If f(x) = 6x +5 and g(x) = 2x – 7 find (fºg)(x)
1 answer:
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Part A) x-intercepts simply show that when the value of the function is zero. Vertex coordinates show that when the function obtains its maximum value. When x=50, function obtains its maximum value and it's 75. The function is increasing in the interval (0, 50) and decreasing in the interval (50, 100). In regard to the height and distance of the tunnel, these numbers show that decreasing and increasing intervals are symmetric. Each number from the intervals has its own pair in the corresponding interval and they are located in the same distance from the midpoint (50,75)
Part B) In order to calculate the average rate of change, we can first write the function. Using the information about the x-intercept and the vertex coordinates, we find that our function is
.
Plugging 15 and 35 in x, we can find the values of the function, i.e.
and 
.
Then, the average change is
Part B) In order to calculate the average rate of change, we can first write the function. Using the information about the x-intercept and the vertex coordinates, we find that our function is
Plugging 15 and 35 in x, we can find the values of the function, i.e.
Then, the average change is
The correct option is: B.
<u><em>Explanation</em></u>
<u>The general form of growth equation</u> is: , where A = final amount, P = initial amount, r = growth rate in decimal form and t = time duration
Here, the speed of the rocket at the beginning was 5,000 kilometers per hour and at the end will be 25,000 kilometers per hour. The speed increases at a rate of 4.3% per minute.
That means,
Now <u>plugging these values into the above equation</u>, we will get......
So, the equation that could be used to determine the time for the speed of the rocket to reach 25,000 kilometers per hour will be: