Answer:
Density of material would be 4.09 ![g/cm^3](https://tex.z-dn.net/?f=g%2Fcm%5E3)
units is ![g/cm^3](https://tex.z-dn.net/?f=g%2Fcm%5E3)
Step-by-step explanation:
Given: The mass of a material is 45 grams and the volume of the material is 11 cubic centimeter
Density is defined as mass per unit volume.
It is given by:
where p is the density , m is the mass and V is the volume of the material respectively.
Here, Density is expressed in grams per centimeter cubed (g/cubic cm)
Here, m = 45 g , V = 11 cubic cm
We get;
= 4.09 ![g/cm^3](https://tex.z-dn.net/?f=g%2Fcm%5E3)
therefore, density of a material would be, ![4.09 g/cm^3](https://tex.z-dn.net/?f=4.09%20g%2Fcm%5E3)
and its units is ![g/cm^3](https://tex.z-dn.net/?f=g%2Fcm%5E3)
Answer:
2, 10, 50, 250
Step-by-step explanation:
Using the formula with a₁ = 2 , then
a₂ = 5a₁ = 5 × 2 = 10
a₃ = 5a₂ = 5 × 10 = 50
a₄ = 5a₃ = 5 × 50 = 250
The first 4 terms are 2, 10, 50, 250
Answer:
D. y - 2 = 2(x + 1)
Step-by-step explanation:
<h3>y - y₁ = m (x - x₁)</h3>
y - 2 = 2 (x - (-1))
y - 2 = 2 (x + 1)
<h3>#CMIIW</h3>
*assuming that ABC is a straight line**
<span>then you have </span>
<span>AB = 17.89 ..... this is the length of the whole line </span>
<span>BC is a part of the line = 7 </span>
<span>therefore the length of the other part = 17.89 - 7 </span>
<span>= 10.89</span>
Given that
![y](https://tex.z-dn.net/?f=y)
attains a maximum at
![x=1](https://tex.z-dn.net/?f=x%3D1)
, it follows that
![y'=0](https://tex.z-dn.net/?f=y%27%3D0)
at that same point. So integrating once gives
![\displaystyle\int\frac{\mathrm d^2y}{\mathrm dx^2}\,\mathrm dx=\int-8x\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D%5C%2C%5Cmathrm%20dx%3D%5Cint-8x%5C%2C%5Cmathrm%20dx)
![\dfrac{\mathrm dy}{\mathrm dx}=-4x^2+C_1](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D-4x%5E2%2BC_1)
![\implies -4(1)^2+C_1=0\implies C_1=4](https://tex.z-dn.net/?f=%5Cimplies%20-4%281%29%5E2%2BC_1%3D0%5Cimplies%20C_1%3D4)
and so the first derivative is
![y'=-4x^2+4](https://tex.z-dn.net/?f=y%27%3D-4x%5E2%2B4)
.
Integrating again, you get
![\displaystyle\int\frac{\mathrm dy}{\mathrm dx}\,\mathrm dx=\int(-4x^2+4)\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5C%2C%5Cmathrm%20dx%3D%5Cint%28-4x%5E2%2B4%29%5C%2C%5Cmathrm%20dx)
![y=-\dfrac43x^3+4x+C_2](https://tex.z-dn.net/?f=y%3D-%5Cdfrac43x%5E3%2B4x%2BC_2)
You know that this curve passes through the point (2, -1), which means when
![x=2](https://tex.z-dn.net/?f=x%3D2)
, you have
![y=-1](https://tex.z-dn.net/?f=y%3D-1)
:
![-1=-\dfrac43(2)^3+4(2)+C_2](https://tex.z-dn.net/?f=-1%3D-%5Cdfrac43%282%29%5E3%2B4%282%29%2BC_2)
![\implies C_2=\dfrac53](https://tex.z-dn.net/?f=%5Cimplies%20C_2%3D%5Cdfrac53)
and so