Answer:
Michael is 38 and Sara is 29
Step-by-step explanation:
Because it says the sum of their age is 47 you do 47-9=38 so that would be Michael's age and than because Sara is 9 years younger than him and then you would do 38-9=29
Answer:
Step-by-step explanation:
Alright, lets get started.
This is the combination of three figures semi circle, rectangle and triangle.
We will find the area of each figure and will add them.
The radius of the circle is half of the diameter, so radius is 6.
Area of semi circle will be : ![\frac{1}{2} \times 3.14 \times 6^2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%203.14%20%5Ctimes%206%5E2)
Area of semi circle is : 56.52
Area of rectangle is: ![length \times width](https://tex.z-dn.net/?f=length%20%5Ctimes%20width)
So, area of rectangle is:![40\times 12=480](https://tex.z-dn.net/?f=40%5Ctimes%2012%3D480)
Area of triangle is : ![\frac{1}{2}\times base\times height](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20base%5Ctimes%20height)
So, area of triangle is :![\frac{1}{2} \times 12\times 5=30](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%2012%5Ctimes%205%3D30)
Adding all these three areas, the area of above figure will be:
[tex]Area = 56.52+480+30
Hence Area is 566.52............... Answer
Answer:
![\sqrt{41}](https://tex.z-dn.net/?f=%5Csqrt%7B41%7D)
Step-by-step explanation:
Answer:
x = 20
Step-by-step explanation:
3x + 6x = 180, if you make them supplementary then they will be parallel
9x = 180
x = 20
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