Answer:
1300
Step-by-step explanation:
Let the amount put in the station's tank = x
4(400 + x) = 8100 - x Remove the brackets
1600 + 4x = 8100 - x Subtract 1600 from both sides
1600 - 1600 + 4x = 8100 - 1600 - x Do the subtraction
4x = 6500 - x Add x to both sides
4x + x = 6500 - x + x
5x = 6500 Divide by 5
5x/5 = 6500/5
x = 1300
1300 gallons were added to the station's tank.
Looking at the given diagram, angle AEC and angle DEB share the same vertex, E. They are described as vertically opposit angles. In geometry, vertically opposite angles are equal. This means that
Angle DEB = angl AEC = 50 degrees
Step-by-step explanation:
3)
2x + 3y = 12
Solve for y. Then you have y = mx + b, and m is the slope.
3y = -2x + 12
y = -2/3 x + 12
slope = -2/3
6x - 4y = 8
-4y = -6x + 8
y = -6/(-4) x + 8/(-4)
y = 3/2 x - 2
slope = 3/2
Since the slopes -2/3 and 3/2 are opposite reciprocals, the lines are perpendicular.
4)
3x - 4y = 12
-4y = -3x + 12
y = -3/(-4) x + 12/(-4)
y = 3/4 x - 3
slope = 3/4
4x + 3y = 15
3y = -4x + 15
y = -4/3 x + 5
slope = -4/3
Since the slopes 3/4 and -4/3 are opposite reciprocals, the lines are perpendicular.
Answer:
Step-by-step explanation:
We have to take the derivatives for both functions and replace in the differential equation. Hence
for y=e^{-5x}:

for y=e^{6x}:

Now we replace in the differential equation y'' − y' − 30y = 0
for y=e^{-5x}:

for y=e^{6x}:

Now, to know if both function are linearly independent we calculate the Wronskian


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