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timofeeve [1]
3 years ago
8

Ben said the graph of the inequality

Mathematics
1 answer:
Ksivusya [100]3 years ago
7 0

Answer:

Ben is incorrect

The solutions are x>-3 and x < 3

Step-by-step explanation:

we have

-x^{2} +9 > 0

Multiply by -1 both sides

x^{2} -9 < 0

Adds 9 both sides

x^{2} < 9

The solutions are

x < 3

and

-x < 3 -----> Multiply by -1 both sides ----> x > -3

therefore

The solution is the interval (-3,3)

Ben is incorrect

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8 0
3 years ago
If y=e5t is a solution to the differential equation
a_sh-v [17]

Answer:

k = 30, y(t) = C_1e^{5t}+C_2e^{6t}

Step-by-step explanation:

Since y=e^{5t} is a solution, then it must satisfy the differential equation. So, we calculate the derivatives and replace the value in the equation. We have that

\frac{d^2y}{dt^2} = 25 e^{5t},\frac{dy}{dt} = 5e^{5t}

Then, replacing the derivatives in the equation we have:

25e^{5t}-11(5)e^{5t}+ke^{5t}=0 e^{5t}(25-55+k) =0

Since e^{5t} is a positive function, we have that

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Now, consider a general solution y(t) = Ae^{rt}, A \in \mathbb{R}, then, by calculating the derivatives and replacing them in the equation, we get

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We already know that r=5 is a solution of the equation, then we can divide the polynomial by the factor (r-5) to the get the other solution. If we do so, we get that (r-6)=0. So the other solution is r=6.

Therefore, the general solution is

y(t) = C_1e^{5t}+C_2e^{6t}

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3 years ago
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