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Semmy [17]
2 years ago
11

How long will it take before twenty percent of our 1,000-gram sample of uranium-235 has decayed? [See Section 6.6 Example 13] Th

e decay equation is A(t)=A_0e^{Kt} , where t is the time for the decay, and K is the characteristic of the material. Suppose T is the time it takes for half of the unstable material in a sample of a radioactive substance to decay, called its half-life. Prove that K= \frac{ln0.5}{T} . What is T for the uranium-235? Show the steps of your reasoning.
Mathematics
1 answer:
horsena [70]2 years ago
8 0

Answer:

From what I can see of the problem, you CANNOT solve for the half-life of U 235 AND then solve for the length of time to determine the 20% decay.

U-235 half-life is 704,000,000 years. (Wikipedia)

The elapsed time formula = half-life * [log (Beginning Amount / ending amount) / log 2]

elapsed time = 7.04 x 10^8 * [log (100 % / 80%) / log 2]

elapsed time =7.04 x 10^8 *  [log (1.25) / .30103]

elapsed time =7.04 x 10^8 *  [0.096910 / .30103]

elapsed time = 7.04 x 10^8 *  0.321928047

elapsed time = 226,637,000 years

Step-by-step explanation:

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75th term

Step-by-step explanation:

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6 points Emily’s family needs to rent a moving truck to move their belongings to a different house. The rental cost for Trucks-A
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Answer/Step-by-step explanation:

Equation to represent the daily rental cost for each type of truck can be written as follows:

Daily rental cost for Trucks-A-Lot = 42 + 0.72m

Daily rental cost for Move-in-Truckers = 70 + 0.12m

Where, m = Emily's mileage

To determine the number of miles for which the truck cost the same amount, set both equations equal to each other and solve for m.

42 + 0.72m = 70 + 0.12m

Collect like terms

0.72m - 0.12m = 70 - 42

0.6m = 28

Divide both sides by 0.6

\frac{0.6m}{0.6} = \frac{28}{0.6}

m = 46.7

At approximately 47 miles, both trucks would cost the same amount.

Check:

Daily rental cost for Trucks-A-Lot = 42 + 0.72m

Plug in the value of x = 47

= 42 + 0.72(47) = $75.84 ≈ $76

Daily rental cost for Move-in-Truckers = 70 + 0.12m

Plug in the value of x = 47

= 70 + 0.12(47) = $75.64 ≈ $76

7 0
2 years ago
During her pre-college years, Elise won 30% of the swim races she entered. During college, Elise won 20% of the swim races she e
svetoff [14.1K]
During her pre-college years, Elise won 30% of the swim races she entered. During college, Elise won 20% of the swim races she entered. We can conclude that, in high school and college combined, Elise won <span>more than 20% but less than 30% of the races she entered</span>
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A band director uses a coordinate plane to plan as how for a football game. During a show, the drummers will march along the lin
LenaWriter [7]

Answer:

The equation in slope-intercept form for the path of the trumpet players is y=\frac{x}{5}+\frac{12}{5}.

Step-by-step explanation:

Consider the provided information.

The drummers will march along the line y=-5x-8.

The trumpets players will march along a perpendicular line that passes through (-2,2).

The slope of line y=-5x-8 is: m₁ = -5.

The slope of perpendicular lines are: m_1\times m_2=-1

-5\times m_2=-1

m_2=\frac{1}{5}

Hence, the slope of the line should be 1/5.

The line passes through (-2,2).

Now use point slope form to find the equation of line.

y-y_1=m(x-x_1)

Substitute m=1/5, x₁=-2 and y₁ = 2 in above formula.

y-2=\frac{1}{5}(x+2)

y-2=\frac{x}{5}+\frac{2}{5}

y=\frac{x}{5}+\frac{2}{5}+2

y=\frac{x}{5}+\frac{12}{5}

Hence, the equation in slope-intercept form for the path of the trumpet players is y=\frac{x}{5}+\frac{12}{5}.

4 0
2 years ago
Prof. okamoto selects 3 different students to report on 3 different current events. if there are 27 students in the class, in ho
kenny6666 [7]
Consider this option:
C³₂₇=27!/(3!*24!)=25*13*9=2925 ways to select 3 students.
8 0
2 years ago
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