Taking the transform of both sides gives
![\mathcal L_s\{x''+8x'+15x\}=0](https://tex.z-dn.net/?f=%5Cmathcal%20L_s%5C%7Bx%27%27%2B8x%27%2B15x%5C%7D%3D0)
![(s^2X(s)-sx(0)-x'(0))+8(sX(s)-x(0))+15X(s)=0](https://tex.z-dn.net/?f=%28s%5E2X%28s%29-sx%280%29-x%27%280%29%29%2B8%28sX%28s%29-x%280%29%29%2B15X%28s%29%3D0)
where
denotes the Laplace transform of
,
. Solve for
to get
![(s^2+8s+15)X(s)=2s+13](https://tex.z-dn.net/?f=%28s%5E2%2B8s%2B15%29X%28s%29%3D2s%2B13)
![X(s)=\dfrac{2s+13}{s^2+8s+15}=\dfrac{2s+13}{(s+3)(s+5)}](https://tex.z-dn.net/?f=X%28s%29%3D%5Cdfrac%7B2s%2B13%7D%7Bs%5E2%2B8s%2B15%7D%3D%5Cdfrac%7B2s%2B13%7D%7B%28s%2B3%29%28s%2B5%29%7D)
Split the right side into partial fractions:
![\dfrac{2s+13}{(s+3)(s+5)}=\dfrac a{s+3}+\dfrac b{s+5}](https://tex.z-dn.net/?f=%5Cdfrac%7B2s%2B13%7D%7B%28s%2B3%29%28s%2B5%29%7D%3D%5Cdfrac%20a%7Bs%2B3%7D%2B%5Cdfrac%20b%7Bs%2B5%7D)
![2s+13=a(s+5)+b(s+3)](https://tex.z-dn.net/?f=2s%2B13%3Da%28s%2B5%29%2Bb%28s%2B3%29)
If
, then
; if
, then
. So
![X(s)=\dfrac72\dfrac1{s+3}-\dfrac32\dfrac1{s+5}](https://tex.z-dn.net/?f=X%28s%29%3D%5Cdfrac72%5Cdfrac1%7Bs%2B3%7D-%5Cdfrac32%5Cdfrac1%7Bs%2B5%7D)
Finally, take the inverse transform of both sides to solve for
:
![x(t)=\dfrac72e^{-5t}-\dfrac32e^{-3t}](https://tex.z-dn.net/?f=x%28t%29%3D%5Cdfrac72e%5E%7B-5t%7D-%5Cdfrac32e%5E%7B-3t%7D)
Answer:
105 ft
Step-by-step explanation:
In this case, the first thing is to calculate the scale, therefore, we must divide the real measurement by the model measurement, like this:
45 ft / 3 ft = 15
Which means that the scale is 15.
Now, to calculate the height, we must multiply the height of the model by the scale, that is:
7 ft * 15 = 105 ft
which means that the height of the building is 105 ft
Median is the middle so the answer is 6.5
Answer:
The degree of the polynomial is 9.
Step-by-step explanation:
9 is the highest power in the polynomial. That's why it is the degree [According To Me]
We have a proportion: ?/50= 40/100
Cross multiply:
100*?= 40*50
⇒ ?= 40*50/100= 20
The student needs to score 20 points~