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ICE Princess25 [194]
3 years ago
9

Which number line shows the solution set to this inequality? -2x + 9 < x − 9

Mathematics
1 answer:
kotykmax [81]3 years ago
5 0

Answer:

see below

Step-by-step explanation:

-2x + 9 < x − 9

Add 2x to each side

2x-2x + 9 < 2x+x − 9

9 < 3x-9

Add 9 to each side

9+9 < 3x

18 < 3x

Divide each side  by 3

18/3 < 3x/3

6 < x

Open circle  at 6 line going to the right

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The answer is (2,6).
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Solve the following ODE's: c) y* - 9y' + 18y = t^2
Nastasia [14]

Answer:

y = C_1e^{3t}+C_2e^{6t} + \dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})

Step-by-step explanation:

y''- 9 y' + 18 y = t²

solution of ordinary differential equation

using characteristics equation

m² - 9 m + 18 = 0

m² - 3 m - 6 m+ 18 = 0

(m-3)(m-6) = 0

m = 3,6

C.F. = C_1e^{3t}+C_2e^{6t}

now calculating P.I.

P.I. = \frac{t^2}{D^2 - 9D +18}

P.I. = \dfrac{t^2}{(D-3)(D-6)}\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1-\frac{D}{6})^{-1}(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1+\frac{D}{6}+\frac{D^2}{36}+....)(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(1+\frac{D}{3}+\frac{D^2}{9}+....)(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})

hence the complete solution

y = C.F. + P.I.

y = C_1e^{3t}+C_2e^{6t} + \dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})

7 0
3 years ago
What are the removable discontinuities of the following function? f (x) = StartFraction x squared minus 36 Over x cubed minus 36
jeyben [28]

Answer:

the removal discontinuity of the following function at x=-6 or x=6.

Step-by-step explanation:

factoring  f(x)  = (x - 6)(x + 6)

                         ----------------

                          x(x - 6)^x + 6)

3 0
3 years ago
Read 2 more answers
Write the missing exponent <br><br> 256 = <br><img src="https://tex.z-dn.net/?f=%20%7B%3F%7D%5E%7B4%7D%20" id="TexFormula1" titl
antiseptic1488 [7]

Answer:

4^4

Step-by-step explanation:

256\div4=64\div4=16\div4=4

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Hope this helps.

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