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2 years ago

Θ এর কোন মানের জন্য sin2θ+cos2θ= 1 হয় ?

Mathematics

1 answer:

Hitman42 [59]2 years ago

3 0

What language is that seriously

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A tank contains 30 lb of salt dissolved in 500 gallons of water. A brine solution is pumped into the tank at a rate of 5 gal/min

Dmitry [639]

At any time $t$ (min), the volume of solution in the tank is

$500\,\mathrm{gal}+\left(5\dfrac{\rm gal}{\rm min}-5\dfrac{\rm gal}{\rm min}\right)t=500\,\mathrm{gal}$

If $A(t)$ is the amount of salt in the tank at any time $t$ , then the solution has a concentration of $\dfrac{A(t)}{500}\dfrac{\rm lb}{\rm gal}$ .

The net rate of change of the amount of salt in the solution, $A'(t)$ , is the difference between the amount flowing in and the amount getting pumped out:

$A'(t)=\left(5\dfrac{\rm gal}{\rm min}\right)\left(\left(2+\sin\dfrac t4\right)\dfrac{\rm lb}{\rm gal}\right)-\left(5\dfrac{\rm gal}{\rm min}\right)\left(\dfrac{A(t)}{50}\dfrac{\rm lb}{\rm gal}\right)$

Dropping the units and simplifying, we get the linear ODE

$A'=10+5\sin\dfrac t4-\dfrac A{10}$

$10A'+A=100+50\sin\dfrac t4$

Multiplying both sides by $e^{10t}$ allows us to identify the left side as a derivative of a product:

$10e^{10t}A'+e^{10t}A=\left(100+50\sin\dfrac t4\right)e^{10t}$

$\left(e^{10}tA\right)'=\left(100+50\sin\dfrac t4\right)e^{10t}$

$e^{10t}A=\displaystyle\int\left(100+50\sin\dfrac t4\right)e^{10t}\,\mathrm dt$

Integrate and divide both sides by $e^{10t}$ to get

$A(t)=10-\dfrac{200}{1601}\cos\dfrac t4+\dfrac{8000}{1601}\sin\dfrac t4+Ce^{-10t}$

The tanks starts off with 30 lb of salt, so $A(0)=30$ and we can solve for $C$ to get a particular solution of

$A(t)=10-\dfrac{200}{1601}\cos\dfrac t4+\dfrac{8000}{1601}\sin\dfrac t4+\dfrac{32,220}{1601}e^{-10t}$

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3 years ago

Solving simple quadratic equations.

Umnica [9.8K]

Answer:

x=5

Step-by-step explanation:

the square root of 25 is 5 and 5*5=25 so the answer is 5

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2 years ago

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(-8)+(-19) i will give brainllest

MrRissso [65]

Answer:

-27

Step-by-step explanation:

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2 years ago

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Last week a pound of strawberries cost $4. This week they are 24% more expensive. What is the current price of a pound of strawb

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Answer:

$5.96

Step-by-step explanation:

I divided 4 by 100 then multipley by 24

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2 years ago

What are the fractions from least to greatest 2/3 2/9 5/6 11/18

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Analogicaly as in the previous question - firstly let's find the common denominator for those fractions:

2/3 = 12/18
2/9 = 4/18
5/6 = 15/18
11/18 = 11/18 :)

From the least to the greatest:

2/9, 11/18, 2/3, 5/6

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3 years ago

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Θ এর কোন মানের জন্য sin2θ+cos2θ= 1 হয় ?​

Θ এর কোন মানের জন্য sin2θ+cos2θ= 1 হয় ?