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2 years ago

HURRY WILL MARK BRAINLIEST what is the value of the output when the input is 20

Mathematics

1 answer:

Juli2301 [7.4K]2 years ago

3 0

Answer:

<u><em>(–20)</em></u> for the resulting output voltages

Step-by-step explanation:

Hope this helped! :)

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When a deposit of $1000 is made into an account paying 2% interest, compounded annually, the balance, $B, in the account after t

labwork [276]

Answer:

The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.

Step-by-step explanation:

Given a function y, the average rate of change S of y=f(x) in an interval $(x_{s}, x_{f})$ will be given by the following equation:

$S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}}$

In this problem, we have that:

$B(t) = 1000(1.02)^{t}$

Find the average rate of change in the balance over the interval t = 0 to t = 5.

$B(0) = 1000(1.02)^{0} = 1000$

$B(5) = 1000(1.02)^{5} = 1104.08$

Then

$S = \frac{1104.08 - 1000}{5-0} = 20.82$

The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.

8 0

3 years ago

Solve using Fourier series.

Olin [163]

With $2L=\pi$ , the Fourier series expansion of $f(x)$ is

$\displaystyle f(x)\sim\frac{a_0}2+\sum_{n\ge1}a_n\cos\dfrac{n\pi x}L+\sum_{n\ge1}b_n\sin\dfrac{n\pi x}L$
$\displaystyle f(x)\sim\frac{a_0}2+\sum_{n\ge1}a_n\cos2nx+\sum_{n\ge1}b_n\sin2nx$

where the coefficients are obtained by computing

$\displaystyle a_0=\frac1L\int_0^{2L}f(x)\,\mathrm dx$
$\displaystyle a_0=\frac2\pi\int_0^\pi f(x)\,\mathrm dx$

$\displaystyle a_n=\frac1L\int_0^{2L}f(x)\cos\dfrac{n\pi x}L\,\mathrm dx$
$\displaystyle a_n=\frac2\pi\int_0^\pi f(x)\cos2nx\,\mathrm dx$

$\displaystyle b_n=\frac1L\int_0^{2L}f(x)\sin\dfrac{n\pi x}L\,\mathrm dx$
$\displaystyle b_n=\frac2\pi\int_0^\pi f(x)\sin2nx\,\mathrm dx$

You should end up with

$a_0=0$
$a_n=0$
(both due to the fact that $f(x)$ is odd)
$b_n=\dfrac1{3n}\left(2-\cos\dfrac{2n\pi}3-\cos\dfrac{4n\pi}3\right)$

Now the problem is that this expansion does not match the given one. As a matter of fact, since $f(x)$ is odd, there is no cosine series. So I'm starting to think this question is missing some initial details.

One possibility is that you're actually supposed to use the even extension of $f(x)$ , which is to say we're actually considering the function

$\varphi(x)=\begin{cases}\frac\pi3&\text{for }|x|\le\frac\pi3\\0&\text{for }\frac\pi3$

and enforcing a period of $2L=2\pi$ . Now, you should find that

$\varphi(x)\sim\dfrac2{\sqrt3}\left(\cos x-\dfrac{\cos5x}5+\dfrac{\cos7x}7-\dfrac{\cos11x}{11}+\cdots\right)$

The value of the sum can then be verified by choosing $x=0$ , which gives

$\varphi(0)=\dfrac\pi3=\dfrac2{\sqrt3}\left(1-\dfrac15+\dfrac17-\dfrac1{11}+\cdots\right)$
$\implies\dfrac\pi{2\sqrt3}=1-\dfrac15+\dfrac17-\dfrac1{11}+\cdots$

as required.

5 0

3 years ago

Raise g to the 7th power, multiply the result by 4, then subtract f from what you have

WINSTONCH [101]

Answer:

f - 4(g^7)

It's simple algebraic operations!

7 0

2 years ago

A rectangle is 7 feet long by 5 feet wide. If 3 feet are removed from the length of the rectangle, what would be the area, in sq

katrin [286]

The answer to your question would be 25 sq ft

6 0

3 years ago

Deacon had 12 1/3 ounces of juice, but he drank 3 2/3 ounces. How much juice is left?

alexandr1967 [171]

You need to know:

$a \frac{b}{c} = a + \frac{b}{c} = \frac{(a*c) + b}{c}$

Be careful though:

$a \frac{b}{c} ≠ a(\frac{b}{c})$

Using this principle, we can say:
12 1/3 = 37/3
3 2/3 = 11/3
Quantity of juice left = Initial quantity - Quantity drunk
So:
Quantity of juice left = 37/3 - 11/3 = 26/3

There will be 26/3 ounces of juice remaining after 3 2/3 are drunk from the total of 12 1/3 ounces that Deacon had initially.

8 0

3 years ago