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3 years ago

The point (0, 2) is the only solution to the system of linear equations that contains the equations

Mathematics

1 answer:

snow_lady [41]3 years ago

5 0

Answer:

D. independent equations

Step-by-step explanation:

The equations are not dependent and not inconsistent, so they can be described as "independent" or "consistent."

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What the answer here?

Brut [27]

Answer:

x230x

Step-by-step explanation:

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3 years ago

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

3 years ago

First one to answer randomly gets brainliest!

s344n2d4d5 [400]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

On a 40 question test students gain 6 points for each correct answer and lose 0.5 points on each incorrect answer. If everyone r

juin [17]

Answer:

$\text{r}=5.5\text{c}-20$

Step-by-step explanation:

GIVEN: On a $40$ question test students gain $6$ points for each correct answer and lose $0.5$ points on each incorrect answer. If everyone required to give an answer to each question.

TO FIND: the formulas that describes how a student's raw score, r, depends on the number of correct answers he or she provided, c.

SOLUTION:

Total number of incorrect questions $=40-\text{c}$

Total marks deducted due to incorrect question $=(40-\text{c})\times0.5=20-0.5\text{c}$

Total correct questions $=\text{c}$

Total marks scored $=6\text{c}$

Total raw marks $\text{r}=\text{total marks gained}-\text{total marks deducted}$

$\text{r}=6\text{c}-(20-0.5\text{c})$

$\text{r}=5.5\text{c}-20$

ormulas that describes how a student's raw score, r, depends on the number of correct answers he or she provided, c is $\text{r}=5.5\text{c}-20$

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3 years ago

Question 1: Find the amount of the FICA deduction: $37890 annually.

Radda [10]

Answer:

b....j..j.jm..e.e.e i didnt get it

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2 years ago