Answer:
t = 4 seconds
Step-by-step explanation:
The height of the projectile after it is launched is given by the function :
![h(t)=-16t^2+32t+128](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%2B32t%2B128)
t is time in seconds
We need to find after how many seconds will the projectile land back on the ground. When it land, h(t)=0
So,
![-16t^2+32t+128=0](https://tex.z-dn.net/?f=-16t%5E2%2B32t%2B128%3D0)
The above is a quadratic equation. It can be solved by the formula as follows :
![t=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
Here, a = -16, b = 32 and c = 128
![t=\dfrac{-32\pm \sqrt{(32)^2-4\times (-16)(128)} }{2\times (-16)}\\\\t=\dfrac{-32+ \sqrt{(32)^2-4\times (-16)(128)} }{2\times (-16)}, \dfrac{-32\- \sqrt{(32)^2-4\times (-16)(128)} }{2\times (-16)}\\\\t=-2\ s\ \text{and}\ 4\ s](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B-32%5Cpm%20%5Csqrt%7B%2832%29%5E2-4%5Ctimes%20%28-16%29%28128%29%7D%20%7D%7B2%5Ctimes%20%28-16%29%7D%5C%5C%5C%5Ct%3D%5Cdfrac%7B-32%2B%20%5Csqrt%7B%2832%29%5E2-4%5Ctimes%20%28-16%29%28128%29%7D%20%7D%7B2%5Ctimes%20%28-16%29%7D%2C%20%5Cdfrac%7B-32%5C-%20%5Csqrt%7B%2832%29%5E2-4%5Ctimes%20%28-16%29%28128%29%7D%20%7D%7B2%5Ctimes%20%28-16%29%7D%5C%5C%5C%5Ct%3D-2%5C%20s%5C%20%5Ctext%7Band%7D%5C%204%5C%20s)
Neglecting negative value, the projectile will land after 4 seconds.
Answer:
2
Step-by-step explanation:
Let's solve the given system of equations.
<u>Given system</u>
x +3y= 10 ----(1)
-2x -2y= 4 ----(2)
From (2):
-2(x +y)= 4
Dividing both sides by -2:
x +y= -2 ----(2)
Thus, options 3 and 4 are incorrect as x +y≠ -2.
(1) -(2):
(x +3y) -(x +y)= 10 -(-2)
Expand:
x +3y -x -y= 10 +2
2y= 12
Divide both sides by 2:
y= 12 ÷2
y= 6
Substitute y= 6 into (2):
x +6= -2
x= -6 -2
x= -8
Options (1) and (2) differs only by the value of the expression of -x +y. Thus, let's find its value in the given system of equations.
-x +y
= -(-8) +6
= 8 +6
= 14
Thus, option 2 is the correct option.
5p+10p+(10p-16)
5p times two is 10p and since Ching baked 16 fewer it is 10p-16
Answer:
I aint never seen two pretty best friends, its always one of em gotta be ugly
Step-by-step explanation: