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harina [27]
3 years ago
5

This graph shows how the length of time a canoe is rented is related to the rental cost. What is the rate of change shown in the

graph? Canoe Rental N Cost (9) g Time (hours) O A. $6/hour O B. 6 hours/dollar O c. $3/hour D. 3 hours/dollar​

Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
4 0

I'm pretty sure that the answer is A

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A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose th
Vsevolod [243]

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

of sugar. Let S(t) be the amount of sugar in the tank at time t. Then S(0)=25.

Sugar is added to the tank at a rate of <em>P</em> lb/min, and removed at a rate of

\left(1\frac{\rm gal}{\rm min}\right)\left(\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm gal}\right)=\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm min}

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}

Separate variables, integrate, and solve for <em>S</em>.

\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt

\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt

-100\ln\left|P-\dfrac S{100}\right|=t+C

\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t

P-\dfrac S{100}=e^{C-100t}=e^Ce^{-100t}=Ce^{-100t}

\dfrac S{100}=P-Ce^{-100t}

S(t)=100P-100Ce^{-100t}=100P-Ce^{-100t}

Use the initial value to solve for <em>C</em> :

S(0)=25\implies 25=100P-C\implies C=100P-25

\implies S(t)=100P-(100P-25)e^{-100t}

The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

1000\,\mathrm{gal}+\left(-1\dfrac{\rm gal}{\rm min}\right)t=5\,\mathrm{gal}\implies t=995\,\mathrm{min}

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

of sugar, so we pick <em>P</em> such that

S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}

5 0
3 years ago
What is the approximate square root of 97
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Your answer is 9.849
8 0
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Determine the intercepts of the line.
Fudgin [204]

Answer:

x-int = (-40,0)

y-int = (0,15)

Step-by-step explanation:

:D

7 0
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Solve (algebraically by any method) 3x to the 2 power +8x - 4= 0
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3 x^{2} + 8x +(-4) = 0
x = <u>-b + √ b² - 4ac</u>
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x = -<u>8 + √16
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x =<u> -2 </u>             x = -2<u>
</u>      3   <u>
</u>
5 0
3 years ago
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