Four more than the quotient of a number and 5 is 8

Mathematics

1 answer:

love history [14]3 years ago

7 0

Answer:

4 + 5 ÷ x = 8

PEMDAS (You would divide the 5 and x before you add teh 4)

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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

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

6 0

1 year ago

Write a description of how a diagram can help you solve 2×40

nasty-shy [4]

Let me explain like this .Suppose There are 40 people gathered somewhere for attending an event.Each Person has to be given 2 sweets for their arrival or for showing their presence in the event. Now 40 other woman joined them..Instead of getting two sweets each of them got one sweet.

Solution: 2 sweets × 40 people = 1 sweet × 80 people = 80

2nd Way:

There are 40 rooms in a building.In Each room we have to fix two bulbs. So How many bulbs are there in the building.

Solution →→→2 bulbs × 40 room = 80 bulbs

Diagram is depicted below for two parts.