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3 years ago

How do I solve? 5 sin 4x = −10 sin 2x

2 answers:

5 0

Move 5cos(x)5cos(x) to the left side of the equation by subtracting it from both sides.5sin(2x)−5cos(x)=05sin(2x)-5cos(x)=0Simplify each term.Apply the sine double-angle identity.5(2sin(x)cos(x))−5cos(x)=05(2sin(x)cos(x))-5cos(x)=0Multiply 22 by 55 to get 1010.10(sin(x)cos(x))−5cos(x)=010(sin(x)cos(x))-5cos(x)=0Remove parentheses around sin(x)cos(x)sin(x)cos(x).10sin(x)cos(x)−5cos(x)=010sin(x)cos(x)-5cos(x)=0Factor 5cos(x)5cos(x) out of 10sin(x)cos(x)−5cos(x)10sin(x)cos(x)-5cos(x).
Factor 5cos(x)5cos(x) out of 10sin(x)cos(x)10sin(x)cos(x).5cos(x)(2sin(x))−5cos(x)=05cos(x)(2sin(x))-5cos(x)=0Factor 5cos(x)5cos(x) out of −5cos(x)-5cos(x).5cos(x)(2sin(x))+5cos(x)(−1)=05cos(x)(2sin(x))+5cos(x)(-1)=0Factor 5cos(x)5cos(x) out of 5cos(x)(2sin(x))+5cos(x)⋅−15cos(x)(2sin(x))+5cos(x)⋅-1.5cos(x)(2sin(x)−1)=0

Goshia [24]3 years ago

5 0

Answer:

Solve 5sin 4x = -10sin 2x

Ans: 0, pi/2, pi

Explanation:

sin 4x = 2sin 2x.cos 2x
10sin 2x.cos 2x + 10sin 2x = 0
10sin 2x(cos 2x + 1) = 0
a. sin 2x = 0 -->
2x = 0 --> x = 0
2x = pi --> x = pi/2
2x = 2pi x = pi
b. cos 2x = -1 --> 2x = pi --> x = pi/2

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The radius r(t)r(t)r, (, t, )of the base of a cylinder is increasing at a rate of 111 meter per hour and the height h(t)h(t)h, (

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The volume is decreasing at a rate 20π cubic meter per hour.

Step-by-step explanation:

We are given the following in the question:

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The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find a second solution y2(x) of the homogeneous equation

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The second solution y2 is

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Step-by-step explanation:

Given the homogeneous differential equation

x²y'' - 7xy' + 16y = 0

And a solution: y1 = x^4

We need to find a second solution y2 using the method of reduction of order.

Let y2 = uy1

=> y2 = ux^4

Since y2 is also a solution to the differential equation, it also satisfies it.

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y2' = u'. x^4 + u. 4x³

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Integrating this

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Since

y2 = uy1

We have

y2 = (Alnx)x^4 = (Ax^4)lnx

Therefore, the second solution y2 is

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Step-by-step explanation:

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