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3 years ago

6

JC is making a poster for Bike Safety Week. The diameter of circle A is 18 in. If the area of circle B is the area of circle A,

what is the area of circle B? (Use 3.14 for .)

1 answer:

Anni [7]3 years ago

8 0

Answer:

254.34

Step-by-step explanation:

area = $\pi r^{2}$

area B = 3.14 x $(\frac{18}{2})^{2}$ = 254.34

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Hello are you there my i please have some help

Katarina [22]

Answer:

3^-5

Step-by-step explanation:

x^-3=1/x^3

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3 years ago

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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4 years ago

If meg cycles 6.2 km every morning how many feet are in 6.2 given that 1 mile = 1.609 and 1 mile =5,280

Minchanka [31]

You just have to multiply. 6.2x1.609x5,280 which would give you 8501.72.

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3 years ago

Travis traveled 330 miles in 6 hours. How far did he travel per hour if he traveled at the same rate?

andrey2020 [161]

Answer:

The time traveled at 50 mp

Step-by-step explanation:

.

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