Answer with Step-by-step explanation:
We are given that a ball is thrown into the air with velocity
![v=40ft/s](https://tex.z-dn.net/?f=v%3D40ft%2Fs)
Height after t seconds is given by
![s(t)=40t-16t^2](https://tex.z-dn.net/?f=s%28t%29%3D40t-16t%5E2)
We have to find the average velocity for the ball during the time [1,2].
We know that average velocity=![\frac{ds}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bds%7D%7Bdt%7D)
Average velocity=v=![\frac{d(40t-16t^2)}{dt}=40-32t](https://tex.z-dn.net/?f=%5Cfrac%7Bd%2840t-16t%5E2%29%7D%7Bdt%7D%3D40-32t)
Substitute t=1 then we get
Average velocity=![40-32(1)=40-32=8 m/s](https://tex.z-dn.net/?f=40-32%281%29%3D40-32%3D8%20m%2Fs)
Substitute t=2 then
Average velocity=![40-32(2)=40-64](https://tex.z-dn.net/?f=40-32%282%29%3D40-64)
Average velocity[/tex]=-24 m/s[/tex]
Follow the order of operations!!
1. Parentheses
2. Exponents
3. Multiplication
4. Division
5. Addition
6. Subtraction
that is in order. follow these and you should figure it out yourself :)
Answer:
Option D. 2.51 is correct.
Step-by-step explanation:
Magnitude of first earthquake = 8.6
Let intensity of first earthquake be x
![Magnitude = \log(\frac{x}{S}),\text{ where S is seismographic factor}\\\\\implies 8.6=\log(\frac{x}{S}).......(1)](https://tex.z-dn.net/?f=Magnitude%20%3D%20%5Clog%28%5Cfrac%7Bx%7D%7BS%7D%29%2C%5Ctext%7B%20where%20S%20is%20seismographic%20factor%7D%5C%5C%5C%5C%5Cimplies%208.6%3D%5Clog%28%5Cfrac%7Bx%7D%7BS%7D%29.......%281%29)
Magnitude of second earthquake = 8.2
Let intensity of second earthquake be y
![Magnitude = \log(\frac{y}{S}),\text{ where S is seismographic factor}\\\\\implies 8.2=\log(\frac{y}{S}).......(2)](https://tex.z-dn.net/?f=Magnitude%20%3D%20%5Clog%28%5Cfrac%7By%7D%7BS%7D%29%2C%5Ctext%7B%20where%20S%20is%20seismographic%20factor%7D%5C%5C%5C%5C%5Cimplies%208.2%3D%5Clog%28%5Cfrac%7By%7D%7BS%7D%29.......%282%29)
Now, to find the factor by which intensity of first earthquake is greater than intensity of second : we divide equation (1) by equation (2)
![\implies\log(\frac{x}{y})=8.6 - 8.2\\\\\implies \log(\frac{x}{y})=0.4\\\\\implies\frac{x}{y}=10^{0.4}\\\\\implies\frac{x}{y}=2.51](https://tex.z-dn.net/?f=%5Cimplies%5Clog%28%5Cfrac%7Bx%7D%7By%7D%29%3D8.6%20-%208.2%5C%5C%5C%5C%5Cimplies%20%5Clog%28%5Cfrac%7Bx%7D%7By%7D%29%3D0.4%5C%5C%5C%5C%5Cimplies%5Cfrac%7Bx%7D%7By%7D%3D10%5E%7B0.4%7D%5C%5C%5C%5C%5Cimplies%5Cfrac%7Bx%7D%7By%7D%3D2.51)
Hence the required factor is 2.51
Therefore, Option D. 2.51 is correct.
Answer:
y = -1/2x + 3
Step-by-step explanation:
y - y₁ = m(x - x₁)
⇒ y - 0 = -1/2(x - 6)
⇒ y = -1/2x + 3