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3 years ago

How to answer h/4 ≤ 2/7

Mathematics

1 answer:

Serjik [45]3 years ago

4 0

I feel you, headaches suck.

Your answer would be h ≤ 8/7

Step 1 :

Simplify —

Equation at the end of step 1 :

h 2

— - — ≤ 0

4 7

Step 2 :

Simplify —

Equation at the end of step 2 :

h 2

— - — ≤ 0

4 7

Step 3 :

Calculating the Least Common Multiple :

3.1 Find the Least Common Multiple

The left denominator is : 4

The right denominator is : 7

After calculating the multipliers you get h ≤ 8/7

Hope this helps!

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3 years ago

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2 years ago

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2 years ago

Ben consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Ben's body decr

Airida [17]

Answer:

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

Step-by-step explanation:

After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.

This means that the amount of caffeine after t hours is given by:

$A(t) = A(0)e^{-kt}$

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.

1 - 0.2722 = 0.7278, thus, $A(10) = 0.7278A(0)$ . We use this to find k.

$A(t) = A(0)e^{-kt}$

$0.7278A(0) = A(0)e^{-10k}$

$e^{-10k} = 0.7278$

$\ln{e^{-10k}} = \ln{0.7278}$

$-10k = \ln{0.7278}$

$k = -\frac{\ln{0.7278}}{10}$

$k = 0.03177289938
$

Then

$A(t) = A(0)e^{-0.03177289938t}$

What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?

We have to find find A(5), as a function of A(0). So

$A(5) = A(0)e^{-0.03177289938*5}$

$A(5) = 0.8531$

The decay factor is:

1 - 0.8531 = 0.1469

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

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3 years ago