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vovikov84 [41]
2 years ago
13

A 41 gram sample of a substance that's used to detect explosives has a k-value of 0.1392. Find the substance's half life, in day

s.
Mathematics
1 answer:
-BARSIC- [3]2 years ago
5 0

Answer:

The substance half-life is of 4.98 days.

Step-by-step explanation:

Equation for an amount of a decaying substance:

The equation for the amount of a substance that decay exponentially has the following format:

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

In which k is the decay rate, as a decimal.

k-value of 0.1392.

This means that:

A(t) = A(0)e^{-0.1392t}

Find the substance's half life, in days.

This is t for which A(t) = 0.5A(0). So

A(t) = A(0)e^{-0.1392t}

0.5A(0) = A(0)e^{-0.1392t}

e^{-0.1392t} = 0.5

\ln{e^{-0.1392t}} = \ln{0.5}

-0.1392t = \ln{0.5}

t = -\frac{\ln{0.5}}{0.1392}

t = 4.98

The substance half-life is of 4.98 days.

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Greg and Erin start at the same point and begin running in different directions. Greg is running east at a speed of 7 miles per
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Answer: The time at which the distance between the two is 150 miles is 1.3 hr.

Step-by-step explanation:

Step 1: Sketch the problem as shown in the attached image.

The problem can be solved using Pythagoras theorem since the sketch is a right angled triangle.

It follows the equation x² + y² = 15².

The distance covered by Greg is given by <em>x mi</em>, and that of Erin is given by <em>y mi</em>.

Step 2: To derive the distance covered by Erin and Greg, we use the formula <em>Speed = distance ÷ time.</em>

Which by cross-multiplying gives <em>distance = speed × time</em>.

Let time taken to cover the distance be <em>t h</em>.

Given that Speed of Erin is 9 mph and that of Greg is 7 mph.

Hence, distance covered by Greg, x = 7 × t = 7t.

Distance covered by Erin, y = 9 × t = 9t.

Step 3: Insert the terms x and y into the Pythagoras equation x² + y² = 15² and solve for <em>time t.</em>

(7t)² + (9t)² = 15²

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(49 + 81)t² = 225

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If any of the points belong to the equation, then the equality will be met.

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3 = 36 - 27

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