The tangent line to <em>y</em> = <em>f(x)</em> at a point (<em>a</em>, <em>f(a)</em> ) has slope d<em>y</em>/d<em>x</em> at <em>x</em> = <em>a</em>. So first compute the derivative:
<em>y</em> = <em>x</em>² - 9<em>x</em> → d<em>y</em>/d<em>x</em> = 2<em>x</em> - 9
When <em>x</em> = 4, the function takes on a value of
<em>y</em> = 4² - 9•4 = -20
and the derivative is
d<em>y</em>/d<em>x</em> (4) = 2•4 - 9 = -1
Then use the point-slope formula to get the equation of the tangent line:
<em>y</em> - (-20) = -1 (<em>x</em> - 4)
<em>y</em> + 20 = -<em>x</em> + 4
<em>y</em> = -<em>x</em> - 24
The normal line is perpendicular to the tangent, so its slope is -1/(-1) = 1. It passes through the same point, so its equation is
<em>y</em> - (-20) = 1 (<em>x</em> - 4)
<em>y</em> + 20 = <em>x</em> - 4
<em>y</em> = <em>x</em> - 24
250 and - 1250
This is a geometric sequence with common ratio r = - 5
multiply each term by - 5 to obtain the next term
- 50 × - 5 = 250
250 × - 5 = - 1250
the sequence is - 2, 10, - 50, 250, - 1250
Answer:
a=he went back home
b=speed=240km/h
Step-by-step explanation:
ps: wouldn't mind brainliest
The measure of the angle m∠CBD that forms an adjacent angle is 35 degrees.
<h3>What are adjacent angles?</h3>
Adjacent angles are angles that have common side and vertex.
Therefore, the common vertex is at point B.
m∠CBD = m∠ABD - m∠ABC
Therefore,
m∠ABD = 75 degrees
m∠ABC = 40 degrees
Hence,
m∠CBD = 75 - 40
m∠CBD = 35 degrees
learn more on angles here; brainly.com/question/1592068
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