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MAVERICK [17]
3 years ago
13

Without graphing, classify the following system as independent, dependent, or inconsistent.

Mathematics
1 answer:
Vlada [557]3 years ago
5 0
Independent I’m pretty sure
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A typical cup of coffee contains about 100 mg of caffeine and every hour approximately 16% ofthe amount of caffeine inthe body i
Over [174]

Answer:

a) \frac{dC}{dt} = rC

And for this case we can rewrite the model like this:

\frac{dC}{C} = r dt

If we integrate both sides we got:

ln C = rt + k

If we use exponentials for both sides we got:

C = e^{rt} e^k = C_o e^{rt}

For this case C_o = 100 mg and r = -0.16

So then our model would be given by:

C(t) = 100 e^{-0.16 t}

Where t represent the number of hours

b) C(5) = 100 e^{-0.16*5}= 44.9329

Step-by-step explanation:

Part a

For this case we can assume the proportional model given by:

\frac{dC}{dt} = rC

And for this case we can rewrite the model like this:

\frac{dC}{C} = r dt

If we integrate both sides we got:

ln C = rt + k

If we use exponentials for both sides we got:

C = e^{rt} e^k = C_o e^{rt}

For this case C_o = 100 mg and r = -0.16

So then our model would be given by:

C(t) = 100 e^{-0.16 t}

Where t represent the number of hours

Part b

For this case we can replace the value t=5 into the model and we got:

C(5) = 100 e^{-0.16*5}= 44.9329

7 0
3 years ago
Question 3
zlopas [31]

Answer:

Area = 19.05 feet squared

Step-by-step explanation:

By applying sine rule in ΔABC,

sin(∠CAB) = \frac{\text{Opposite side }}{\text{Hypotenuse}}

sin(60°) = \frac{BC}{AC}

\frac{\sqrt{3}}{2}=\frac{BC}{4}

BC = 2√3

Area of a parallelogram is given by the formula,

Area = Base × Height

        = 5.5 × 2√3

        = 11√3

        = 19.05 ft²

Therefore, answer is Area = 19.05 ft squared.

3 0
3 years ago
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