The average rate of change (AROC) of a function f(x) on an interval [a, b] is equal to the slope of the secant line to the graph of f(x) that passes through (a, f(a)) and (b, f(b)), a.k.a. the difference quotient given by
![f_{\mathrm{AROC}[a,b]} = \dfrac{f(b)-f(a)}{b-a}](https://tex.z-dn.net/?f=f_%7B%5Cmathrm%7BAROC%7D%5Ba%2Cb%5D%7D%20%3D%20%5Cdfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D)
So for f(x) = x² on [1, 5], the AROC of f is
![f_{\mathrm{AROC}[1,5]} = \dfrac{5^2-1^2}{5-1} = \dfrac{24}4 = \boxed{6}](https://tex.z-dn.net/?f=f_%7B%5Cmathrm%7BAROC%7D%5B1%2C5%5D%7D%20%3D%20%5Cdfrac%7B5%5E2-1%5E2%7D%7B5-1%7D%20%3D%20%5Cdfrac%7B24%7D4%20%3D%20%5Cboxed%7B6%7D)
Answer:
x>3, on a number line, first draw a circle over the number , if the sign has equal to (≥ or ≤), fill in the circle. If the sign does not have equal to (> or <), leave the circle unfilled in.
Step-by-step explanation:
For this case we have the following function:
By the time the stone is thrown, x = 0.
We must evaluate this value of x in the function.
We have then:
Answer:
The height of the stone at the time is thrown is given by:
h (0) = 15 meters
Use Pythagorus theorem:
a²+b²=c²
(12)²+(16)²=c²
400=c²
√400=c
20=c
Therefore, the hypotenuse would be 20 ft.
Hope I helped :)
Answer:
Oh my gosh!
Step-by-step explanation:
Good job, nice!
