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2 years ago

Ming rented a bike from Castel's Bikes. It

Mathematics

1 answer:

Marina CMI [18]2 years ago

5 0

Answer:

Ming rented the bike for 8 hours. Hope this helps!

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A large tank is filled to capacity with 300 gallons of pure water. brine containing 5 pounds of salt per gallon is pumped into t

Licemer1 [7]

If $A(t)$ is the amount of salt in the tank at time $t$ , then the rate at which this amount changes over time is given by the ODE

$A'(t)=\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{5\text{ lb}}{1\text{ gal}}-\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{300+(3-3)t\text{ gal}}$

$A'(t)+\dfrac1{100}A(t)=15$

We're told that the tank initially starts with no salt in the water, so $A(0)=0$ .

Multiply both sides by an integrating factor, $e^{t/100}$ :

$e^{t/100}A'(t)+\dfrac1{100}e^{t/100}A(t)=15e^{t/100}$
$\left(e^{t/100}A(t)\right)'=15e^{t/100}$
$e^{t/100}A(t)=1500e^{t/100}+C$
$A(t)=1500+Ce^{-t/100}$

Since $A(0)=0$ , we have

$0=1500+C\implies C=-1500$

so that the amount of salt in the tank over time is given by

$A(t)=1500(1-e^{-t/100})$

After 10 minutes, the amount of salt in the tank is

$A(10)=1500(1-e^{-1/10})\approx142.74\text{ lb}$

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3 years ago

What is the sum of the angle measures of 24 - gon

Wewaii [24]

$\bf \textit{sum of all \underline{interior angles} in a polygon}\\\\ S=180(n-2)~~ \begin{cases} n=\textit{number of sides}\\ \cline{1-1} n=24 \end{cases}\implies \begin{array}{llll} S=180(24-2)\\\\ S=3960 \end{array}$

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2 years ago

-2(x-4)^2+1 in standard form

zepelin [54]

Answer:

the standard form is : -2x²+16x -31

Step-by-step explanation:

hello :

-2(x-4)²+1 = -2(x²-8x+16)+1 = -2x²+16x-32+1

-2(x-4)²+1 =-2x²+16x -31

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2 years ago

For the inverse variation equation xy = k, what is the constant of variation, k, when x = 7 and y = 3?

Artyom0805 [142]

Answer:

k=21

Step-by-step explanation:

x=7 X y=3 = 21

7 x 3 = 21

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2 years ago

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A bus and a car leave Houston at the same time and travel in opposite directions. The bus

Vlada [557]

Answer:

They will be 400 mi apart after 4 hours.

Step-by-step explanation:

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2 years ago