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3 years ago

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The point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = y minus 1 equals StartFract

ion one-fourth EndFraction left-parenthesis x minus 12 right-parenthesis.(x – 12). What is the standard form of the equation for this line?

1 answer:

Illusion [34]3 years ago

3 0

Answer:

x-4y=8

Step-by-step explanation:

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Use the method of reduction of order to find a second solution to t^2y' + 3ty' – 3y = 0, t> 0 Given yı(t) = t y2(t) = Preview

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Let $y_2(t)=tv(t)$ . Then

${y_2}'=tv'+v$

${y_2}''=tv''+2v'$

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$t^2(tv''+2v')+3t(tv'+v)-3tv=0$

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Let $u(t)=v'(t)$ , so that $u'(t)=v''(t)$ . Then the ODE is linear in $u$ , with

$tu'+5u=0$

Multiply both sides by $t^4$ , so that the left side can be condensed as the derivative of a product:

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Integrate again to solve for $v(t)$ :

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3 years ago

Find the area of the shaded region

FrozenT [24]

Answer:

16 square units

Step-by-step explanation:

The area of the large triangle is

A = 1/2 bh

A = 1/2 (9) * 8 = 36

The area of the small triangle is

A = 1/2 bh

A = 1/2 (8) (5) = 20

The difference is the shaded region

A = 36-20 = 16

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3 years ago