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:
The answer is 20 hours
Step-by-step explanation:
20x60=1200
1200÷60=20
Answer:
The first number is 20, the second one is 11
Step-by-step explanation:
Let the first number be x and the second number be y
Since it says "9 is the difference between two numbers", the first equation will be x-y=9
It also says that "their sum is 31". That means the second equation will be x+y=31
here are the two equations:
x-y=9
x+y=31
You can solve this any way you like, but I'll show elimination
add the two equations
x-y=9
x+y=31
2x=40
divide by 2
x=20
Substitute 20 as x in one of the equations
20+y=31
subtract 20 from both sides
y=11
That means the two numbers are 20 and 11
Hope this helps!
Answer:
x = 20
Step-by-step explanation:
Answer:
tan = opposite / adjacent
Step-by-step explanation:
opposite is rhe height we have to find
adjacent is 2
angle is 40
so to find the height
adjacent x tan(angle)
2(tan40)
