The matrices are
S =(4 11 T= ( -8 11
-3 -8) 3 4 )
Inverse of a matrix is a matrix derived from another matrix such that if you pre- multiply it with the original matrix you get a unit matrix.
if we multiply S and T
ST will be
( 4 11 × (-8 11 = ( 1 0
-3 -8) -3 -4) 0 1)
and also TS
( -8 11 × (4 11 = ( 1 0
-3 -4) -3 -8) 0 1)
therefore, matrices S and T are inverses of each other because ST = TS= I
.
Answer:
X, process, y
-2, 3(-2), -6
-1, 3(-1), -3
0, 3(0), 0
1, 3(1), 3
2, 3(2), 6
X = -2, -1, 0, 1, 2,
Y = -6, -3, 0, -3, -6
Step-by-step explanation:
Coordinates for the graph: (-2,-6), (-1,-3), (0,0), (1,3), (2,6)
Graph is the image I added onto this.
Solving for Y below:
3(-2)= -6
3(-1)= -3
3(0)= 0
3(1)= 3
3(2)= 6
Hope this helps.
6. It is asking you to find the surface area for this one:
1 litre = 0.001 cubic meters
15.4 litres = 0.0154 cubic meters
The volume of the cylinder has to be 0.0154m^3.
V = (pi(r)^2)h
0.0154 = (pi(r)^2)(1)
r^2 = 0.0154/pi
r = 0.07m
Surface Area of Circles on Bottom:
A = pi(r)^2
A = pi(0.07)^2
A = 0.0154
0.0154*2 = 0.0308m^2
Surface Area of Walls:
This will be the circumference of the circle times the height, since the walls are just like a big rectangle.
C = 2pi(r)
C = 2pi(0.07)
C = 0.44m
0.44*1 = 0.44m^2
Finally, add the two surface areas:
0.44 + 0.0308 = 0.47m^2
You will need 0.47m^2 of sheet metal to make this cylinder.
7. Find the volume of everything and just the graphite, and subtract the graphite’s volume from everything to get just the wood. The volume of a cylinder is pi((r)^2)h.
Everything:
Watch out for units, since the diameter is in mm and the length is in cm.
r = 3.5mm or 0.35cm
V = pi((0.35)^2)(14)
V = 5.34cm^3
Graphite:
r = 0.5mm or 0.05cm
V = pi((0.05)^2)(14)
V = 0.11cm^3
5.34 - 0.11 = 5.23cm^3
8. For this problem, it wants your answer in cm^3. Find the volume of one bowl and multiply it by 250:
r = 3.5cm
V = pi((3.5)^2)(4)
V = 153.94cm^3
153.94*250 = 38484.51cm^3 of soup needed.
I sure hope that I didn’t confuse you too much with all of my math gibberish (sorry). Please let me know if there is anything else that I can help with. Have a nice day
