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3 years ago

Question below thanks

Mathematics

1 answer:

Over [174]3 years ago

8 0

Answer:

x = 11

Step-by-step explanation:

Based on the two secants intersecting theorem, thus, we have:

(x + 5)*5 = (38 + 2)2

5x + 25 = (40)2

5x + 25 = 80

5x = 80 - 25 (subtraction property of equality)

5x = 55

Divide both sides by 5

x = 11

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adell [148]

Answer:

$\frac{dx}{dt}=2-\frac{3}{40}x+\frac{y}{15}$

$\frac{dy}{dt}=\frac{3}{40}x-\frac{y}{5}$

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Step-by-step explanation:

We are given that

Tank A contains water=80 gallons

x(0)=20,y(0)=5

Tank B contains water=30 gallons

Rate=4 gallon/min

Concentration of salt is pumped into tank=0.5 pound /gallon of water

Solution pumped from tank A to tank B at the rate=6 gallons/min

Solution pumped from tank B to tank A at the rate=2gallon/min

Solution from tank B is pumped out of the system at the rate=4 gallon/min

We have to find the DE at time t

For x

Rate in= $0.5\times 4+y(t)/30\times 2$

Rate in= $2+y/15$

Rate out= $x/80\times 6$

Rate out=3x/40[/tex]

$\frac{dx}{dt}=$ Rate in-Rate out

$\frac{dx}{dt}=2+y/15-3x/40$

$\frac{dx}{dt}=2-\frac{3}{40}x+\frac{y}{15}$

For y

Rate in= $x/80\times 6$

Rate in=3/40x

Rate out= $y/30\times (4+2)$

Rate out=y/5

$\frac{dy}{dt}=$ Rate in-Rate out

$\frac{dy}{dt}=\frac{3}{40}x-\frac{y}{5}$

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