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3 years ago

You deposit $300 in a savings account. The account earns 10% simple interest per year.

Mathematics

1 answer:

Phantasy [73]3 years ago

3 0

Answer:

Step-by-step explanation:

The interest after 8 years is $240

The balance after 8 years is $540

Hope this helps!

Plz, Mark Brainliest!

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use Taylor's Theorem with integral remainder and the mean-value theorem for integrals to deduce Taylor's Theorem with lagrange r

Vadim26 [7]

Answer:

As consequence of the Taylor theorem with integral remainder we have that

$f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x-a)^n + \int^a_x f^{(n+1)}(t)\frac{(x-t)^n}{n!}dt$

If we ask that $f$ has continuous $(n+1)$ th derivative we can apply the mean value theorem for integrals. Then, there exists $c$ between $a$ and $x$ such that

$\int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}dt = \frac{f^{(n+1)}(c)}{n!} \int^a_x (x-t)^n d t = \frac{f^{(n+1)}(c)}{n!} \frac{(x-t)^{n+1}}{n+1}\Big|_a^x$

Hence,

$\int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}d t = \frac{f^{(n+1)}(c)}{n!} \frac{(x-t)^{(n+1)}}{n+1} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1} .$

Thus,

$\int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}d t = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}$

and the Taylor theorem with Lagrange remainder is

$f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x-a)^n + \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}$ .

Step-by-step explanation:

5 0

3 years ago

How can you choose values for x when making a table of value representing a real world situation?

coldgirl [10]

You can simply count 0,1,2,3 when zero is your starting point

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3 years ago

Which expressions are equivalent to 2[3/4x+7]-3(1/2x-5)? Check all that apply

emmainna [20.7K]

Answer:

B, C, E

Step-by-step explanation:

This is correct. Trust me.

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3 years ago

If M(6,9) is the midpoint of the line segment AB, and if A has coordinates (3,5), find the coordinates of B.

ANEK [815]

(9,13) .................

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3 years ago

Two brothers have a total age of 28 if one brother is older by 20 years how old is the second brother

svlad2 [7]

Answer:

Step-by-step explanation:

Total meaning addition, you would use the opposite operation to find the answer.

28 - 20 = 8

And to check your work you would add;

20 + 8 = 28

which is the brothers total combined age.

6 0

3 years ago

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