What numbers have an absolute value of 2 1/2
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 )
Answer:
.
Step-by-step explanation:
Let and
denote the two endpoints.
The formula for the midpoint of these two points would be:
.
(Similar to taking the average of each coordinate.)
In this question, it is given that whereas
. Substitute these two values into the expression for the coordinate of the midpoint:
-coordinate of the midpoint:
.
-coordinate of the midpoint:
.
Solve these two equations for and
:
whereas
.
Hence, the coordinate of the other point would be .