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a_sh-v [17]
2 years ago
6

Find the domain and range of the graph

Mathematics
1 answer:
Rainbow [258]2 years ago
3 0

Answer:

Domain: [-2,1)

Range: [0,4]

Step-by-step explanation:

<u>Domain</u>

We can see that the piecewise function starts at x=-2, which is included, and ends at x=1, which isn't included. To represent the x-values that lie in between these two endpoints, you would write [-2,1). Brackets show that one endpoint is included while parentheses show that one endpoint isn't included.

<u>Range</u>

Following this logic, the range has its y-values go from 0 to 4 with both endpoints included if you were to trace the function. Thus, your range would be [0,4].

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Use the procedures developed to find the general solution of the differential equation. (Let x be the independent variable.)
makkiz [27]

Solution :

Given :

2y''' + 15y'' + 24y' + 11y= 0

Let x = independent variable

(a_0D^n + a_1D^{n-1}+a_2D^{n-2} + ....+ a_n) y) =  Q(x)  is a differential equation.

If Q(x) \neq 0

It is non homogeneous then,

The general solution  = complementary solution + particular integral

If Q(x) = 0

It is called the homogeneous then the general solution =  complementary solution.

2y''' + 15y'' + 24y' + 11y= 0

$(2D^3+15D^2+24D+11)y=0$

Auxiliary equation,

$2m^3+15m^2+24m +11 = 0$

-1  | 2    15    24     11

   <u> | 0   -2    - 13    -11  </u>

      2    13    11       0

∴ 2m^2+13m+11=0

The roots are

$=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$=\frac{-13\pm \sqrt{13^2-4(11)(2)}}{2(2)}$

$=\frac{-13\pm9}{4}$

$=-5.5, -1$

So, m_1, m_2, m_3 = -1, -1, -5.5

Then the general solution is :

$= (c_1+c_2 x)e^{-x} + c_3 \ e^{-5.5x}$

 

8 0
3 years ago
How to solve j 5/6=17/18?
erma4kov [3.2K]
5/6 j = 17/18
6/5 x 5/6 j =6/5 x 17/18
j = 1/5 x 17/3
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5 0
3 years ago
How to solve system <br> X+y=10<br> X-y=2
pickupchik [31]

Answer:

x=6, y=4. (6, 4).

Step-by-step explanation:

x+y=10

x-y=2

----------

x=y+2

y+2+y=10

2y+2=10

2y=10-2

2y=8

y=8/2=4

x+4=10

x=10-4=6

3 0
4 years ago
–24 + 12d = 2(d – 3) + 22 what does e=?
olchik [2.2K]

Answer:

-24 + 12d = 2(d - 3) + 22

-24 + 12d = 2d - 6 + 22

-24 + 12d = 2d + 16

        12d = 2d + 40

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Step-by-step explanation:

8 0
2 years ago
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Please help me solve questions 1&amp;2
zaharov [31]

Answer:

1) Volume of prism is (V=Area of base×Height)

Volume " " "(V=22÷7×rsquare×h)

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