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Sliva [168]
3 years ago
10

find the average rate of change from t=2 to t=5 for the velocity function v(t)=t^2-t+10. WILL GIVE THE BRAINLIEST ANSWER--EXPLAI

N!!
Mathematics
1 answer:
Elina [12.6K]3 years ago
8 0
Answer: The average rate of change is 6.
First, plug in each value of <em>t</em> into the function, v(t) to find there coordinate pairs.

v(2) = (2)^2 - (2) + 10
v(2) = 4 + 8
v(2) = 12

v(5) = (5)^2 - (5) + 10
v(5) = 25 + 5
v(5) = 30

You can write these values as coordinate pairs, like so: (2, 12) and (5, 30).
The formula for the average rate of change is A(x) =  \frac{f(x)-(f(a)}{x-a}. When you plug in the values from this particular case, the average rate of change formula becomes A(t) = \frac{30-12}{5-2}, or A(t)= \frac{18}{3}.

Looking at the equation, you can solve for the average rate of change between t = 2 and t = 5, which equals 6.
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A function f(x)=3x+12.
seraphim [82]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2822258

_______________


•  Function:   f(x) = 3x + 12.


A.  Finding the inverse of f.

The composition of f with its inverse results in the identity function:

(f o g)(x) = x

f[ g(x) ] = x

3 · g(x) + 12 = x

3 · g(x) = x – 12

              x – 12
g(x)  =  ⸺⸺
                 3

               x 
g(x)  =  ⸺  –  4    <———    this is the inverse of f.
               3

________


B.  Verifying that the composition of f and g gives us the identity function:

•  \mathsf{(f\circ g)(x)}

\mathsf{=f\big[g(x)\big]}\\\\\\ \mathsf{=3\cdot \left(\dfrac{x}{3}-4\right)+12}\\\\\\&#10;\mathsf{=\diagup\hspace{-7}3\cdot \dfrac{x}{\diagup\hspace{-7}3}-3\cdot 4+12}\\\\\\&#10;\mathsf{=x-12+12}\\\\&#10;\mathsf{=x\qquad\quad\checkmark}


and also

•  \mathsf{(g\circ f)(x)}

\mathsf{=g\big[f(x)\big]}\\\\\\ \mathsf{=\dfrac{f(x)}{3}-4}\\\\\\ \mathsf{=\dfrac{3x+12}{3}-4}\\\\\\&#10;\mathsf{=\dfrac{\diagup\hspace{-7}3\cdot (x+4)}{\diagup\hspace{-7}3}-4}\\\\\\&#10;\mathsf{=x+4-4}\\\\&#10;\mathsf{=x\qquad\quad\checkmark}

________


C.  Since f and g are inverse, then

f(g(– 2))

= (f o g)(– 2)

= – 2          <span>✔
</span>

•  Call h the compositon of f and g. So,

h(x) = (f o g)(x)

h(x) = x


As you can see above, there is no restriction for h. Therefore, the domain of h is R (all real numbers).


I hope this helps. =)

5 0
3 years ago
Please can you help me​
Zanzabum
A= 47
b=60
c=37
d=130
e=38
3 0
2 years ago
Read 2 more answers
What is 3.12 as a fraction
Vitek1552 [10]
3 3/25 is the answer..
7 0
2 years ago
Describe the continuity of the graphed function (please help)
oksian1 [2.3K]

Answer:

Step-by-step explanation:

c

6 0
3 years ago
2. In a random sample of 130 World Campus students, 92 were employed full-time.
liberstina [14]

Answer:


Step-by-step explanation:

Given that sample size is 130 >30.  Also by central limit theorem, we know that mean (here proportion) of all means of different samples would tend to become normal with mean = average of all means(here proportions)

Hence we can assume normality assumptions here.

Proportion sample given = 92/130 = 0.7077

The mean proportion of different samples for large sample size will follow normal with mean = sample proportion and std error = square root of p(1-p)/n

Hence mean proportion p= 0.7077

q = 1-p =0.2923

Std error = 0.0399

For 95% confidence interval we find that z critical for 95% two tailed is 1,.96

Hence margin of error = + or - 1.96(std error)

= 0.0782

Confidence interval = (p-margin of error, p+margin of error)

= (0.7077-0.0782,0.7077+0.0782)

=(0.6295, 0.7859)

We are 95% confident that average of sample proportions of different samples would lie within these values in the interval for large sample sizes.

7 0
3 years ago
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