Expand and simplify 4(2x +7) – 3(x + 5)

Mathematics

1 answer:

Tema [17]3 years ago

5 0

Answer:

The answers is 5x + 13

It Equal to 5x + 13

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Please help! Name an angle adjacent and congruent to angle AOC ( diagram in picture)

kipiarov [429]

Answer:

Angle DOC

Step-by-step explanation:

Since angle AOC and angle DOC are ajacent angles that form a straight line, they are supplementary to each other.

By the definition of supplementary angles, you can determine that angle AOC + angle DOC = 180.

Also notice that angle DOC is a right angle (90 degrees), so you can also determine that angle AOC is also a right angle since they are supplementary.

7 0

3 years ago

Integration by Parts Evaluate e-2x cos(2x) dx.

kifflom [539]

Let

$I = \displaystyle \int e^{-2x} \cos(2x) \, dx[/]texIntegrate by parts:[tex]\displaystyle \int u \, dv = uv - \int v \, du$

with

$u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \cos(2x) \, dx \implies v = \dfrac12 \sin(2x)$

Then

$\displaystyle I = \frac12 e^{-2x} \sin(2x) + \int e^{-2x} \sin(2x) \, dx + C$

Integrate by parts again, this time with

$u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \sin(2x) \, dx \implies v = -\dfrac12 \cos(2x)$

so that

$\displaystyle I = \frac12 e^{-2x} \sin(2x) - \frac12 e^{-2x} \cos(2x) - \int e^{-2x} \cos(2x) \, dx + C\\\\ \implies I = \frac{\sin(2x)-\cos(2x)}{2e^{2x}} - I + C \\\\ \implies 2I = \frac{\sin(2x) - \cos(2x)}{2e^{2x}} + C \\\\ \implies I = \boxed{\frac{\sin(2x) - \cos(2x)}{4e^{2x}} + C}$