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3 years ago

Can anyone help with fine answer for this question?

Mathematics

1 answer:

Reika [66]3 years ago

5 0

Answer:

domain: all real numbers

range: y≥0

Step-by-step explanation:

This graph includes all real numbers for values of x (the domain), but only includes 0 and above for the y values (the range)

Hope this helps :)

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Evaluate 42 ÷ (5 − 3)

Sidana [21]

You do 5-3 and you get 2 then divide 42 by 2 and your answer is 21

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4 years ago

Read 2 more answers

A city park has a large circular garden with a path around it. The diameter of the garden is 60 feet. Jason works for the City P

Angelina_Jolie [31]

Answer:

He will cover 2,827.433 feet² area of the park with plant food.

Step-by-step explanation:

The diameter of the garden is 60 feet and the radius will be 60 feet/2 = 30 feet.

diameter= 60 feet

radius = diameter/ 2= 60/2= 30 feet

The area of the circle can be found by the formula πr²

Area= πr²=π(30)²

Area = 900π= 2,827.433 feet²

He will cover 2,827.433 feet² area of the park with plant food.

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3 years ago

Compare. Choose the correct symbol.<br> 1 [?] - 1<br> ><br> <<br> =

lora16 [44]

Answer:

Step-by-step explanation:

The top symbol (>) means greater then, the middle symbol (<) means less then, and the bottom symbol (=) means equal to.

1, is greater then -1, so the correct symbol is

8 0

4 years ago

Two events A and B are _______ if the occurrence of one does not affect the probability of the occurrence of the other.

igomit [66]

Answer:

Independent

Step-by-step explanation:

From the word independent, which means being able ot stand alone, that is the absence or presence of one has no impact on the outcome of each phenomenon. Two events A and B are said to be independent, if the occurence of one has no bearing on the probability or chance that B will occur. This means that each event occurs without reliance on the occurence of the other. This is different from mutually exclusive event whereby event A has direct bearing in the probability of the occurence of event B.

7 0

3 years ago

A 500 gallon tank initially contains 200 gallons of water with 5 lbs of salt dissolved in it. Water enters the tank at a rate of

Lapatulllka [165]

Until the concerns I raised in the comments are resolved, you can still set up the differential equation that gives the amount of salt within the tank over time. Call it $A(t)$ .

Then the ODE representing the change in the amount of salt over time is

$\dfrac{\mathrm dA}{\mathrm dt}=\text{rate in}-\text{rate out}$
$\dfrac{\mathrm dA}{\mathrm dt}=\dfrac{2\text{ gal}}{1\text{ hr}}\times\dfrac{\frac15(1+\cos t)\text{ lbs}}{1\text{ gal}}-\dfrac{2\text{ gal}}{1\text{ hr}}\times\dfrac{A(t)\text{ lbs}}{500+(2-2)t}$
$\dfrac{\mathrm dA}{\mathrm dt}=\dfrac25(1+\cos t)-\dfrac1{250}A(t)$

and this with the initial condition $A(0)=5$

You have

$\dfrac{\mathrm dA}{\mathrm dt}+\dfrac1{250}A(t)=\dfrac25(1+\cos t)$
$e^{t/250}\dfrac{\mathrm dA}{\mathrm dt}+\dfrac1{250}e^{t/250}A(t)=\dfrac25e^{t/250}(1+\cos t)$
$\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/250}A(t)\right]=\dfrac25e^{t/250}(1+\cos t)$

Integrating both sides gives

$e^{t/250}A(t)=100e^{t/250}\left(1+\dfrac1{62501}\cos t+\dfrac{250}{62501}\sin t\right)+C$
$A(t)=100\left(1+\dfrac1{62501}\cos t+\dfrac{250}{62501}\sin t\right)+Ce^{-t/250}$

Since $A(0)=5$ , you get

$5=100\left(1+\dfrac1{62501}\right)+C\implies C=-\dfrac{5937695}{62501}$

so the amount of salt at any given time in the tank is

$A(t)=100\left(1+\dfrac1{62501}\cos t+\dfrac{250}{62501}\sin t\right)-\dfrac{5937695}{62501}e^{-t/250}$

The tank will never overflow, since the same amount of solution flows into the tank as it does out of the tank, so with the given conditions it's not possible to answer the question.

However, you can make some observations about end behavior. As $t\to\infty$ , the exponential term vanishes and the amount of salt in the tank will oscillate between a maximum of about 100.4 lbs and a minimum of 99.6 lbs.

5 0

4 years ago