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2 years ago

Is this a function ? explain your reasoning. can someone help me pleasee !

Mathematics

1 answer:

TiliK225 [7]2 years ago

6 0

Yes it’s a function since every input has at least 1 output and there’s not multiple lines coming from the input side

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1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING

iogann1982 [59]

$y=\displaystyle\sum_{n=0}^\infty a_nx^n$

then

$y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n$

The ODE in terms of these series is

$\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0$

$\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0$

$\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}$

We can solve the recurrence exactly by substitution:

$a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0$

$\implies a_n=\dfrac{(-2)^n}{n!}a_0$

So the ODE has solution

$y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}$

which you may recognize as the power series of the exponential function. Then

$\boxed{y(x)=a_0e^{-2x}}$

7 0

2 years ago

In 3/4 pound of cake mix, there are 2/5 cups of flour. How much flour does the cake mix contain per pound?

Firdavs [7]

Answer:

5/9

Step-by-step explanation:

5 0

2 years ago

Rylee is baking cupcakes for a bake sale. She spends $35 on supplies and she plans to sell the cupcakes for $2.50 each. How many

Setler [38]

Answer:

44 cupcakes

Step-by-step explanation:

Since she spent $35, and she wants to profit $75, she needs to make $110.

110/2.5 = 44

6 0

2 years ago

triangle ABC above is isosceles with AB=AC and BC =48. the ratio of DE is 5:7. what is the length of DC

marshall27 [118]

Answer:

Step-by-step explanation:

Question Image is attached.

Triangle BED and Triangle CFD are similar.

We can let the length of BD be 5x and DC 7x

We also know BC = 48, thus we can write:

5x + 7x = 48

12x = 48

x = 4

Now, Since DC = 7x, we plug in x = 4 into it.

DC = 7x

DC = 7(4)

DC = 28

Length of DC is 28

6 0

2 years ago

Read 2 more answers

1.055.

Stella [2.4K]

Given:

The statement is:

{5, 6, 7} = {5, 5, 6, 7, 7}

To find:

Whether the given statement is true or false.

Solution:

Two sets are equal if they have exactly the same elements.

The given set {5, 6, 7} has three elements and the set {5, 5, 6, 7, 7} has five elements but we known that all the elements of a set are distinct. It means, it has no repeated element.

Set {5, 5, 6, 7, 7} has three distinct elements 5, 6, 7. So,

{5, 5, 6, 7, 7} = {5, 6, 7}

Therefore, the given statement is true.

5 0

2 years ago