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3 years ago

Determine the truth value of the given conditional statement

Mathematics

1 answer:

Dovator [93]3 years ago

5 0

Answer: c

A false statement implies a true statement, so the conditional statement is true

Step-by-step explanation: just took the test

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Please help me with the below question.

VMariaS [17]

By letting

$y = \displaystyle \sum_{n=0}^\infty c_n x^{n+r}$

we get derivatives

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

$y'' = \displaystyle \sum_{n=0}^\infty (n+r) (n+r-1) c_n x^{n+r-2}$

a) Substitute these into the differential equation. After a lot of simplification, the equation reduces to

$5r(r-1) c_0 x^{r-1} + \displaystyle \sum_{n=1}^\infty \bigg( (n+r+1) c_n + (n + r + 1) (5n + 5r + 1) c_{n+1} \bigg) x^{n+r} = 0$

Examine the lowest degree term $\left(x^{r-1}\right)$ , which gives rise to the indicial equation,

$5r (r - 1) + r = 0 \implies 5r^2 - 4r = r (5r - 4) = 0$

with roots at r = 0 and r = 4/5.

b) The recurrence for the coefficients $c_k$ is

$(k+r+1) c_k + (k + r + 1) (5k + 5r + 1) c_{k+1} = 0 \implies c_{k+1} = -\dfrac{c_k}{5k+5r+1}$

so that with r = 4/5, the coefficients are governed by

$c_{k+1} = -\dfrac{c_k}{5k+5} \implies \boxed{g(k) = -\dfrac1{5k+5}}$

c) Starting with $c_0=1$ , we find

$c_1 = -\dfrac{c_0}5 = -\dfrac15$

$c_2 = -\dfrac{c_1}{10} = \dfrac1{50}$

so that the first three terms of the solution are

$\displaystyle \sum_{n=0}^2 c_n x^{n + 4/5} = \boxed{x^{4/5} - \dfrac15 x^{9/5} + \frac1{50} x^{13/5}}$

4 0

2 years ago

The system has

vladimir2022 [97]

Answer:

One solution

Step-by-step explanation:

In this graph, the two lines only intersect once, meaning there is only one solution. If they intersect twice, then there are two solutions. If the two lines are parallel, there are no solutions. If the lines are the same, there are an infinite amount of solutions.

7 0

2 years ago

What annual rate of interest would you have to earn on an investment of $3500 to ensure receiving $273.00 interest after 1 year?

kogti [31]

To find the answer, we will have to find the percentage of $273 to $ 3500, and we can use the formula:

$\frac{interest received}{investment amount} \times 100%$

In this case:

273/3500 x 100%

=39/500 x 100%

=7.8%

Therefore the annual interest rate would be 7.8%.

Hope it helps!

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3 years ago

Which of the following represents a function?

Molodets [167]

What are the functions?

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3 years ago

Please answer this question

galben [10]

Answer:

Step-by-step explanation:

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3 years ago