Y=-12x+6. I used the slope intercept form y=mx+b to solve.
Answer:
![A(x) = 243](https://tex.z-dn.net/?f=A%28x%29%20%3D%20243)
Step-by-step explanation:
Given
![f(x) = x^3 - 9x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E3%20-%209x)
![Interval: (12,6)](https://tex.z-dn.net/?f=Interval%3A%20%2812%2C6%29)
Required
Determine the average rate of change
Average rate is calculated as thus;
![A(x) = \frac{f(b) - f(a)}{b - a}](https://tex.z-dn.net/?f=A%28x%29%20%3D%20%5Cfrac%7Bf%28b%29%20-%20f%28a%29%7D%7Bb%20-%20a%7D)
<em>In this case; b = 12 and a = 6</em>
Calculating f(12)
![f(12) = 12^3 - 9 * 12](https://tex.z-dn.net/?f=f%2812%29%20%3D%2012%5E3%20-%209%20%2A%2012)
![f(12) = 1728 - 108](https://tex.z-dn.net/?f=f%2812%29%20%3D%201728%20-%20108)
![f(12) = 1620](https://tex.z-dn.net/?f=f%2812%29%20%3D%201620)
Calculating f(6)
![f(6) = 6^3 - 9 * 6](https://tex.z-dn.net/?f=f%286%29%20%3D%206%5E3%20-%209%20%2A%206)
![f(6) = 216 - 54](https://tex.z-dn.net/?f=f%286%29%20%3D%20216%20-%2054)
![f(6) = 162](https://tex.z-dn.net/?f=f%286%29%20%3D%20162)
Substitute 12 for b and 6 for a in ![A(x) = \frac{f(b) - f(a)}{b - a}](https://tex.z-dn.net/?f=A%28x%29%20%3D%20%5Cfrac%7Bf%28b%29%20-%20f%28a%29%7D%7Bb%20-%20a%7D)
![A(x) = \frac{f(12) - f(6)}{12 - 6}](https://tex.z-dn.net/?f=A%28x%29%20%3D%20%5Cfrac%7Bf%2812%29%20-%20f%286%29%7D%7B12%20-%206%7D)
Substitute values for f(6) and f(12)
![A(x) = \frac{1620 - 162}{12 - 6}](https://tex.z-dn.net/?f=A%28x%29%20%3D%20%5Cfrac%7B1620%20-%20162%7D%7B12%20-%206%7D)
![A(x) = \frac{1458}{ 6}](https://tex.z-dn.net/?f=A%28x%29%20%3D%20%5Cfrac%7B1458%7D%7B%206%7D)
![A(x) = 243](https://tex.z-dn.net/?f=A%28x%29%20%3D%20243)
Answer:
![v = u + at \\ v = 3 + (1.5 \times 7) \\ v = 3 +10.5 \\ \boxed{v = 13.5 \: m {s}^{ - 1}}](https://tex.z-dn.net/?f=v%20%3D%20u%20%2B%20at%20%5C%5C%20v%20%3D%203%20%2B%20%281.5%20%5Ctimes%207%29%20%5C%5C%20v%20%3D%203%20%2B10.5%20%5C%5C%20%20%5Cboxed%7Bv%20%3D%2013.5%20%5C%3A%20m%20%7Bs%7D%5E%7B%20-%201%7D%7D%20)
<h3>13.5 m/s is the right answer.</h3>
Answer:
Step-by-step explanation:
y = 3x - 5
y = 1/3x + 3
3x - 5 = 1/3x + 3....multiply everything by 3 to get rid of the fraction
9x - 15 = x + 9
9x - x = 9 + 15
8x = 24
x = 24/8
x = 3
y = 3x - 5
y = 3(3) - 5
y = 9 - 5
y = 4
solution is : x = 3 and y = 4...or (3,4) <==
Answer:
24 people borrowed the books on Friday
Step-by-step explanation:
Every day, the number of books is being subtracted by 2.
56 - Monday (-8)
48 - Tuesday (-8)
40 - Wednesday (-8)
32 - Thursday (-8)
24- Friday