If a substance has a half life of 850 years, and there are 35 milligrams present now, how long will it take for the substance to be reduced to 10 miligrams calculus
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dP/dt = kA
where k = proportionality constant, A = amount of subtance.
Integrating that equation yields,
A = ce^(kt)
where c = constant of integration.
The constant of integration is represented mostly as an initial amount of substance.
We have given two initial condition:
(1) t = 0, A = 35 milligrams (present)
(2) t = 850 years, A = 35/2 milligrams (half-life)
We are going to solve for c:
35 = ce^0
c = 35
Next, solving for k:
35/2 = 35e^(k*850)
1/2 = e^(k*850)
Multiplying natural logarithm on both sides to bring down k:
ln (1/2) = k*850
k = ln (1/2) / 850
k = -0.00081547
Finally, the time when the amount of substance has 10 milligrams remaining is:
10 = 35e^(-0.00081547*t)
10/35 = e^(-0.00081547*t)
Multiplying natural logarithm on both sides to bring down t:
ln (2/7) = -0.00081547*t
t = ln (2/7) / -0.00081547
t = 1536.25 years (ANSWER)
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50 dozen donuts should be produced before your average cost per dozen drops to $2.45
Let x be the number of dozen donuts produced.
The total cost to produce x dozen donuts is:
Total cost = cost of raw materials + overhead costs
Total cost = 0.65x + 0.55x
Total cost = 1.20x
The average cost per dozen can be expressed as:
Average cost per dozen = Total cost / number of dozens
2.45 = 1.20x / x
To solve for x, we can cross-multiply and simplify:
2.45x = 1.20x
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Therefore, you must produce 50 dozen donuts before your average cost per dozen drops to $2.45.
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What is the opposite of 10?
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Answer:
-10
Step-by-step explanation:
Answer:
1. 5.4
2. The additive inverse is the negative value, -10.
The multiplicative inverse (reciprocal) is 1/10.
Step-by-step explanation:
1. Since the value within the absolute value is not negative then the value remains the same.
2, The opposite of positive 10 could be -10. The reciprocal is 1/10.
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68% percentage of the balls weigh within one standard deviation of the mean. Option b is correct.
The weights of tennis balls are normally distributed, with the mean being 5.15 ounces and the standard deviation being 0.10. what percentage of the balls weigh within one standard deviation of the mean to be determined.
What is the empirical rule?
Empirical Rule is defined as an elongation of the prior reading Understanding the Normal Distribution. In the prior reading, the aim was to develope an instinct of the relations between lowered probability and expanded distance from the mean.
Since, from the empirical rule, it can be said that 68% percent of the balls weigh within one standard deviation of the mean because Approx 68% of the data occurs within 1 Standard Deviation of the mean.
Thus, 68% percentage of the balls weigh within one standard deviation of the mean. Option b is correct.
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The answer is 68%.
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(Apparently the answer has to be 20 long so im judt adding in this note, hi!)
(1) 4/(2+root3+root7)
(2) 4/(2root3+root5)
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