Answer:
0.675 m/s
Step-by-step explanation:
Let height of shadow= y,CD=x
Height of man=2 m
Speed of man= ![\frac{dx}{dt}=1. 8 m/s](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%3D1.%208%20m%2Fs)
![\triangle ABD\sim\triangle ECD](https://tex.z-dn.net/?f=%5Ctriangle%20ABD%5Csim%5Ctriangle%20ECD)
Therefore, ![\frac{AB}{EC}=\frac{BD}{CD}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BEC%7D%3D%5Cfrac%7BBD%7D%7BCD%7D)
![\frac{y}{2}=\frac{12}{x}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B2%7D%3D%5Cfrac%7B12%7D%7Bx%7D)
![xy=24](https://tex.z-dn.net/?f=xy%3D24)
Differentiate w.r.t t
![x\frac{dy}{dt}+y\frac{dx}{dt}=0](https://tex.z-dn.net/?f=x%5Cfrac%7Bdy%7D%7Bdt%7D%2By%5Cfrac%7Bdx%7D%7Bdt%7D%3D0)
![x\frac{dy}{dt}=-y\frac{dx}{dt}](https://tex.z-dn.net/?f=x%5Cfrac%7Bdy%7D%7Bdt%7D%3D-y%5Cfrac%7Bdx%7D%7Bdt%7D)
![\frac{dy}{dt}=-\frac{y}{x}\frac{dx}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%3D-%5Cfrac%7By%7D%7Bx%7D%5Cfrac%7Bdx%7D%7Bdt%7D)
When the man is 4 m from the building
Then, we have x=12-4=8 m
![\frac{dx}{dt}=1.8 m/s](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%3D1.8%20m%2Fs)
Substitute the values in above equation then, we get
![8y=24](https://tex.z-dn.net/?f=8y%3D24)
![y=\frac{24}{8}=3](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B24%7D%7B8%7D%3D3)
Substitute the values then we get
![\frac{dy}{dt}=-\frac{3}{8}\times 1.8=-0.675 m/s](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%3D-%5Cfrac%7B3%7D%7B8%7D%5Ctimes%201.8%3D-0.675%20m%2Fs)
Hence, the length of his shadow on the building decreasing at the rate 0.675 m/s.
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You must add up all of the values and then divide them by the number of the values.
Answer:
A) 7x^3 + 13x^2 + 8x + 9
Step-by-step explanation:
(3x^2 + 2x + 7x^3) + (10x^2 + 6x + 9)
I like to line them up vertically
7x^3 +3x^2 + 2x
+ (10x^2 + 6x + 9)
-----------------------------------
7x^3 +13x^2 +8x +9
Answer:
0.04395604395
Step-by-step explanation: