<h3>
Answer: angle X = 70.5 degrees</h3>
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Work Shown:
Law of Cosines
c^2 = a^2 + b^2 - 2ab*cos(C)
22^2 = 20^2 + 18^2 - 2*20*18*cos(X)
484 = 724 - 720*cos(X)
484 + 720*cos(X) = 724
720*cos(X) = 724 - 484
720*cos(X) = 240
cos(X) = 240/720
cos(X) = 1/3
X = arccos(1/3)
X = 70.528779
X = 70.5
Make sure your calculator is in degree mode.
It looks like the ODE is

with the initial condition of
.
Rewrite the right side in terms of the unit step function,

In this case, we have

The Laplace transform of the step function is easy to compute:

So, taking the Laplace transform of both sides of the ODE, we get

Solve for
:

We can split the first term into partial fractions:

If
, then
.
If
, then
.


Take the inverse transform of both sides, recalling that

where
is the Laplace transform of the function
. We have


We then end up with

Answer: In step 1, Andrew used the commutative property
Explanation:
In step 1 he used commutative, which is a + b = b + a
(- 5.7 + 2.2) = 2.2 + (- 5.7)
Step 2, he used associative property, not the distributive.
Step 3, he just added5.7 + 1.1 = 6.8
Step 4, he distributed the negative sign:
- (6.8) = - 6.8