Which graph represents the solution set of the compound inequality below? x + 3 < (4x – 12) < 20
2 answers:
Answer:
5<x<8
Step-by-step explanation:
x + 3 < (4x – 12) < 20
Solve the inequality
x + 3 < 4x – 12 < 20
We break the inequality
x+3<4x-12 and 4x-12<20
solve it separately
x+3<4x-12
subtract 4x on both sides
-3x +3< -12
subtract 3 on both sides
-3x < -15
divide by -3 on both sides
x> 5
4x-12<20
add 12 on both sides
4x <32
divide by 4
x<8
x>5 and x<8
so x lies between 5 and 8, 5<x<8
the graph is attached below
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Answer:
a) The height of the small object 3 seconds after being launched is 2304 feet.
b) The small object ascends 128 feet between 5 seconds and 7 seconds.
c) The object will take 6 and 10 seconds after launch to reach a height of 2640 feet.
d) The object will take 21 seconds to hit the ground.
Step-by-step explanation:
The correct formula for the height of the small object is:
(1)
Where:
- Height above the ground, measured in feet.
- Time, measured in seconds.
a) The height of the small object at given time is found by evaluating the function:
The height of the small object 3 seconds after being launched is 2304 feet.
b) First, we evaluate the function at and
:
We notice that the small object ascends in the given interval.
The small object ascends 128 feet between 5 seconds and 7 seconds.
c) If we know that , then (1) is reduced into this second-order polynomial:
(2)
All roots of the resulting equation come from the Quadratic Formula:
and
The object will take 6 and 10 seconds after launch to reach a height of 2640 feet.
d) If we know that , then (1) is reduced into this second-order polynomial:
(3)
All roots of the resulting equation come from the Quadratic Formula:
and
Just the first root offers a solution that is physically reasonable.
The object will take 21 seconds to hit the ground.