Suppose a toy rocket is launched vertically upward from the top of a building with an initial velocity of 128 feet per second. i
f air resistance is ignored, the rocket's h height after t seconds is given by the equation h = −16t2 +128t + 100. How long will the rocket's flight last? (to the nearest tenth of a second) A) 7.6 seconds B) 7.9 seconds C) 8.7 seconds D) 9.3 seconds
1 answer:
Answer:
Option C)
t = 8.7 s
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.
Please see the attached image below, to find more information about the graph
The projectile formula is
h(t) = a*t^2 + v*t + h0
Where,
v = initial vertical velocity of the rocket in feet per second
h0 = initial height of the rocket in feet
h(t) = −16t^2 +128t + 100
If we look at the graph, we can find the point in which the height becomes zero. The value for t at this point will represent the rocket's fight duration
For this problem,
t = 8.717 s
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Given this equation:
That represents t<span>he height of a tree in feet over (x) years. Let's analyze each statement according to figure 1 that shows the graph of this equation.
</span>
The tree's maximum height is limited to 30 ft.
As shown in figure below, the tree is not limited, so this statement is false.
<span>The tree is initially 2 ft tall
The tree was planted in x = 0, so evaluating the function for this value, we have:
</span>
<span>
<span>So, the tree is initially
tall.
</span>
Therefore this statement is false.
</span>Between the 5th and 7th years, the tree grows approximately 7 ft.
<span>
if x = 5 then:
</span>
<span>
</span>if x = 7 then:
So, between the 5th and 7th years the height of the tree remains constant
:
This is also a false statement.
<span>After growing 15 ft, the tree's rate of growth decreases.</span>
It is reasonable to think that the height of this tree finally will be 301ft. Why? well, if x grows without bound, then the term
approaches zero.
Therefore this statement is also false.
Conclusion: After being planted this tree won't grow.
That represents t<span>he height of a tree in feet over (x) years. Let's analyze each statement according to figure 1 that shows the graph of this equation.
</span>
The tree's maximum height is limited to 30 ft.
As shown in figure below, the tree is not limited, so this statement is false.
<span>The tree is initially 2 ft tall
The tree was planted in x = 0, so evaluating the function for this value, we have:
</span>
<span>
<span>So, the tree is initially
</span>
Therefore this statement is false.
</span>Between the 5th and 7th years, the tree grows approximately 7 ft.
<span>
if x = 5 then:
</span>
</span>if x = 7 then:
So, between the 5th and 7th years the height of the tree remains constant
:
This is also a false statement.
<span>After growing 15 ft, the tree's rate of growth decreases.</span>
It is reasonable to think that the height of this tree finally will be 301ft. Why? well, if x grows without bound, then the term
Therefore this statement is also false.
Conclusion: After being planted this tree won't grow.
Answer:
m = 3
Step-by-step explanation:
For slope intercept of (y+4)=3(x+2) use the slope-intercept form
y = m x + b to find the slope m.
