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:
x = 3
Step-by-step explanation:
7(x + 1) + 2 = 5x + 15
~Simplify left side
7x + 7 + 2 = 5x + 15
~Combine like terms
7x + 9 = 5x + 15
~Subtract 9 to both sides
7x = 5x + 6
~Subtract 5x to both sides
2x = 6
~Divide 2 to both sides
x = 3
Best of Luck!
Answer:
(c) For p = 15, 
leaves a remainder of -2 when divided by (x-3).
Step-by-step explanation:
Here, The dividend expression is = E(x)
The Divisor = (x-3)
Remainder = -2
Now, by <u>REMAINDER THEOREM</u>:
Dividend = (Divisor x Quotient) + Remainder
If ( x -3 ) divides the given polynomial with a remainder -2.
⇒ x = 3 is a solution of given polynomial E(x) - (-2) =
= S(x)
Now, S(3) = 0
⇒
or, p =1 5
Hence, for p = 15, leaves a remainder of -2 when divided by (x-3).
Answer: C 4
Step-by-step explanation:
Use the formula: distance = rate x time
We can say that train 1 travels a distance of x, and train 2 travels a distance of 700 - x
The rate of train 1 is 75 mph, and the rate of train 2 is 100 mph
The time traveled for the two trains will be the same. We can represent that with the variable t.
We have the following equation for train 1:
x = 75t
For train 2, we have this equation:
700 - x = 100t
Use the Substitution Method by replacing x in the equation for train 2 with the value 75t.
700 - 75t = 100t
700 = 175t
700/175 = 4 hours.
It will take 4 hours for the two trains to meet.
Answer:
Your selection is appropriate
Step-by-step explanation:
A negative exponent in the numerator is equivalent to a positive exponent in the denominator, and vice versa.
... a⁻² = 1/a²
____
2⁴ multiplies the variable expression no matter which way it is written.
