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3 years ago

9

Find all real values of t that satisfy the equation t^2 = 324. If you find more than one, then list your values in increasing or

der, separated by commas.

1 answer:

vredina [299]3 years ago

4 0

Answer:

t = -18, 18

Step-by-step explanation:

Take the square root of both sides of the equation.

... t = ±√324 = ±18

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VMariaS [17]

4.5 and maybe 16-64. If they count -

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2 years ago

Evaluate the function:<br><br> f(x)=4x−1, find f(9)

Eddi Din [679]

Answer:

f(9) = 35

Step-by-step explanation:

To solve this, you can take 9 and replace both x's with it and then complete the equation;

f(x) = 4x - 1

f(9) = 4(9) - 1

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2 years ago

7 qt. of a 27% saline solution was mixed

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Answer:

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Step-by-step explanation:

Find how much saline is in both solutions:

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3(0.17)

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Add this together:

1.89 + 0.51

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2.4/10

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3 years ago

$210 at 8% for 7 years

Genrish500 [490]

The answer is $327.60

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3 years ago

Consider the differential equation:

Wewaii [24]

(a) Take the Laplace transform of both sides:

$2y''(t)+ty'(t)-2y(t)=14$

$\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s$

where the transform of $ty'(t)$ comes from

$L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)$

This yields the linear ODE,

$-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s$

Divides both sides by $-s$ :

$Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}$

Find the integrating factor:

$\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C$

Multiply both sides of the ODE by $e^{3\ln|s|-s^2}=s^3e^{-s^2}$ :

$s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}$

The left side condenses into the derivative of a product:

$\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}$

Integrate both sides and solve for $Y(s)$ :

$s^3e^{-s^2}Y(s)=7e^{-s^2}+C$

$Y(s)=\dfrac{7+Ce^{s^2}}{s^3}$

(b) Taking the inverse transform of both sides gives

$y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]$

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that $\frac{7t^2}2$ is one solution to the original ODE.

$y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7$

Substitute these into the ODE to see everything checks out:

$2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14$

5 0

3 years ago