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kirill115 [55]
2 years ago
8

Which of the following rational functions is graphed below?

Mathematics
1 answer:
Radda [10]2 years ago
3 0
The answer is B, f(x)=1/(x-6)
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52b - 43
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Find the slope of a line perpendicular to each given line
andre [41]

k:\ y=m_1x+b_1\\l:\ y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}

115)\ -x-y=3\ \ \ |+x\\-y=x+3\ \ \ |\cdot(_1)\\y=-x-3\to m_1=-1\to\boxed{m_2=-\dfrac{1}{-1}=1}\\\\116)\ 0=-4x-y+5\ \ \ |+y\\y=-4x+5\to m_1=-4\to\boxed{m_2=-\dfrac{1}{-4}=\dfrac{1}{4}}\\\\117)\ 6-2y=x\ \ \ \ |-6\\-2y=x-6\ \ \ \ |:(-2)\\y=-\dfrac{1}{2}x+3\to m_1=-\dfrac{1}{2}\to\boxed{m_2=-\dfrac{1}{-\frac{1}{2}}=2}\\\\118)\ 5y=25+4x\ \ \ \ |:5\\y=5+\dfrac{4}{5}x\to m_1=\dfrac{4}{5}\to\boxed{m_2=-\dfrac{1}{\frac{4}{5}}=-\dfrac{5}{4}}

119)\ -15x-9y=9\ \ \ \ |+15x\\-9y=15x+9\ \ \ \ |:(-9)\\y=-\dfrac{15}{9}x-1\\y=-\dfrac{5}{3}x-1\to m_1=-\dfrac{5}{3}\to\boxed{m_2=-\dfrac{1}{-\frac{5}{3}}=\dfrac{3}{5}}

8 0
3 years ago
Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = [inf
Alla [95]

f(t)=\begin{cases}-1&\text{for }0\le t

Write f(t) in terms of the unit step function u(t):

f(t)=-1(u(t)-u(t-1))+1u(t-1)=2u(t-1)-u(t)

where

u(t)=\begin{cases}1&\text{for }t\ge0\\0&\text{for }t

Then the Laplace transform of f(t), denoted F(s), is

F(s)=\displaystyle\int_0^\infty f(t)e^{-st}\,\mathrm dt

F(s)=\displaystyle2\int_1^\infty e^{-st}\,\mathrm dt-\int_0^\infty e^{-st}\,\mathrm dt

\implies F(s)=\dfrac{2e^{-s}}s-\dfrac1s=\dfrac{2e^{-s}-1}s

3 0
3 years ago
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