Answer:
Option B. 1.8 seconds
Step-by-step explanation:
h=-16t^2+56t+1
This is a quadratic equation, and its graph is a parabola
h=at^2+bt+c; a=-16, b=56, c=1
Like a=-16<0 the parabola opens downward, and it has a maximum value (height) at the vertex, at the abscissa:
![t=-\frac{b}{2a}](https://tex.z-dn.net/?f=t%3D-%5Cfrac%7Bb%7D%7B2a%7D)
Replacing the known values:
![t=-\frac{56}{2(-16)}\\ t=-\frac{56}{(-32)}\\ t= 1.75](https://tex.z-dn.net/?f=t%3D-%5Cfrac%7B56%7D%7B2%28-16%29%7D%5C%5C%20t%3D-%5Cfrac%7B56%7D%7B%28-32%29%7D%5C%5C%20t%3D%201.75)
Approximately 1.8 seconds.
Answer: It takes approximately 1.8 seconds the airplane to reach its maximum height.
Answer:
2.5e+16
Step-by-step explanation:
Hi there!
To solve this problem, we should simplify.
0.06x - 0.18 = 0.12
First, we should add 0.18 to both sides:
0.06x = 0.12 + 0.18
0.06x = 0.3
Now, we can convert 0.06 into a fraction and multiply both sides of the equation by its receprical to isolate x:
0.06 = 6/100
6/100 × 100/6 = 1
0.3 × 100/6 = 30/6
x = 30/6
x = 15/3
x = 5
So, x is 5.
Hope this helps!
<h3>
Answer: -6</h3>
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Explanation:
Plug in x = 1
f(x) = 17-x^2
f(1) = 17-1^2
f(1) = 17-1
f(1) = 16
Repeat for x = 5 to find that f(5) = -8
Now we'll use the formula below to find the average rate of change from x = a to x = b.
![m = \frac{f(b)-f(a)}{b-a}\\\\m = \frac{f(5)-f(1)}{5-1}\\\\m = \frac{-8-16}{4}\\\\m = \frac{-24}{4}\\\\m = -6\\\\](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7Bf%285%29-f%281%29%7D%7B5-1%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B-8-16%7D%7B4%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B-24%7D%7B4%7D%5C%5C%5C%5Cm%20%3D%20-6%5C%5C%5C%5C)
The average rate of change is -6
The formula is basically the slope formula, more or less. So that's why I used 'm' to represent the average rate of change.
The average rate of change on the interval [1,5] is the same as finding the slope through the lines (1, 16) and (5, -8)