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olga_2 [115]
3 years ago
8

Use the equation m Subscript PQ Baseline equals StartFraction f left parenthesis x 1 plus h right parenthesis minus f left paren

thesis x 1 right parenthesis Over h EndFraction mPQ= fx1+hâfx1 h to calculate the slope of a line tangent to the curve of the function y equals f left parenthesis x right parenthesis equals 2 x squared y=f(x)=2x2 at the point Upper P left parenthesis x 1 comma y 1 right parenthesis equals Upper P left parenthesis 3 comma 18 right parenthesis Px1,y1=P(3,18).

Mathematics
1 answer:
babunello [35]3 years ago
3 0

Answer:

  m = 12

Step-by-step explanation:

For f(x) = 2x² you want to find the slope m using ...

  m = (f(x+h) -f(x))/h

at x=3.

Filling in the function definition and its arguments, we have ...

  m = (2(x+h)² -2x²)/h = (2x² +4hx +2h² -2x²)/h = 4x +2h

The value of this as h goes to zero is ...

  m = 4x

At x=3, the slope is ...

  m = 4·3 = 12

_____

The attached graph shows a numerical estimate of the slope (f'(3)=12) and the line with that slope through the point P(3, 18). The line certainly appears to be tangent to the curve at that point.

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The ratio of boys to girls is 5:3 there are 80 more boys than girls how many girls are there
shtirl [24]

Answer: 120

<u>Step-by-step explanation:</u>

              Ratio      Quantity

Boys:        5           80 + x                  

Girls:         3              x

                 \dfrac{5}{3}=\dfrac{80+x}{x}\\\\\\5x=3(80+x)\\\\5x=240+3x\\\\2x=240\\\\x=120

         

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Determine whether the system of equations below has one solution, infinitely many
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The points A, B and C have position vectors OA = 6,2, OB = 3,4 and OC = 12, -2 respectively.
kari74 [83]

Answer:(a) BA = (-3,2)   (b) BC = (-9,6)

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William has a regular hexagon with sides that are 2 units each. How many equilateral triangles with 1- unit sides can be put tog
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In a regular hexagon, each side is contained in a separate equilateral triangle with side of 2-units.  That makes six equilateral triangles with side 2-units.
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