Answer:
9 hours
Step-by-step explanation:
Answer:
t = 0.293 s and 14.52 s
Step-by-step explanation:
The heights of the ball in feet is given by the equation as follows :
![S = -2.7t^2+40t+6.5](https://tex.z-dn.net/?f=S%20%3D%20-2.7t%5E2%2B40t%2B6.5)
Where t is the number of seconds after the ball was thrown.
We need to find is the ball 18 ft above the moon's surface.
Put S = 18 ft
![-2.7t^2+40t+6.5=18\\\\-2.7t^2+40t=18-6.5\\\\-2.7t^2+40t-11.5=0](https://tex.z-dn.net/?f=-2.7t%5E2%2B40t%2B6.5%3D18%5C%5C%5C%5C-2.7t%5E2%2B40t%3D18-6.5%5C%5C%5C%5C-2.7t%5E2%2B40t-11.5%3D0)
It is a quadratic equation. Its solution is given by :
![t=\dfrac{-40+\sqrt{40^{2\ }-4\left(-2.7\right)\left(-11.5\right)}}{2\left(-2.7\right)},\dfrac{-40-\sqrt{40^{2\ }-4\left(-2.7\right)\left(-11.5\right)}}{2\left(-2.7\right)}\\\\t=0.293\ s,14.52\ s](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B-40%2B%5Csqrt%7B40%5E%7B2%5C%20%7D-4%5Cleft%28-2.7%5Cright%29%5Cleft%28-11.5%5Cright%29%7D%7D%7B2%5Cleft%28-2.7%5Cright%29%7D%2C%5Cdfrac%7B-40-%5Csqrt%7B40%5E%7B2%5C%20%7D-4%5Cleft%28-2.7%5Cright%29%5Cleft%28-11.5%5Cright%29%7D%7D%7B2%5Cleft%28-2.7%5Cright%29%7D%5C%5C%5C%5Ct%3D0.293%5C%20s%2C14.52%5C%20s)
So, the ball is at first 0.293 s and then 14.52 s above the Moon's surface.
Answer: The cost of one rose bush is $7 and the cost of one shrub is also $7
Step-by-step explanation:
The situtation can be represented by the systems of the equations.
10x + 4y = 98 x in this case is the cost of one rose bushes
9x + 9y = 126 y is the cost of one shrub.
Solve the system of equation using the elimination method.
10x +4y = 98
9x + 9y = 126 eliminate the y variable so you will have to multiply 9 on top and -4 down.
9(10x +4) = (98)(9)
-4(9x + 9y) = 126(-4)
You will now have the new two systems of equations
90x +36y = 882
-36x +-36y = -504 Now add the equations
0 + 54x = 378
54x = 378
x= 7
Now we know that the cost of one rose bush is 7 so we will plot it into one of the equations and solve for the cost of one shrub.
90(7) +36y=882
630 +36y = 882
-630 -630
36y = 252
y = 7
Check: 10(7) + 4(7)= 98
70 + 28 = 98
98= 98
so one rose bush is actually 7 dollars the same as 1 shrub.
Answer:
Number of trucks (y) that can be shipped if the number of cars (x) is known![=\frac{21,600-3.6x}{7.5}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B21%2C600-3.6x%7D%7B7.5%7D)
Step-by-step explanation:
A cargo ship can carry 21,600 Tons.
Let x denotes number of cars and y denotes number of trucks.
The cars weigh 3.6 tons each and the trucks weigh 7.5 tons each.
Therefore,
![3.6x+7.5y=21,600](https://tex.z-dn.net/?f=3.6x%2B7.5y%3D21%2C600)
Now write y in terms of x.
![7.5y=21,600-3.6x\\y=\frac{21,600-3.6x}{7.5}](https://tex.z-dn.net/?f=7.5y%3D21%2C600-3.6x%5C%5Cy%3D%5Cfrac%7B21%2C600-3.6x%7D%7B7.5%7D)
Number of trucks (y) that can be shipped if the number of cars (x) is known![=\frac{21,600-3.6x}{7.5}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B21%2C600-3.6x%7D%7B7.5%7D)