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3 years ago

A separable differential equation is a first-order differential equation that can be algebraically manipulated to look like:

1 answer:

iogann1982 [59]3 years ago

4 0

<span>A separable differential equation is a first-order differential equation that can be algebraically manipulated to look like:

A) f(y)dy = g(x)dx

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Larry has 9 yards of fabric. He will use 2 yards to make each vest. How many vests

elena-14-01-66 [18.8K]

Answer:

4 vests

Step-by-step explanation:

Larry has 9 yards of fabric, in which 2 are needed to make a vest.

Divide 9 with 2: 9/2 = 4.5

However, note that you cannot have half a vest, so you must round down.

4.5 becomes 4.

4 vests is the maximum Larry can make with 9 yards of fabric.

8 0

3 years ago

Read 2 more answers

7x-2y=37 4x+y=19 soliving system by elimation

Maru [420]

Answer:

x=5 y=-1

Step-by-step explanation:

7x-2y=37

[2(4x+y=19)]=

8x+2y=38

---------------------

15x/15=75/15

x=5

[4(5)+y=19]

y=-1

5 0

3 years ago

chegg Y=4X−2 XX has a PDF of f_X(x)=\begin{cases} 3e^{-3x} & 0 \leq x \\ 0 & \text{otherwise}\end{cases}f X (x)={ 3e −

Licemer1 [7]

$\Bbb E[Y^2] = \Bbb E[(4X - 2)^2]$

so by definition of expectation,

$\Bbb E[Y^2] = \displaystyle \int_{-\infty}^\infty (4x-2)^2 f_X(x) \, dx = \int_0^\infty 3(4x-2)^2 e^{-3x} \, dx$

Integrate by parts (twice).

$\displaystyle \int_a^b u\,dv = uv\bigg|_a^b - \int_a^b v\,du$

First, let

$u = (4x-2)^2 \implies du = 8(4x-2)\,dx \\\\ dv = 3e^{-3x} \, dx \implies v = -e^{-3x}$

so that

$\displaystyle \Bbb E[Y^2] = -(4x-2)^2 e^{-3x} \bigg|_{x=0}^{x\to\infty} + 8 \int_0^\infty (4x-2) e^{-3x} \, dx \\\\ ~~~~ = 4 + 8 \int_0^\infty (4x-2) e^{-3x} \, dx$

Next,

$u = 4x-2 \implies du = 4\,dx \\\\ dv = e^{-3x} \, dx \implies v = -\dfrac13 e^{-3x}$

so that

$\displaystyle \Bbb E[Y^2] = 4 + 8 \left(-\frac13 (4x-2) e^{-3x} \bigg|_{x=0}^{x\to\infty} + \frac43 \int_0^\infty e^{-3x} \, dx\right) \\\\ ~~~~ = 4 + 8 \left(-\frac23 - \frac49 e^{-3x}\bigg|_{x=0}^{x\to\infty}\right) \\\\ ~~~~ = 4 - \frac{16}3 + \frac{32}9 = \boxed{\frac{20}9}$