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 value of x is 155/79.
Step-by-step explanation:
13(6x -5 )-x= 13 -2(x +1)
78x - 65- x = 13 -2x -2
77x -65 = 11-2x
79x -65 =11
79x =76
x = 76/79 76/ 79 + 1/1 = 155/79
The answer to this question is 10 cm
In this question, you asked the height and given the volume of water(2400cm3), aquarium length(20cm), and aquarium width(12cm).
Then you need to divide the volume with the length and width. The equation would be:
Aquarium height= volume / length / width
Aquarium height= 2400 cm3 / 20cm / 12 cm = 10cm.
Answer:
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