The average rate of change of h(x) in the closed interval [ a, b ] is
Here [a, b ] = [ - 2, 2 ], thus
f(b) = f(2) = × 2³ - 2² = 1 - 4 = - 3
f(a) = × (- 2)³ - (- 2)² = - 1 - 4 = - 5
average rate of change = = =
Answer:
a
Step-by-step explanation:
The y intercept is 2, because that is the value of y when it crosses the y axis.
Since the line is pointing down, it has a negative slope, and since the y value goes down 2 for every 3 x values, the slope is -2/3. You should always right the slope in rise/run form, or change in y/change in x.
Finally, write the equation in the form of y=mx+b, where m is the slope and b is the y intercept. This means the equation of the line is y=-2/3x+2.
The length of the rope in this case becomes the radius of the circle that the goat is able to graze. The area of the circle is calculated through the equation,
A = πr²
Substituting,
A = π(5m)² = 78.54 m²
Thus, the area that the goat is able to graze is equal to 78.54 m².
