The answer is x=22 Hopefully
Answer:
At time t = 0.408 sec diver will be at maximum height
Step-by-step explanation:
We have given equation of the height ![f(t)=-4.9t^2+4t+9](https://tex.z-dn.net/?f=f%28t%29%3D-4.9t%5E2%2B4t%2B9)
We know that velocity is the rate of change of distance with respect to time
So ![v=\frac{df(t)}{dt}=\frac{df(-4.9t^2+4t+10)}{dt}=-9.8t+4+0=-9.8t+4](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bdf%28t%29%7D%7Bdt%7D%3D%5Cfrac%7Bdf%28-4.9t%5E2%2B4t%2B10%29%7D%7Bdt%7D%3D-9.8t%2B4%2B0%3D-9.8t%2B4)
At maximum height velocity will be zero
So ![-9.8t+4=0](https://tex.z-dn.net/?f=-9.8t%2B4%3D0)
t = 0.408 sec
So at time t = 0.408 sec diver will be at maximum height
Answer: 4
Step-by-step explanation:
Slope: ![\frac{y_{2} -y_{1} }{x_{2}- x_{1} }](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D%20-y_%7B1%7D%20%7D%7Bx_%7B2%7D-%20x_%7B1%7D%20%7D)
y₂ = -7
y₁ = 5
x₂ = 0
x₁ = 3
![\frac{-7 -5 }{0- 3 }=\frac{-12}{-3} = \frac{4}{1} = 4](https://tex.z-dn.net/?f=%5Cfrac%7B-7%20-5%20%7D%7B0-%203%20%7D%3D%5Cfrac%7B-12%7D%7B-3%7D%20%3D%20%5Cfrac%7B4%7D%7B1%7D%20%3D%204)
Slope: 4
Answer:
The population will be 39400 in approximately 17 years
Step-by-step explanation:
The increase in population after t years is given by the formula
![P_t = P_0(1+r)^t](https://tex.z-dn.net/?f=P_t%20%3D%20P_0%281%2Br%29%5Et)
Here
P_0 is the initial population
r is the growth rate and t is time in years
So far we know,
P_0 = 20000
r = 4%
P_t = 39400
Putting the values in the formula
![39400 = 20000(1+0.04)^t\\39400 =20000(1.04)^t\\\frac{39400}{20000} = (1.04)^t\\1.97 = (1.04)^t](https://tex.z-dn.net/?f=39400%20%3D%2020000%281%2B0.04%29%5Et%5C%5C39400%20%3D20000%281.04%29%5Et%5C%5C%5Cfrac%7B39400%7D%7B20000%7D%20%3D%20%281.04%29%5Et%5C%5C1.97%20%3D%20%281.04%29%5Et)
Taking natural log on both sides
![ln |(1.04)^t| = ln |1.97|\\t\ ln\ |1.04| = ln\ |1.97|\\t = \frac{ln\ 1.97}{ln\ 1.04}\\t = 17.287\\t \approx 17](https://tex.z-dn.net/?f=ln%20%7C%281.04%29%5Et%7C%20%3D%20ln%20%7C1.97%7C%5C%5Ct%5C%20ln%5C%20%7C1.04%7C%20%3D%20ln%5C%20%7C1.97%7C%5C%5Ct%20%3D%20%5Cfrac%7Bln%5C%201.97%7D%7Bln%5C%201.04%7D%5C%5Ct%20%3D%2017.287%5C%5Ct%20%5Capprox%2017)
Hence,
The population will be 39400 in approximately 17 years
Substitution....
y = 5x - 40...so we sub in 5x - 40 in for y in the other equation
y - 3x = -24
5x - 40 - 3x = -24
5x - 3x = -24 + 40
2x = 16
x = 16/2
x = 8
y = 5x - 40
y = 5(8) - 40
y = 40 - 40
y = 0
solution is (8,0)