All categories

2 years ago

Write 2.3181818 as a mixed number

1 answer:

5 0

We convert 2.3181818 to fraction as follows:

Let x = 2.3181818 . . . . . (1)

as can be seen, the repeating digits are 18

Multiply both sides of equation (1) by 1,000 to get
1,000x = 2318.1818 . . . . . (2)

Also, multiply both sides of equation (1) by 10 to get
10x = 23.181818 . . . . . (3)

Subtract equation (3) from equation (2) to get
990x = 2,295

Thus,
$x= \frac{2,295}{990} =2 \frac{7}{22}$

You might be interested in

The mass of a colony of bacteria, in grams, is modeled by the function P given by P(t)=2+5tan^−1.(t/2), where t is measured in d

ira [324]

Answer:

1.21 g/day

Step-by-step explanation:

We are given that

The mass of a colony of bacteria (in (grams) is given by

$P(t)=2+5tan^{-1}(\frac{t}{2})$

Where t=Time(in days)

Differentiate w.r.t t

$P'(t)=5(\frac{1}{1+\frac{t^2}{4}}\times \frac{1}{2})$

By using the formula $\frac{d(tan^{-1}(x)}{dx}=\frac{1}{1+x^2}$

$P'(t)=\frac{5}{2}(\frac{4}{4+t^2})$

$P'(t)=\frac{10}{4+t^2}$

We are given P(t)=6

Substitute the value

$6=2+5tan^{-1}(\frac{t}{2})$

$5tan^{-1}(\frac{t}{2})=6-2=4$

$tan^}{-1}(\frac{t}{2})=\frac{4}{5}$

$\frac{t}{2}=tan(\frac{4}{5})$

$t=2tan(\frac{4}{5})$

Substitute the value of t

$P'(2tan\frac{4}{5})=\frac{10}{4+4tan^2(\frac{4}{5})}$

$P'(2tan\frac{4}{5})=\frac{10}{4}\times \frac{1}{1+tan^2(\frac{4}{5})}$

We know that $1+tan^2\theta=sec^2\theta$

Using the formula

$P'(2tan(\frac{4}{5})=\frac{5}{2}\times \frac{1}{sec^2(\frac{4}{5})}$

$P'(2tan\frac{4}{5})=\frac{5}{2}\times cos^2(\frac{4}{5})$

By using $cos^2x=\frac{1}{sec^2x}$

$P'(2tan\frac{4}{5})=\frac{5}{2}\times (0.696)^2=1.21$ g/day

Hence,the instantaneous rate of change of the mass of the colony=1.21g/day

7 0

2 years ago

Read 2 more answers

On a construction project, you estimate a total of 80 hours of labor. You will work 40 of the hours. Assistant A will work 25 ho

Angelina_Jolie [31]

Answer:

$1,630

Step-by-step explanation:

Assistant 2 hours: 80-40-25 = 15

YOU: 22 x 40 = $880

ASSISTANT 1: 15 x 25 = $375

ASSISTANT 2: 10 x 15 = $150

880+375+150 = $1,630

4 0

2 years ago

The ratio of the perimeter of square RSTU to the perimeter of square WXYZ is 1 to 3. The area of square RSTU is 36 square inches

Ainat [17]

√36 square inches = 6 inches (length of sq RSTU)
6 inches x 4=24 inches (per. of sq RSTU)
-----------------------------------
1u=24 inches
3u=24 inches x 3=72 inches (per. of sq WXYZ)
-----------------------------------
72 inches ÷ 4=18 inches (length of sq WXYZ)
18 inches x 18 inches = 324 square inches( area of sq WXYZ)

Ans: 324 square inches

5 0

2 years ago

Read 2 more answers

How many leap years occur between the<br> years 1700 and 1875?

Zina [86]

Step-by-step explanation:

A leap year occurs every 4th year.

So, 1875 - 1700 = 175

Now let us divide 175 by 4

$175 \div 4 = 43.75 \\ here \: 43 \: represents \: the \: number \: of \: \\ leap \: years.$