so the 5 gallons ones is 40% acid, how much acid solute is in it anyway? well just 40% of 5 or namely 0.4*5 = 2 gallons.
the 3 gallons one is 50%, likewise it has 0.50 * 3 = 1.5 gallons of acid solute in it.
3/4 − 2/5 in a fraction
2 answers:
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Answer:
And if we integrate both sides we got:
Where C is a constant., we can rewrite the expression like this:
If we square both sides we got:
If we use the initial condition we have that:
And we can solve for C like this:
And now we can find the derivate of the function and we got:
Using the condition we got:
k= 1
And then the model is defined as:
And for t =12 months we have:
Step-by-step explanation:
For this case we cna use the proportional model given by:
Where k is a proportional constant, P the population and the represent the number of months
For this case we know the following initial condition and
we can rewrite the differential equation like this:
And if we integrate both sides we got:
Where C is a constant., we can rewrite the expression like this:
If we square both sides we got:
If we use the initial condition we have that:
And we can solve for C like this:
And now we can find the derivate of the function and we got:
Using the condition we got:
k= 1
And then the model is defined as:
And for t =12 months we have:
In order to answer you need to keep in mind what is a logarithm:
logb x = n is the equivalent of asking "you should raise the base b <span>to <span>what number n</span></span> in order to get x?": bⁿ = x
From this follows that b must be positive, otherwise the function is not defined everywhere in R: for example, take log(-2) x = 0.5 ? This means:
=√(-2) which is impossible in R.
Therefore, both answers A and C are not correct because they take in consideration negative values.
If we take the base between 0 and 1 excluded, we have a fraction whose denominator is bigger than the numerator. Such a fraction, elevated to increasing exponents get smaller, for example:
(1/2)² = 1/4
(1/2)³ = 1/8
(1/2)⁴ = 1/16
Therefore the function is dereasing and answer B is incorrect.
The right answer is, therefore, D) b > 1.
logb x = n is the equivalent of asking "you should raise the base b <span>to <span>what number n</span></span> in order to get x?": bⁿ = x
From this follows that b must be positive, otherwise the function is not defined everywhere in R: for example, take log(-2) x = 0.5 ? This means:
Therefore, both answers A and C are not correct because they take in consideration negative values.
If we take the base between 0 and 1 excluded, we have a fraction whose denominator is bigger than the numerator. Such a fraction, elevated to increasing exponents get smaller, for example:
(1/2)² = 1/4
(1/2)³ = 1/8
(1/2)⁴ = 1/16
Therefore the function is dereasing and answer B is incorrect.
The right answer is, therefore, D) b > 1.
<HAC = 16.26 degrees
see the attachment for detailed solution
see the attachment for detailed solution