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3 years ago

The quadratic equation x2 + mx + q = 0, where m and q are real numbers, has the complex root a + bi.?

1 answer:

3 0

Remember the quadratic formula determinant?
If b^2 -4ac < 0, a complex root exists.

So for this problem, m^2 - 4q is the determinant, and if less than 0, is complex.

So a=-m/2 and b=(1/2)SQRT(m^2 - 4q)

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The sum of two numbers, one is as large as the other is 24. Find two numbers

lakkis [162]

Answer:

4 and 20

Step-by-step explanation:

The sum of two numbers is 24.

One of the numbers is 5 times larger than the other.

Let x be the first number.

Let y be the second number.

x + y = 24

x = 5y

Put x as 5y in the first equation.

5y + y = 24

6y = 24

y = 4

Put y as 4 in the second equation.

x = 5(4)

x = 20

7 0

3 years ago

Which is the graph of the system x + 3y > –3 and y < One-halfx + 1?

gregori [183]

Answer:

D, or the last graph.

Step-by-step explanation:

I got it right when I was doing the assignment :)

3 0

2 years ago

Read 2 more answers

Write the given differential equation in the form L(y) = g(x), where L is a linear differential operator with constant coefficie

melamori03 [73]

Answer:

The complete solution is

$\therefore y= Ae^{3x}+Be^{-\frac13 x}-\frac43$

Step-by-step explanation:

Given differential equation is

3y"- 8y' - 3y =4

The trial solution is

$y = e^{mx}$

Differentiating with respect to x

$y'= me^{mx}$

Again differentiating with respect to x

$y''= m ^2 e^{mx}$

Putting the value of y, y' and y'' in left side of the differential equation

$3m^2e^{mx}-8m e^{mx}- 3e^{mx}=0$

$\Rightarrow 3m^2-8m-3=0$

The auxiliary equation is

$3m^2-8m-3=0$

$\Rightarrow 3m^2 -9m+m-3m=0$

$\Rightarrow 3m(m-3)+1(m-3)=0$

$\Rightarrow (3m+1)(m-3)=0$

$\Rightarrow m = 3, -\frac13$

The complementary function is

$y= Ae^{3x}+Be^{-\frac13 x}$

y''= D², y' = D

The given differential equation is

(3D²-8D-3D)y =4

⇒(3D+1)(D-3)y =4

Since the linear operation is

L(D) ≡ (3D+1)(D-3)

For particular integral

$y_p=\frac 1{(3D+1)(D-3)} .4$

$=4.\frac 1{(3D+1)(D-3)} .e^{0.x}$ [since $e^{0.x}=1$ ]

$=4\frac{1}{(3.0+1)(0-3)}$ [ replace D by 0 , since L(0)≠0]

$=-\frac43$

The complete solution is

y= C.F+P.I

$\therefore y= Ae^{3x}+Be^{-\frac13 x}-\frac43$

4 0

2 years ago

Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 68 miles per hour, with a standard

Vladimir79 [104]

About 99.7% of vehicles whose speeds are between 59 miles per hour and 77 miles per hour.

Empirical rule states that for a normal distribution, 68% lie within one standard deviations, 95% lie within two standard deviations, and 99.7% lie within three standard deviations of the mean.

Given that mean (μ) = 68 miles per hour, standard deviation (σ) = 3 miles per hour.

68% lie within one standard deviation = (μ ± σ) = (68 ± 3) = (65, 71).

Hence 68% of the vehicle speed is between 65 miles per hour and 71 miles per hour.

95% lie within two standard deviation = (μ ± 2σ) = (68 ± 2*3) = (62, 74).

Hence 95% of the vehicle speed is between 62 miles per hour and 74 miles per hour.

99.7% lie within three standard deviation = (μ ± 3σ) = (68 ± 3*3) = (59, 77).

Hence 99.7% of the vehicle speed is between 59 miles per hour and 77 miles per hour.

Find out more at: brainly.com/question/14468516

3 0

2 years ago

Read 2 more answers

How do you express height in feet by only using a mixed number

guajiro [1.7K]

Height and then the inches over 12.
Ex. 5'4" = 5 4/12 or 5 1/3

8 0

3 years ago