{2})$

$3 *(x - 2) = (y + \frac{1}{2})$

$3(x - 2) = (y + \frac{1}{2})$

$3(x - 2) = y + \frac{1}{2}$

Reorder

$y + \frac{1}{2} = 3(x - 2)$

Hence, the equation that represents the line is $y + \frac{1}{2} = 3(x - 2)$

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3 years ago