Type the correct answer in each box. Use numerals instead of words.
2 answers:
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Given:
Student ticket price = $7
A group of 4 students and 3 adults paid $64 in all for movie tickets.
To find:
Each of the adult ticket cost.
Solution:
Let x be the cost of each adult ticket.
Then, cost of 3 adult tickets = 3x.
Cost of 1 student ticket = $7
Cost of 4 student ticket = $7(4)
According to the question,
Divide both sides by 3.
Therefore, the cost of each adult ticket is $12.
The maximum height of the rocket is 43.89 feet
<h3>How to write the function</h3>The general function is given as:
h(t) = -16t^2 + vt + h
The initial velocity is
v = 53
So, we have:
h(t) = -16t^2 + 53t + h
The initial height is
h = 0
So, we have:
h(t) = -16t^2 + 53t
Hence, the function of the height is h(t) = -16t^2 + 53t
<h3>The maximum height of the rocket</h3>
In (a), we have:
h(t) = -16t^2 + 53t
Differentiate the function
h'(t) = -32t + 53
Set to 0
-32t + 53 = 0
This gives
-32t = -53
Divide by -32
t = 1.65625
Substitute t = 1.65625 in h(t) = -16t^2 + 53t
h(1.65625) = -16 * 1.65625^2 + 53 * 1.65625
Evaluate
h(1.65625) = 43.890625
Approximate
h(1.65625) = 43.89
Hence, the maximum height of the rocket is 43.89 feet
<h3>Time to hit the ground</h3>In (a), we have
h(t) = -16t^2 + 53t
Set to 0
-16t^2 + 53t = 0
Divide through by -t
16t - 53 = 0
Add 53 to both sides
16t = 53
Divide by 16
t = 3.3125
Hence, the time to hit the ground is 3.3125 seconds
<h3>The graph of the function h(t)</h3>See attachment for the graph of the function h(t)
Read more about height functions at:
#SPJ1
Answer:
1) For :
and
, 2) For
:
and
Step-by-step explanation:
The polynomial is a second-order polynomial of the form
. By direct comparison, we construct the following system of equations:
(1)
(2)
By (1) we know that there are a family of pairs such that the system of equations is satisfied. Let suppose that both and
are integers. We assume two arbitrary integers for
:
1)
2)