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3 years ago

Consider that lines a and b are parallel. What is the measurement of ∠12?

Mathematics

1 answer:

tia_tia [17]3 years ago

5 0

76 degrees

∠4 + 42 + 62 = 180

∠4 = 76 degrees; therefore,∠12 also equals 76 degrees

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3 years ago

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Two cyclists, 55 miles apart, start riding toward each other at the same time. One cycles 5 miles per hour faster than the other

tangare [24]

Answer:

r = 6 mph and f = 11 mph

Step-by-step explanation:

Representations:

1) speed of faster cyclist: f = r + 5

2) speed of slower cyclist: r

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mixer [17]

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$\dfrac{\mathrm dA}{\mathrm dt}=\underbrace{\dfrac{11\text{ lb}}{1\text{ gal}}\times\dfrac{44\text{ gal}}{1\text{ min}}}_{\text{rate in}}-\underbrace{\dfrac{A(t)}{200+(44-11)t}\times\dfrac{11\text{ gal}}{1\text{ min}}}_{\text{rate out}}$
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Find the integrating factor:

$\mu(t)=\exp\left(\displaystyle\int\frac{11}{200+33t}\,\mathrm dt\right)=(200+33t)^{1/3}$

Distribute $\mu(t)$ along both sides of the ODE:

$(200+33t)^{1/3}A'(t)+11(200+33t)^{-2/3}A(t)=484(200+33t)^{-1/3}$
$\bigg((200+33t)^{1/3}A(t)\bigg)'=484(200+33t)^{-1/3}$
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Since $A(0)=100$ , we get

$100=22(200)^{2/3}+C\implies C\approx-652.39$

so that the particular solution for $A(t)$ is

$A(t)=22(200+33t)^{2/3}-652.39$

The tank becomes full when the volume of solution in the tank at time $t$ is the same as the total volume of the tank:

$200+(44-11)t=500\implies 33t=300\implies t\approx9.09$

at which point the amount of salt in the solution would be

$A(9.09)\approx733.47\text{ lb}$

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IrinaVladis [17]

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2 years ago

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