Performing laplace transform of the equation.
sY(s) - y(0) + 6Y(s) = 1/(s-4)
(s+6)Y(s) - 2 = 1/(s-4)
Y(s) = 2/(s+6) + 1/(s-4)(s+6), by partial fraction decomposition
Y(s) = 2/(s+6) + 1/10 * (1/(s-4) + 1/(s+6))
Y(s) = 0.1/(s-4) + 2.1/(s+6)
Performing inverse laplace transform,
y(t) = 0.1e^4t + 2.1e^(-6t)
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-ax-20=-14
add 20 to both sides
-ax=6
Answer:
2x + 8y = 16
Step-by-step explanation:
Subtract 2x from both sides of the equation.
8y = 16 − 2x
Divide each term by 8 and simplify.
Answer:
Option (B)
Step-by-step explanation:
Length of PR = 4
RS = 4
QS = 4
For the length of PT,
PT² = RT² + PR² [Since, PT is the diagonal of rectangle PRT]
PT² = QS² + PR² [Since, RT ≅ QS]
PT² = 4² + 7²
PT² = 16 + 49
PT² = 65
Now for the length of PQ,
PQ² = QT² + PT²
PQ² = RS² + PT² [Since, QT ≅ RS]
PQ² = 4² + 65
PQ² = 16 + 65
PQ = √81
PQ = 9
Therefore, length of diagonal PQ is 9 units.
Option (B) will be the answer.
9514 1404 393
Answer:
- vertical change: 1 unit
- horizontal change: 2 units
- rate of change: 0.5
Step-by-step explanation:
The marks on the graph show the vertical change is 1 unit, and the horizontal change is 2 units.
The "rate of change" is the ratio of vertical change to horizontal change:
rate of change = slope = Δy/Δx = 1/2 = 0.5
Expressed as a decimal, the rate of change is 0.5.
