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3 years ago

Y = x Squared - 2x - 15

Mathematics

1 answer:

antoniya [11.8K]3 years ago

5 0

Answer:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y. x-intercept(s): (5,0),(−3,0)y-intercept(s): (0,−15)

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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

3 years ago

N+3/4=1/4 solve for n

Hitman42 [59]

Answer:

N = -1/2

Step-by-step explanation:

We are adding in this, so we need to do the opposite to both sides, to get N by itself.

N + 3/4 - 3/4 = 1/4 - 3/4

N = -2/4 or, simplified, -1/2

6 0

2 years ago

Convert the polar representation of this complex number into its standard form z=4(cos150+isin150).

Katen [24]

Answer:

Step-by-step explanation:

Using the exact values

cos150° = - cos30° = - $\frac{\sqrt{3} }{2}$

sin150° = sin30° = $\frac{1}{2}$

Given

z = 4(cos150° + isin150° ) , substitute values

= 4(- $\frac{\sqrt{3} }{2}$ + $\frac{1}{2}$ i )

= - 2 $\sqrt{3}$ + 2i , that is

(- 2 $\sqrt{3}$ , 2 ) → B

7 0

3 years ago

How many $0.21 pencils can be purchased for $7.00? Show your work.

IgorLugansk [536]

N*(21/100)=(700/100)

n=(700/100)/(21/100)

n=(700/100)*(100/21)

n=700/21

n=33+1/3

So <em><u>thirty three</u></em> $0.21 pencils can be purchased for $7.00.

8 0

3 years ago

Read 2 more answers

Select the expression that is equal to (-2x +9) – (3x – 4).

Anna [14]

Answer:

Step-by-step explanation:

(-2x+9-3x-4)

-2x-3x+9-4

-5x+5

3 0

3 years ago