13 people are in a race. If there are no ties , in how many ways can the first 3 places be awarded?
1 answer:
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Answer:
( , 8 )
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 10x - 2 ← is in slope- intercept form
with slope m = 10
Parallel lines have equal slopes
then the tangent to the parabola with a slope of 10 is required.
the slope of the tangent at any point on the parabola is
differentiate each term using the power rule
(a
) = na
, then
= 6x + 2
equating this to 10 gives
6x + 2 = 10 ( subtract 2 from both sides )
6x = 8 ( divide both sides by 6 )
x = =
substitute this value into the equation of the parabola for corresponding y- coordinate.
y = 3( )² + 2
= (3 × ) + 2
= +
=
= 8
the point on the parabola with tangent parallel to y = 10x - 2 is ( , 8 )
This is a more difficult one to explain. Let's start with the line to the right. It has a slope (m) of = -1 and a y-intercept of +3 (continue the line to see where it crosses the y-axis). So, the equation of that line is: y = -x + 3 when x ≥ 2. This can also be written as y = 3 - x when x ≥ 2. The only option that has that equation is A.
Answer: A