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3 years ago

Convert the fraction 3/22 into a repeating decimal

Mathematics

2 answers:

MrRa [10]3 years ago

4 0

Answer:

5/4

Step-by-step explanation:

krek1111 [17]3 years ago

3 0

Answer:

Convert the fraction to a decimal by dividing the numerator by the denominator.

0.1

¯¯¯¯

Step-by-step explanation:

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The general solution of 2 y ln(x)y' = (y^2 + 4)/x is

Sav [38]

Replace $y'$ with $\dfrac{\mathrm dy}{\mathrm dx}$ to see that this ODE is separable:

$2y\ln x\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y^2+4}x\implies\dfrac{2y}{y^2+4}\,\mathrm dy=\dfrac{\mathrm dx}{x\ln x}$

Integrate both sides; on the left, set $u=y^2+4$ so that $\mathrm du=2y\,\mathrm dy$ ; on the right, set $v=\ln x$ so that $\mathrm dv=\dfrac{\mathrm dx}x$ . Then

$\displaystyle\int\frac{2y}{y^2+4}\,\mathrm dy=\int\dfrac{\mathrm dx}{x\ln x}\iff\int\frac{\mathrm du}u=\int\dfrac{\mathrm dv}v$

$\implies\ln|u|=\ln|v|+C$

$\implies\ln(y^2+4)=\ln|\ln x|+C$

$\implies y^2+4=e^{\ln|\ln x|+C}$

$\implies y^2=C|\ln x|-4$

$\implies y=\pm\sqrt{C|\ln x|-4}$

4 0

3 years ago

A school district transported a total of 409 students and teachers to a zoo in buses and vans.

valina [46]

Answer: There are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.

Step-by-step explanation:

Since we have given that

Total number of students and teachers = 409

Let the number of vans be x

Let the number of buses be x+5

Number of students and teachers each bus transported = 55

Number of students and teachers each van transported = 12

According to question,

$55(x+5)+12x=409\\\\55x+275+12x=409\\\\67x=409-275\\\\67x=134\\\\x=\frac{134}{67}\\\\x=2$

Total number of students and teachers who rode to the zoo in buses will be

$55(x+5)\\\\=55(2+5)\\\\=55\times 7\\\\=385$

Total number of students and teachers who rode to the zoo in vans will be

$12x\\\\=12\times 2=24$

Hence, there are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.

6 0

3 years ago

Point Q is the center of dilation. Line segment L M is dilated to created line segment L prime M prime. The length of L Q is 4 a

koban [17]

Answer:

The length of segment QM' = 6

Step-by-step explanation:

Given:

Q is the center of dilation

Pre-image (original image) = segment LM

New image = segment L'M'

The length of LQ = 4

The length of QM = 3

The length of LL' = 4

The original image was dilated with scale factor = 2

QM' = ?

To determine segment QM', first we would draw the diagram obtained from the given information.

Find attached the diagram

When a figure is dilated, we would have similar shape in thus cars similar triangles.

Segment L'M' = scale factor × length of LM

Let LM = x

L'M' = 2x

Using similar triangles theorem, ratio of their corresponding sides are equal.

QM/LM = QM'/L'M'

3/x = QM'/2x

6x = QM' × x

Q'M' = 6

The length of segment QM' = 6

5 0

3 years ago

Read 2 more answers

What is the midpoint of CD?<br> • (1/2,-5/2)<br> •(1,-5/2)<br> •(1/2,-3/2)<br> •(1,-3/2)

polet [3.4K]

Answer:

(1/2,-5/2)

Step-by-step explanation:

$\frac{ - 3 + 4 }{2} = \frac{1}{2} \\ \frac{ - 4 + - 1}{2} = \frac{ - 5}{2}$

7 0

3 years ago

Read 2 more answers

describe how making a list can help you solve a math problem.Write a problem that could be solved by making a list.

uranmaximum [27]

Making a list helps organize the information in a word problem that can otherwise be overwhelming and confusing. Making lists put out a straightforward guide and help you break down the problem so you really understand what you need to do.
Word problem:
Maya has $55 and she gives her brother $10. She also gives her friend $15 and her sister $5. Her sister pays her back fully but her brother only pays back half of what he owed, promising to pay her back later. Her friend gives back 1/3 of what she owed, also promising to pay her back as soon as she can. How much money does Maya currently have?

In this problem, you have to process the money transactions and making a list will help you go step by step.

6 0

3 years ago