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Ivenika [448]
3 years ago
9

What is 50/400 simplified

Mathematics
2 answers:
tresset_1 [31]3 years ago
7 0
50/400 is 1/8 simplified
evablogger [386]3 years ago
5 0

Step-by-step explanation:

\frac{50}{400}  =  \frac{5}{40}  =  \frac{1}{8}  = 0.125

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Can someone check whether its correct or no? this is supposed to be the steps in integration by parts​
Gwar [14]

Answer:

\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}

Step-by-step explanation:

\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}

Given integral:

\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x

\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:

\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x

Using <u>integration by parts</u>:

\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)

\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}

Therefore:

\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}

\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:

\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)

\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}

\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}

Therefore:

\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x

\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:

\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}

Divide both sides by 2:

\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}

Rewrite in the same format as the given integral:

\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}

5 0
2 years ago
Find the distance between each pair of points
dolphi86 [110]

Answer: the correct answer is 20

Step-by-step explanation:

The formula for determining the distance between two points on a straight line is expressed as

Distance = √(x2 - x1)² + (y2 - y1)²

Where

x2 represents final value of x on the horizontal axis

x1 represents initial value of x on the horizontal axis.

y2 represents final value of y on the vertical axis.

y1 represents initial value of y on the vertical axis.

From the graph given,

x2 = - 7

x1 = 5

y2 = - 7

y1 = 9

Therefore,

Distance = √(- 7 - 5)² + (- 7 - 9)²

Distance = √(- 12²) + (- 16)²

= √(144 + 256) = √400

Distance = 20

5 0
3 years ago
Patients in a hospital are classified as surgical or medical. A record is kept of the number of times patients require nursing s
GREYUIT [131]

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Given:

N= 177\\\\a=46\\\\b=52\\\\c=36\\\\d=43

\to \chi _{1}^{2}=\frac{N(ad-bc)^{2}}{(a+c)(b+d)(a+b)(c+d)}

         =\frac{177((46\times 43)-(52 \times 36))^{2}}{(98)(79)(82)(95)}\\\\=\frac{177((1978)-(1872))^{2}}{60310180}\\\\=\frac{177(106)^{2}}{60310180}\\\\=\frac{177(11236)}{60310180}\\\\=\frac{1988772}{60310180}\\\\= 0.032976

P-value= CHIDIST(0.032976,1) = 0.86.

thus, the surgical-medical patients and Medicare are dependent.

5 0
2 years ago
If g(x) = x3 - 5 and h(x) = 2x - 2, then h(g(-2))= ?
mixas84 [53]
Please, write "x^3" for "the cube of x," not "x3."  "^" denotes exponentiation.

Then you have g(x) = x^3 - 5 and (I assume) h(x) = 2x - 2.

1)  evaluate g(x) at x = -2:  g(-2) = (-2)^3 - 5 = -8 - 5 = -13

2) let the input to h(x) be -13:  h(-13) = 2(-13) - 2 = -28 (answer)
4 0
3 years ago
Find the equation, in point-slope form, of the line that passes -3 and passes through the point (1,2). plz show your work.
Maslowich
Substitute the given values for the parameters in the point-slope form of the equation of a line. That form is
  y - k = m(x - h)
for point (h, k) and slope m.

You have (h, k) = (1, 2) and m=-3, so your equation is
  y - 2 = -3(x - 1)
4 0
3 years ago
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