Answer:
a) 8.13
b) 4.10
Step-by-step explanation:
Given the rate of reaction R'(t) = 2/t+1 + 1/√t+1
In order to get the total reaction R(t) to the drugs at this times, we need to first integrate the given function to get R(t)
On integrating R'(t)
∫ (2/t+1 + 1/√t+1)dt
In integration, k∫f'(x)/f(x) dx = 1/k ln(fx)+C where k is any constant.
∫ (2/t+1 + 1/√t+1)dt
= ∫ (2/t+1)dt+ ∫ (1/√t+1)dt
= 2∫ 1/t+1 dt +∫1/+(t+1)^1/2 dt
= 2ln(t+1) + 2(t+1)^1/2 + C
= 2ln(t+1) + 2√(t+1) + C
a) For total reactions from t = 1 to t = 12
When t = 1
R(1) = 2ln2 + 2√2
≈ 4.21
When t = 12
R(12) = 2ln13 + 2√13
≈ 12.34
R(12) - R(1) ≈ 12.34-4.21
≈ 8.13
Total reactions to the drugs over the period from t = 1 to t= 12 is approx 8.13.
b) For total reactions from t = 12 to t = 24
When t = 12
R(12) = 2ln13 + 2√13
≈ 12.34
When t = 24
R(24) = 2ln25 + 2√25
≈ 16.44
R(12) - R(1) ≈ 16.44-12.34
≈ 4.10
Total reactions to the drugs over the period from t = 12 to t= 24 is approx 4.10
Answer: 100 minutes
Step-by-step explanation:
With the given information, we can use a proportion to figure out how long it would take for Jen to bike 30 miles.
I'll give a practice problem to help explain it a bit better.
Here, let's try to solve 45% of of 60.
First, we convert the percentage into a decimal. To turn any percentage into a decimal you move the point two spaces to the left.
That means 45% as a decimal is .45.
Next, we multiply our number, 60, by the decimal .45.
60×.45=27.
That means 45% of 60 is 27.
To sum it all up, you have to get the percentage, move the decimal point two spaces to the left, and multiply it by the number you were trying to find the percentage of.
Have a wonderful day! :)
The formula for the circumference of a circle is pi * r * 2
First we solve for r (the radius)
pi*r*2 = C
pi*r*2 = 18
Divide 18 by 2
pi*r = 9
Then divide 9 by 3.14
pi= 9/3.14 which is 2.866
The diameter is 2 times length of the radius so multiply 2.866 by 2
The diameter is about 5.732
(And you can round of course)
Hope that helped
No 5/8 is bigger because half of 8 is 4 and 5 is greater than 4
