L[ y(t) ] = Y(s)
L[ y' ] = sY-y(0) = sY-0 = sY
L[ y'' ] = s^2*Y - sy(0) - y'(0) = s^2*Y - 1
laplace trasform both sides
L[ y'' - 6y' + 9y ] = L[ t ]
= L[ y'' ] - 6 L[ y' ] + 9 L[ y ] = 1/s
= [ s^2*Y - 1 ] - 6[ sY ] + 9Y = 1/s
( s^2 - 6s + 9 ) Y - 1 = 1/s
⇒ ( s^2 - 6s + 9 ) Y = (1/s) + 1
⇒Y = [ 1 / ( s(s^2 - 6s + 9 ) ) ] + [ 1 / ( s^2 - 6s + 9 ) ]
Let inverse laplace trasform , find y(t) :
y(t) = L^(-1)[ Y(s) ] = L^(-1) { [ 1 / ( s(s^2 - 6s + 9 ) ) ] + [ 1 / ( s^2 - 6s + 9 ) ] }
= [ (1/3)*t*e^(3t) - (1/9)*e^(3t) + (1/9) ] + [ t*e^(3t) ]
= (4/3)*t*e^(3t) - (1/9)*e^(3t) + (1/9)
15% of 14.25.....turn percent to decimal..." of " means multiply
0.15(14.25) = 2.1375 rounds to 2.14....its B
Answer:
150 in^2
Step-by-step explanation:
Each of the 6 identical faces is a triangle with a base of 5 in and a height of 10 in. The area of a triangle is given by the formula ...
A = 1/2·bh
For the given values, the area of one face is ...
A = (1/2)(5 in)(10 in) = 25 in^2
The figure has 6 identical faces of this area, so the total surface area is ...
A = 6×(25 in^2) = 150 in^2
1) calculate 12% of 3000
3000=100%
x=12%
3000•12=100•x
x=360
2) calculate 3% of 3000
3000=100%
y=3%
3•3000=100y
y=90
3) calculate 1% of 3000
3000=100%
z=1%
3000•1=100z
z=30
4) calculate 6% of 3000
3000=100%
k=6%
3000•6=100k
k=180
5) now we need to add all this numbers to each other to see total money he has to spend in taxes (but we will take 180 twice because there where two 6%_s)
360+90+30+180+180=840
6) to calculate his take-home pay, we need to subtract 3000 by tax pay that we just calculated
3000-840=2160
FINALL ANAWER—his take home pay is $2160
Answer:
<u>Width = 7 inches</u>
<u>Length = 23 inches</u>
Step-by-step explanation:
Let :
Equating to area :
- (2x + 9)(x) = 161
- 2x² + 9x = 161
- 2x² + 9x - 161 = 0
- 2x² - 14x + 23x - 161 = 0
- 2x(x - 7) + 23(x - 7) = 0
- x - 7 = 0
- x = 7
Dimensions are :
- <u>Width = 7 inches</u>
- Length = 2(7) + 9
- <u>Length = 23 inches</u>
