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2 years ago

E = { 2 4 6 8} List the members

Mathematics

1 answer:

Vadim26 [7]2 years ago

5 0

W={a, b, c, d}

n(W) =4

No of subsets =2^n=2^4=16

The subsets are

{a, b};

{a, c};

{a, d};

{b, c};

{b, d};

{c, d};

{a};

{b};

{c};

{d};

{a, b, c};

{a, b, d};

{a, c, d};

{b, c, d},

{a, b, c, d};

{0}

Your Welcome

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Find the solution of the given initial value problem:<br><br> y''- y = 0, y(0) = 2, y'(0) = -1/2

igor_vitrenko [27]

Answer: The required solution of the given IVP is

$y(x)=\dfrac{3}{4}e^x+\dfrac{5}{4}e^{-x}.$

Step-by-step explanation: We are given to find the solution of the following initial value problem :

$y^{\prime\prime}-y=0,~~~y(0)=2,~~y^\prime(0)=-\dfrac{1}{2}.$

Let $y=e^{mx}$ be an auxiliary solution of the given differential equation.

Then, we have

$y^\prime=me^{mx},~~~~~y^{\prime\prime}=m^2e^{mx}.$

Substituting these values in the given differential equation, we have

$m^2e^{mx}-e^{mx}=0\\\\\Rightarrow (m^2-1)e^{mx}=0\\\\\Rightarrow m^2-1=0~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mx}\neq0]\\\\\Rightarrow m^2=1\\\\\Rightarrow m=\pm1.$

So, the general solution of the given equation is

$y(x)=Ae^x+Be^{-x},$ where A and B are constants.

This gives, after differentiating with respect to x that

$y^\prime(x)=Ae^x-Be^{-x}.$

The given conditions implies that

$y(0)=2\\\\\Rightarrow A+B=2~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$y^\prime(0)=-\dfrac{1}{2}\\\\\\\Rightarrow A-B=-\dfrac{1}{2}~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Adding equations (i) and (ii), we get

$2A=2-\dfrac{1}{2}\\\\\\\Rightarrow 2A=\dfrac{3}{2}\\\\\\\Rightarrow A=\dfrac{3}{4}.$

From equation (i), we get

$\dfrac{3}{4}+B=2\\\\\\\Rightarrow B=2-\dfrac{3}{4}\\\\\\\Rightarrow B=\dfrac{5}{4}.$

Substituting the values of A and B in the general solution, we get

$y(x)=\dfrac{3}{4}e^x+\dfrac{5}{4}e^{-x}.$

Thus, the required solution of the given IVP is

$y(x)=\dfrac{3}{4}e^x+\dfrac{5}{4}e^{-x}.$

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3 years ago

Scientists are measuring the thickness of ice on a large lake. When they first measure the ice, it is 3.1 inches thick. Three we

yaroslaw [1]

Answer:

Step-by-step explanation:

What is the question?

Amount of change = 5.5-3.1 = 2.4 inches

Percentage change = 2.4/3.1 ≈ 77.4% increase

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3 years ago

Which center processes aluminum faster, and why?

garri49 [273]

Answer:

Recycling

Step-by-step explanation:

because i see recyling bins everywhere

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2 years ago

A garden hose supplies 36 gallons of water in 3 minutes. Use a table of equivalent ratios to show the garden hose's water flow i

tino4ka555 [31]

Answer:

The flow per-minute is 12 gallons every minute

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x-y

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2 years ago

Tobias dropped a tennis ball from a height of 60 meters. The time in seconds it takes for the ball to fall 60 feet is 0.25(radic

AnnZ [28]

We are given

Tobias dropped a tennis ball from a height of 60 meters. The time in seconds it takes for the ball to fall 60 feet is 0.25(radical60).

so, time is

$T=0.25\sqrt{60} =\frac{1}{4} \sqrt{60}$

we have to approximate it's value

First approximation set:

we know that

$49$

we can take sqrt all the sides

$\sqrt{49}$

we can simplify it

$7$

Divide all sides by 4

$\frac{7}{4}< \frac{1}{4} \sqrt{60}$

Second approximation set:

$7.7$

Divide all sides by 4

$\frac{7.7}{4}$

$1.925$

Third approximation set:

$7.74$

Divide all sides by 4

$\frac{7.74}{4}$

$1.935$

so, we get

$t=1.94seconds$ ......Answer

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2 years ago