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oksian1 [2.3K]
3 years ago
15

What is the value of x?

Mathematics
1 answer:
tekilochka [14]3 years ago
4 0

Answer:

Step-by-step explanation:

since we can see that the lines are parallel

and we can see that the both are interior angles and when we sum up both angles we get 180

2x - 5  + 45 = 180

2x  + 40 =180

2x = 180 - 40

2x =140

x = 140/2

x = 70

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Answer:

\left \{ {{u'=v} \atop {v'=5v-6u-5\sin(2t)}} \right. \\u(0)=-5;u'(0)=2

Step-by-step explanation:

The given initial value problem is;

y''-5y'+6y=-5\sin(2t)---(1)\\y(0)=-5,y'(0)=2

Let

u(t)=y(t)----(2)\\v(t)=y'(t)----(3)

Differentiating both sides of equation (1) with respect to t, we obtain:

u'(t)=y'(t)---(4)\\ \\\implies u'(t)=v(t)---(5)

Differentiating both sides of equation (2) with respect to t gives:

v'(t)=y''(t)----(6)

From equation (1),

y''=5y'-6y-5\sin(2t)\\y''=5v(t)-6u(t)-5\sin(2t)\\\implies v'(t)=5v(t)-6u(t)-5\sin(2t)----(7)

Putting t=0 into equation (2) yields

u(0)=y(0)\\\implies u(0)=-5

Also putting t=0 into equation (3)

u'(0)=y'(0)\\u'(0)=2

The system of first order equations is:

\left \{ {{u'=v} \atop {v'=5v-6u-5\sin(2t)}} \right. \\u(0)=-5;u'(0)=2

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