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3 years ago

Which of the following equations represents a line that is perpendicular to

Mathematics

1 answer:

Andreyy893 years ago

8 0

Answer:

$\large\boxed{y=\dfrac{1}{2}x}$

Step-by-step explanation:

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

$\text{We have the equation:}\ y=-2x+4\to m_1=-2.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-2}=\dfrac{1}{2}.\\\\\text{We have the equation:}\ y=\dfrac{1}{2}x+b.\\\\\text{Put the coordinate of the point (4, 2) to the equation:}\\\\2=\dfrac{1}{2}(4)+b\\\\2=2+b\qquad\text{subtract 2 from both sides}\\\\0=b\to b=0.\\\\\text{Finally:}\\\\y=\dfrac{1}{2}x$

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If f(x)f(x) is an exponential function where f(1.5)=5f(1.5)=5 and f(7.5)=79f(7.5)=79, then find the value of f(3)f(3), to the ne

stiv31 [10]

Answer: $7.93$

Step-by-step explanation:

Given

$f(x)$ is an exponential function. Suppose $f(x)$ is $ae^{bx}$

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$\Rightarrow 5=ae^{1.5b}\\\Rightarrow \ln 5=\ln a-1.5b\quad \ldots(i)$

Similarly,

$\Rightarrow 79=ae^{7.5b}\\\Rightarrow \ln(79)=\ln a+7.5b\quad \ldots(ii)$

Subtract (i) and (ii)

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This said, your formula is not set up correctly: the linear speed can be found with the formula:
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Substituting this into the one above, you find the correct formula:
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The problem gives you directly Δα, which is 1/3 rad, because does not say at what angle the point started moving and at what angle it stopped.
Similarly, for the time you have Δt, which is 20 s.

Therefore, plugging in the numbers you get:
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