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1 year ago

6

This side of square S is twice the diameter of circle C what is the greatest possible number of points of intersection of perime

ter of square S and the circumference of circle C

1 answer:

Dafna1 [17]1 year ago

5 0

Answer:

2

Step-by-step explanation:

C is too small to have more.

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A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound o

Valentin [98]

Answer:

47.25 pounds

Step-by-step explanation:

$\dfrac{dA}{dt}=R_{in}-R_{out}$

<u>First, we determine the Rate In</u>

Rate In=(concentration of salt in inflow)(input rate of brine)

$=(0.5\frac{lbs}{gal})( 6\frac{gal}{min})\\R_{in}=3\frac{lbs}{min}$

Change In Volume of the tank, $\frac{dV}{dt}=6\frac{gal}{min}-4\frac{gal}{min}=2\frac{gal}{min}$

Therefore, after t minutes, the volume of fluid in the tank will be: 100+2t

<u>Rate Out</u>

Rate Out=(concentration of salt in outflow)(output rate of brine)

$R_{out}=(\frac{A(t)}{100+2t})( 4\frac{gal}{min})\\\\R_{out}=\frac{4A(t)}{100+2t}$

Therefore:

$\dfrac{dA}{dt}=3-\dfrac{4A(t)}{100+2t}\\\\\dfrac{dA}{dt}=3-\dfrac{4A(t)}{2(50+t)}\\\\\dfrac{dA}{dt}=3-\dfrac{2A(t)}{50+t}\\\\\dfrac{dA}{dt}+\dfrac{2A(t)}{50+t}=3$

This is a linear differential equation in standard form, therefore the integrating factor:

$e^{\int \frac{2}{50+t}dt}=e^{2\ln|50+t|}=e^{\ln(50+t)^2}=(50+t)^2$

Multiplying the DE by the integrating factor, we have:

$(50+t)^2\dfrac{dA}{dt}+(50+t)^2\dfrac{2A(t)}{50+t}=3(50+t)^2\\\{(50+t)^2A(t)\}'=3(50+t)^2\\$Taking the integral of both sides\\\int \{(50+t)^2A(t)\}'= \int 3(50+t)^2\\(50+t)^2A(t)=(50+t)^3+C $ (C a constant of integration)\\Therefore:\\A(t)=(50+t)+C(50+t)^{-2}$

Initially, 20 pounds of salt was dissolved in the tank, therefore: A(0)=20

$20=(50+0)+C(50+0)^{-2}\\20-50=C(50)^{-2}\\C=-\dfrac{30}{(50)^{-2}} =-30X50^2=-75000$

Therefore, the amount of salt in the tank at any time t is:

$A(t)=(50+t)-75000(50+t)^{-2}$

After 15 minutes, the amount of salt in the tank is:

$A(15)=(50+15)-75000(50+15)^{-2}\\=47.25$ pounds$

8 0

1 year ago

Fill in the blanks. a. A relative-frequency distribution is to a variable as a __________ distribution is to a random variable

RideAnS [48]

Answer:

a. A relative-frequency distribution is to a variable as a ___probability_______ distribution is to a random variable. b. A relative-frequency histogram is to a variable as a _____probability_____ histogram is to a random variable.

Step-by-step explanation:

Probability is a type of mathematics which deals with numerical descriptions of how likely an event would occur, or how likely it is that a the occurrence would be true. The probability of an event is usually between 0 and 1,

where 0 represent impossibility and 1 represents the chance of it occurring.

4 0

2 years ago

What is -1 2/3 + 5/6

Monica [59]

Answer:

-5/6

Step-by-step explanation:

-1 2/3=-5/3

-5/3+5/6=-10/6+5/6=-5/6

5 0

2 years ago

Read 2 more answers

This year, druehl, inc., will produce 57 comma 60057,600 hot water heaters at its plant in delaware, in order to meet expecte

ivolga24 [154]

If one labour works 200 hours per month, the amount of hot water heaters the labour can produce is = 200 × 0.25 = 50 hot water heaters

The demand is to produce 57600 hot water heaters

The number of labourers employed is 57600 ÷ 50 = 1152 labourers

5 0

2 years ago

What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve.

babymother [125]

We can use t=x^2 to solve this
Once we do that we will have simple square equation which we know how to solve.

t^2 + 3t + 2 = 0

t1 = -1
t2 = -2

x1 = √-1 = i
x2 = -i

x3 = √-2 = i√2
x4 = -i√2

Make sure you know that i^2 = -1 and (-i)^2 = -1 which gives us solutions we got...

3 0

2 years ago

Read 2 more answers