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2 years ago

Solve For X. 5 - 2x^2 = -15

Mathematics

2 answers:

Dvinal [7]2 years ago

4 0

Answer:

$\sqrt{10}$

Step-by-step explanation:

5 - 2x^2 = -15

2x^2 = 20

x^2=10

x= $\sqrt{10}$

DiKsa [7]2 years ago

3 0

-15-5= -20
Thus, -2x^2 = -20
Then -20/-2= 10
So, x^2 = 10
When you square root both of them, the answer is root 10

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(b) Sugar flows in at a rate of

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and flows out at a rate of

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so that the net rate of change of $A(t)$ is governed by the ODE,

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Multiply both sides by the integrating factor $e^{7t/1080}$ to condense the left side into the derivative of a product:

$e^{\frac{7t}{1080}}A'(t)+\dfrac7{1080}e^{\frac{7t}{1080}}A(t)=\dfrac{49}{100}e^{\frac{7t}{1080}}$

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Integrate both sides:

$e^{\frac{7t}{1080}}A(t)=\displaystyle\frac{49}{100}\int e^{\frac{7t}{1080}}\,\mathrm dt$

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Given that $A(0)=0$ , we find

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so that the amount of sugar at any time $t$ is

$\boxed{A(t)=\dfrac{378}5\left(1-e^{-\frac{7t}{1080}}\right)}$

(c) As $t\to\infty$ , the exponential term converges to 0 and we're left with

$\displaystyle\lim_{t\to\infty}A(t)=\frac{378}5$

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