2x + 3 = 4x^2 completing the square

Mathematics

1 answer:

ch4aika [34]2 years ago

6 0

Answer:

$\frac{1+\sqrt{13} }{4}, \frac{1-\sqrt{13} }{4}$

Step-by-step explanation:

First, make them on one side of the formula in the form of $ax^2+bx+c=0$ which is $4x^{2} -2x-3=0$

Next, insert the corresponding number in the quadratic formula, $\frac{-b+\sqrt{b^{2}-4ac } }{2a} ,\frac{-b-\sqrt{b^{2}-4ac } }{2a}$ , and the answer can be calculated.

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Masteriza [31]

Answer:

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Step-by-step explanation:

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3 years ago

Write the given second order equation as its equivalent system of first order equations. u′′−5u′−4u=1.5sin(3t),u(1)=1,u′(1)=2.5

lakkis [162]

Answer:

hi your question options is not available but attached to the answer is a complete question with the question options that you seek answer to

Answer: v = 5v + 4u + 1.5sin(3t),

1.5sin(3t)

Step-by-step explanation:

u" - 5u' - 4u = 1.5sin(3t) where u'(1) = 2.5 u(1) = 1

v represents the "velocity function" i.e v = u'(t)

As v = u'(t)

u' = v

since u' = v

v' = u"

v' = 5u' + 4u + 1.5sin(3t) ( given that u" - 5u' - 4u = 1.5sin(3t) )

= 5v + 4u + 1.5sin(3t) ( noting that v = u' )

so v' = 5v + 4u + 1.5sin(3t)

d/dt $\left[\begin{array}{ccc}u&\\v&\\\end{array}\right]$ = $\left[\begin{array}{ccc}0&1&\\4&5&\\\end{array}\right]$ $\left[\begin{array}{ccc}u&\\v&\\\end{array}\right]$ + $\left[\begin{array}{ccc}0&\\1.5sin(3t)&\\\end{array}\right]$