Solve the system using an equivalent system
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
For the given piecewise function,
Let the equation of the segment AB is,
y = ax + 7 where x < -2
Since a point (-2, 3) lies on the given line,
3 = a(-2) + 7
3 - 7 = -2a
a = 2
Therefore, f(x) = 2x + 7 when x < -2
For the segment BC,
f(x) = 3 where -2 ≤ x ≤ 2
For the segment CD,
f(x) = bx + 9
Since a point (2, 3) lies on this segment,
f(2) = 2b + 9 = 3
2b = 3 - 9
b = -3
Therefore, equation of segment CD will be,
f(x) = (-3)x + 9 where x > 2
Answer:
Step-by-step explanation:
Given that a rectangle is inscribed with its base on the x-axis and its upper corners on the parabola
the parabola is open down with vertex at (0,2)
We can find that the rectangle also will be symmetrical about y axis.
Let the vertices on x axis by (p,0) and (-p,0)
Then other two vertices would be (p,2-p^2) (-p,2-p^2) because the vertices lie on the parabola and satisfy the parabola equation
Now width =
Area = l*w =
Use derivative test
I derivative =
II derivative =
Equate I derivative to 0 and consider positive value only since we want maximum
p =
Thus width=
Length =
Width =