At noon, Trevor and Kim start running from the same point. Trevor runs east at a speed of 5 mph and Kim runs west at a speed of
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Answer:
(a, b, c) = (-0.425595, 11.7321, 2.16667)
f(x) = -0.425595x² +11.7321x +2.16667
f(1) ≈ 13.5
Step-by-step explanation:
A suitable tool makes short work of this. Most spreadsheets and graphing calculators will do quadratic regression. All you have to do is enter the data and make use of the appropriate built-in functions.
Desmos will do least-squares fitting of almost any function you want to use as a model. It tells you ...
a = -0.425595
b = 11.7321
c = 2.16667
so
f(x) = -0.425595x² +11.7321x +2.16667
and f(1) ≈ 13.5
_____
<em>Additional comment</em>
Note that a quadratic function doesn't model the data very well if you're trying to extrapolate to times outside the original domain.
Answer:
The x-intercept of CD is B(18/5,0). The point C(32,-71) lies on the line CD.
Step-by-step explanation:
the x-intercept of CD is[ A(3,0) B(18/5,0) C(9,0) D(45/2,0) ] . Point [ A(-52,117) B(-20,57) C(32,-71) D(-54,-128) ] lies on CD.
Given :
CD is perpendicular bisector of AB.
The coordinates of point A are (-3, 2) and the coordinates of point B are (7, 6).
C is the midpoint of AB.
The coordinates of C are (2,4).
Line AB has a slope of:
The product of slopes of two perpendicular lines is -1. Since the line CD is perpendicular to AB, therefore the slope of CD :
The point slope form of a line is given by:
The slope of line CD is and the line passing through the point (2,4), the equation of line CD can be written as:
The equation of CD is
In order to find the x-intercept, put y=0.
Therefore the x-intercept of CD is B(18/5,0).
Put x=-52 in eq(1).
Put x=-20 in eq(1).
Put x=32 in eq(1)
Put x=-54 in eq1).
Thus, only point (32,-71) satisfies the equation of CD. Therefore the point C(32,-71) lies on the line CD.