Answer:
ghcfhfdh
Step-by-step explanation:
Answer:
30 pounds
Step-by-step explanation:
Amount of tin in first alloy + amount of tin in second alloy = amount of tin in mixture
0.15 (20) + 0.10 x = 0.12 (20 + x)
3 + 0.10 x = 2.4 + 0.12 x
0.6 = 0.02 x
x = 30
Answer:
f(-2) = -5
f(0) = 5
f(1) = 10
Step-by-step explanation:
f(-2) = 5(-2) + 5 → -10 + 5 = -5
f(0) = 5(0) + 5 → 0 + 5 = 5
f(1) = 5(1) + 5 → 5 + 5 = 10
Answer:
a) The maximum height is approx 15.5 unit.
b) The time it will take for Joey to reach the water is 1.45 hour.
Step-by-step explanation:
Given : When Joey dives off a diving board, the equation of his pathway can be modeled by ![h(t)= -16t^2+15t + 12](https://tex.z-dn.net/?f=h%28t%29%3D%20-16t%5E2%2B15t%20%2B%2012)
To find : a) Find Joey's maximum height.
b) Find the time it will take for Joey to reach the water.
Solution :
Modeled
....(1)
a) To find maximum height
Derivate (1) w.r.t. t,
![h'= -32t+15](https://tex.z-dn.net/?f=h%27%3D%20-32t%2B15)
For critical point put h'=0,
![-32t+15=0](https://tex.z-dn.net/?f=-32t%2B15%3D0)
![t=\frac{15}{32}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B15%7D%7B32%7D)
![t=0.46875](https://tex.z-dn.net/?f=t%3D0.46875)
Derivate again w.r.t. t,
![h''= -32](https://tex.z-dn.net/?f=h%27%27%3D%20-32%3C0)
It is maximum at t=0.46875.
Substitute t in equation (1),
![h(0.46875)= -16(0.46875)^2+15(0.46875)+12](https://tex.z-dn.net/?f=h%280.46875%29%3D%20-16%280.46875%29%5E2%2B15%280.46875%29%2B12)
![h(0.46875)= -3.515625+7.03125+12](https://tex.z-dn.net/?f=h%280.46875%29%3D%20-3.515625%2B7.03125%2B12)
![h(0.46875)= 15.515625](https://tex.z-dn.net/?f=h%280.46875%29%3D%2015.515625)
The maximum height is approx 15.5 unit.
b) To find the time it will take for Joey to reach the water.
Put h=0 in equation (1),
Apply quadratic formula, ![x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Here, a=-16 , b=15, c=12
Reject negative value.
The time is t=1.45.
The time it will take for Joey to reach the water is 1.45 hour.
The answer to this is x<-3.63 repeating