It would be 32 for your answer
Answer:
After 10 seconds
Step-by-step explanation:
In this problem, the height of the object after t seconds is described by the function
![h(t)=-16t^2+144t+160](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%2B144t%2B160)
where
160 ft is the initial height of the object at t = 0
+144 ft/s is the initial velocity
is the acceleration due to gravity (downward)
Here we want to find the time at which the object hits the ground, so the time t at which
![h(t)=0](https://tex.z-dn.net/?f=h%28t%29%3D0)
Therefore we can write
![-16t^2+144t+160 =0](https://tex.z-dn.net/?f=-16t%5E2%2B144t%2B160%20%3D0)
Simplifying (dividing each term by 16), we get
![-t^2+9t+10=0](https://tex.z-dn.net/?f=-t%5E2%2B9t%2B10%3D0)
This is a second-order equation in the form
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
Which has solutions given by the formula
(2)
Here we have:
a = -1
b = 9
c = 10
Substituting into (2) we find the solutions:
![t_{1,2}=\frac{-9\pm \sqrt{9^2-4(-1)(10)}}{2(-1)}=\frac{-9 \pm 11}{-2}](https://tex.z-dn.net/?f=t_%7B1%2C2%7D%3D%5Cfrac%7B-9%5Cpm%20%5Csqrt%7B9%5E2-4%28-1%29%2810%29%7D%7D%7B2%28-1%29%7D%3D%5Cfrac%7B-9%20%5Cpm%2011%7D%7B-2%7D)
Which gives:
![t_1=10 s\\t_2 =-1 s](https://tex.z-dn.net/?f=t_1%3D10%20s%5C%5Ct_2%20%3D-1%20s)
Since time cannot be negative, the only solution is
t = 10 seconds
(x - 2 < 5) ∩ (x + 7 > 6)
Let's resolve each one
x - 2 < 5
x < 5 + 2
x < 7
x + 7 > 6
x > 6 - 7
x > -1
So we have 2 conditions: x > -1 and x < 7 plus, we need the values that's equal in x < 7 and x > -1 because we have an intersection
S = {x e R / -1 < x < 7}
Let x represent the smallest angle. Then the largest is 3x, and the remaining angle is 180-4x. The problem statement tells us
.. 3x > 180 -4x > x
Adding 4x gives us
.. 7x > 180 > 5x
or
.. 36 > x > 180/7 = 25 5/7
The angles, smallest to largest, are
.. x, 4(45 -x), 3x
where 25 5/7 < x < 36
The angles could be, for example, any of ...
.. 26°, 76°, 78°
.. 30°, 60°, 90°
.. 32°, 52°, 96°
.. 35°, 40°, 105°
and an infinite number of other possibilities.