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3 years ago

Which of the following is an irrational number o 18 o 2.6 o π o -16/3

Mathematics

2 answers:

Nikitich [7]3 years ago

7 0

Answer:

The answer is π

Step-by-step explanation:

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio.

Georgia [21]3 years ago

6 0

Answer:

Step-by-step explanation:

A rational number can be written as a fraction

18/1 is a fraction

2.6666666 can be written as 2 2/3 = 8/3

-16/3 is a fraction

pi is a non repeating non termination decimal which is irrational

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Can someone check whether its correct or no? this is supposed to be the steps in integration by parts

Gwar [14]

Answer:

$\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

Step-by-step explanation:

$\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}$

Given integral:

$\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x$

$\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:$

$\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x$

Using <u>integration by parts</u>:

$\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

Therefore:

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}$

$\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:$

$\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}$

Therefore:

$\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x$

$\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:$

$\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}$

Divide both sides by 2:

$\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}$

Rewrite in the same format as the given integral:

$\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

5 0

2 years ago

Graph the line using a point and a slope. Write the equation of each line.

SpyIntel [72]

Answer:

y=1.2x-3

Step-by-step explanation:

I had this as an rsm problem a few weeks ago and forgot how to solve it lol hope this helps

6 0

3 years ago

Is 7/12 bigger than 1/2

Varvara68 [4.7K]

Lets think of it this way:-

1/2 is one half

Whats half of 12? 6

Now, 7 is greater than 6, which means the fraction 7/12 is greater than 1/2

Answer: 7/12 is bigger

7 0

4 years ago

Read 2 more answers

Suppose you wish to borrow $600 for two weeks and the amount of interest you must pay is $25 per $100 borrowed. What is the APR

Yuliya22 [10]

Answer:

The APR at which the money is borrowed, is approximately 651.79%

Step-by-step explanation:

The amount which one wishes to borrow for two weeks, P = $600

The amount of interest that one must pay back = $25 per $100 borrowed

Therefore;

The total interest on the $600 loan (borrowed) for two weeks = 25/100× $600 = $150

The number of days for which the amount was borrowed = 2 weeks = 14 days

The Annual Percentage Rate, APR is given as follows;

$APR = \left (\dfrac{\left (\dfrac{Interest \ Paid \ for \ the \ Loan \ duration}{The \ amount \ borrowed} \right )}{The \ number \ of \ days \ the \ amount \ was \ borrowed } \right ) \times 365 \times 100$