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:
1.7*10^3 greater
Step-by-step explanation:
So just divide the two numbers
3.4 * 10^5/ 2 * 10^3
Answer:
We know that, two quantities are proportional when they vary directly with each other.
i.e. quantities x and y are proportional when they have the relation y = kx, where k is any constant called constant of proportionality.
Since, the quantities are in relation y = kx.
So, for x = 0 we get that the value of y = 0.
As, the point ( 0,0 ) satisfies this relation i.e. it is a solution of y = kx.
Hence, in proportional relationship, the graph will pass through ( 0,0 ).
The answer is -10 because when u plug in -2 for x u get 4(-2)=-8 then -2+-8=-10
To solve for y, you need to separate it in one side and the other terms in the other side..... as follows:
<span>a(n+y)=10y+32a
an + ay = 10y + 32a
an - an + ay = 10y + 32a - an
ay = 10y + 32a - an
ay -10y = 32a - an
y (a-10) = (32 - n)a
y = {a(32-n)} / (a-10)
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