Answer:
- <u>The sum of the series = 198.</u>
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Step-by-step explanation:
In the given arithmetic series,
- The first term (a) = 6
- Common difference (d) = (aₙ – aₙ₋₁) = 10 - 6 = 4
- Last term (aₙ) = 38
To find the sum of the series, we need to find the number of terms (n) at first. So,
Now, let's find the sum of the arithmetic series (Sₙ).
- The sum of the series = <u>198</u>.
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Hope it helps!
Let
, so that
. Then the ODE becomes linear in
with
Find an integrating factor:
Multiply both sides of the ODE by
:
The left side can be consolidated as a derivative:
Integrate both sides with respect to
to get
where the right side can be computed with a simple substitution. Then
Back-substitute to solve for
.
Remember, for |a|=b, assume and solve a=b and a=-b
so
first get into |a|=b form
-3|x-3|=-6
divide both sides by -3
|x-3|=2
so solve
x-3=2 and x-3=-2
add 3 to both sides
x=5 and x=1
the solutionsa re x=1 and 5
Let the speed of the bus be x,
Distance = speed × time
(90+x) (16:20 –13:20) = 510
=> 3(90+x) = 510
=> 270 + 3x = 510
=> 3x = 510–270
=> x = 240/3
=> x = 80
Thus, the speed of the bus is 80km/hr.
There are 3 available methods- Substitution , Elimination and <span>Matrix.
To solve this </span><span>linear equations lets use Matrix's.
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