1. let k(x)=-(x + 1)^2+11. find the average rate of change of k(x) between x=-2 and x = 4.\n2. the…

1. let k(x)=-(x + 1)^2+11. find the average rate of change of k(x) between x=-2 and x = 4.\n2. the temperature of a mug of hot chocolate, t minutes after it is prepared is given by the function h(t) where h is measured in degrees fahrenheit. selected values of h(t) are given below.\n|t|0|2|5|10|13|20|\n|h(t)|170|137|107|83|77|72|\nfind the average rate of change of the temperature of the hot chocolate between t = 0 and t = 20. use proper units in your answer.\n3. the graph of y = h(x) is shown. find the average rate of change of h on -3,2.

1. let k(x)=-(x + 1)^2+11. find the average rate of change of k(x) between x=-2 and x = 4.\n2. the temperature of a mug of hot chocolate, t minutes after it is prepared is given by the function h(t) where h is measured in degrees fahrenheit. selected values of h(t) are given below.\n|t|0|2|5|10|13|20|\n|h(t)|170|137|107|83|77|72|\nfind the average rate of change of the temperature of the hot chocolate between t = 0 and t = 20. use proper units in your answer.\n3. the graph of y = h(x) is shown. find the average rate of change of h on -3,2.

Answer

1.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = k(x)$ over the interval $[a,b]$ is $\frac{k(b)-k(a)}{b - a}$. Here, $a=-2$, $b = 4$, and $k(x)=-(x + 1)^2+11$.

Step2: Calculate $k(-2)$

Substitute $x=-2$ into $k(x)$: $k(-2)=-(-2 + 1)^2+11=-(-1)^2+11=-1 + 11=10$.

Step3: Calculate $k(4)$

Substitute $x = 4$ into $k(x)$: $k(4)=-(4 + 1)^2+11=-25 + 11=-14$.

Step4: Calculate the average rate of change

$\frac{k(4)-k(-2)}{4-(-2)}=\frac{-14 - 10}{4 + 2}=\frac{-24}{6}=-4$.

2.

Explanation:

Step1: Recall average - rate - of change formula

The average rate of change of a function $H(t)$ over the interval $[a,b]$ is $\frac{H(b)-H(a)}{b - a}$. Here, $a = 0$, $b = 20$, $H(0)=170$, and $H(20)=72$.

Step2: Calculate the average rate of change

$\frac{H(20)-H(0)}{20-0}=\frac{72-170}{20}=\frac{-98}{20}=-4.9$ degrees Fahrenheit per minute.

3.

Explanation:

Step1: Recall average - rate - of change formula

The average rate of change of a function $y=h(x)$ over the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a=-3$, $b = 2$, $h(-3)=-2.4$, and $h(2)=-5.4$.

Step2: Calculate the average rate of change

$\frac{h(2)-h(-3)}{2-(-3)}=\frac{-5.4-(-2.4)}{2 + 3}=\frac{-5.4 + 2.4}{5}=\frac{-3}{5}=-0.6$.

Answer:

  1. -4
  2. -4.9 degrees Fahrenheit per minute
  3. -0.6