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
Answer:
Step-by-step explanation:
Given the equation
Use distributive property:
Use commutative property to rewrite the equation:
Add 10 th both sides:
Subtract 
Divide by 13:
( 1 / 4 ) * 30000 =7500 words in 1 / 6 of an hour ;
2 * 7500 words in 2 * ( 1 / 6 ) of an hour => 15000 in 1 / 3 of an hour ;
2 * 15000 words in 2 / 3 of an hour => 30000 words in 40 minutes ;
Answer:
The is answer is the last one.
Step-by-step explanation:
I just took the test
Answer:
3hours and 12.5 minutes
Step-by-step explanation:
45/6=7.5x25=187.5/60=3hours and 12.5 minutes
