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3 years ago

Is 0.36279979176191 rational or irrational

1 answer:

5 0

Answer is: Irrational because if the answer doesn’t repeat for an example 0.392827263, it’s irrational if it does repeat like this 0.3434343434 it’s rational! Hoped this helped!!

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A bicycle is on sale at a store for 15% off it’s original price. The original price, in dollars, of the bicycle is represented b

ASHA 777 [7]

Answer:

The answer to the question is 2

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2 years ago

How many line segments are in the 20th figure?

Trava [24]

The first figure has 3 line segments.

the second figure has 3+3 =3*2 = 6 line segments

the third figure has 3+3+3 = 3*3 = 9 line segments

the fourth figure has 3+3+3+3=3*4=12 line segments...

so it is clear that:

the 20th figure has 3*20=60 line segments.

Answer: 60

5 0

3 years ago

A swimming pool with a volume of 30,000 liters originally contains water that is 0.01% chlorine (i.e. it contains 0.1 mL of chlo

SpyIntel [72]

Answer:

$R_{in}=0.2\dfrac{mL}{min}$

$C(t)=\dfrac{A(t)}{30000}$

$R_{out}= \dfrac{A(t)}{1500} \dfrac{mL}{min}$

$A(t)=300+2700e^{-\dfrac{t}{1500}},$ A(0)=3000$

Step-by-step explanation:

The volume of the swimming pool = 30,000 liters

(a) Amount of chlorine initially in the tank.

It originally contains water that is 0.01% chlorine.

0.01% of 30000=3000 mL of chlorine per liter

A(0)= 3000 mL of chlorine per liter

(b) Rate at which the chlorine is entering the pool.

City water containing 0.001%(0.01 mL of chlorine per liter) chlorine is pumped into the pool at a rate of 20 liters/min.

$R_{in}=$ (concentration of chlorine in inflow)(input rate of the water)

$=(0.01\dfrac{mL}{liter}) (20\dfrac{liter}{min})\\R_{in}=0.2\dfrac{mL}{min}$

Volume of the pool =30,000 Liter

$Concentration, C(t)= \dfrac{Amount}{Volume}\\C(t)=\dfrac{A(t)}{30000}$

(d) Rate at which the chlorine is leaving the pool

$R_{out}=$ (concentration of chlorine in outflow)(output rate of the water)

$= (\dfrac{A(t)}{30000})(20\dfrac{liter}{min})\\R_{out}= \dfrac{A(t)}{1500} \dfrac{mL}{min}$

(e) Differential equation representing the rate at which the amount of sugar in the tank is changing at time t.

$\dfrac{dA}{dt}=R_{in}-R_{out}\\\dfrac{dA}{dt}=0.2- \dfrac{A(t)}{1500}$

We then solve the resulting differential equation by separation of variables.

$\dfrac{dA}{dt}+\dfrac{A}{1500}=0.2\\$The integrating factor: e^{\int \frac{1}{1500}dt} =e^{\frac{t}{1500}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{1500}}+\dfrac{A}{1500}e^{\frac{t}{1500}}=0.2e^{\frac{t}{1500}}\\(Ae^{\frac{t}{1500}})'=0.2e^{\frac{t}{1500}}$

Taking the integral of both sides

$\int(Ae^{\frac{t}{1500}})'=\int 0.2e^{\frac{t}{1500}} dt\\Ae^{\frac{t}{1500}}=0.2*1500e^{\frac{t}{1500}}+C, $(C a constant of integration)\\Ae^{\frac{t}{1500}}=300e^{\frac{t}{1500}}+C\\$Divide all through by e^{\frac{t}{1500}}\\A(t)=300+Ce^{-\frac{t}{1500}}$

Recall that when t=0, A(t)=3000 (our initial condition)

$3000=300+Ce^{0}\\C=2700\\$Therefore:\\A(t)=300+2700e^{-\dfrac{t}{1500}}$

3 0

3 years ago

What is the area of the shaded region to the nearest tenth?

Aleks04 [339]

Answer:

15.1

Step-by-step explanation:

We know that the area of the circle is $\pi r^{2}$ , but we are looking for the portion of the circle, this means we multiply it by the portion of the circle that is shaded.

Area of shaded region = $\pi r^{2} (\frac{x}{360} )$

where r = 4 and x = 108, the 360 comes from the fact that the total degrees around the circle is 360, so dividing the total amount of degrees by the angle will give us the portion we are looking for.

Area of shaded region = $\frac{108}{360} \pi 4^{2}$ = 15.1

Another way to think about it is that the area of the total circle is $\pi r^{2}$ , multiplying it by a fraction, a number less than 1, would give us a smaller value.

Hope this helps.

5 0

3 years ago

Use the set of ordered pairs to determine whether the relation is a one-to-one function. {(−6,21),(−23,21),(−12,9),(−24,−10),(−2

GenaCL600 [577]

Answer:

the relation is not one-to-one.

Step-by-step explanation:

it can't because every number is in the 4th quadrant.

5 0

3 years ago