Answer:
3
Step-by-step explanation:
lim(t→∞) [t ln(1 + 3/t) ]
If we evaluate the limit, we get:
∞ ln(1 + 3/∞)
∞ ln(1 + 0)
∞ 0
This is undetermined. To apply L'Hopital's rule, we need to rewrite this so the limit evaluates to ∞/∞ or 0/0.
lim(t→∞) [t ln(1 + 3/t) ]
lim(t→∞) [ln(1 + 3/t) / (1/t)]
This evaluates to 0/0. We can simplify a little with u substitution:
lim(u→0) [ln(1 + 3u) / u]
Applying L'Hopital's rule:
lim(u→0) [1/(1 + 3u) × 3 / 1]
lim(u→0) [3 / (1 + 3u)]
3 / (1 + 0)
3
Answer:
(6,1)
Step-by-step explanation:
after switching the equations from y=mx+b, graph both equations. you will see that the point of intersection is (6,1)
Let x = the minutes that Tom has remaining before exceeding 500 minutes.
Because he has already used 230 minutes, the total minutes he has is
x + 230
We want this total to be less than or equal to 500 minutes.
Therefore
x + 230 ≤ 500
Answer: x + 230 ≤ 500
Given the equation:

You know that a lab technician finds that a sample of fluid has this pH:

Then, in order to find the hydrogen ion concentration of the fluid, you need to follow these steps:
1. Substitute the pH given in the exercise into the equation:

Multiply both sides by -1:

2. Solve for:

Remember that, by definition:

In this case, you can identify that:

Hence, substituting values and simplifying, you get:

Therefore, the answer is:
Answer:
$248.75
Step-by-step explanation:
We are told that the interest rate is 13% per Annum = 13% per year
Hence, the interest rate in a month = 13% /12
= 1.0833333333% in a month
Tony Giacomin deposited $1600 on July 3rd in a special investment account which earns 13% p.A. Simple interest.
Interest = Principal × rate × time
Rate = 13% = 0.13
Time = July 3rd - November 12 = 132 days
= $1600 × 0.13 × 132/365
= $75.221917808
On August 17th he deposited another $5600 in the account. If he closed the account on November 12th
Interest = Principal × rate × time
Rate = 13% = 0.13
Time = August 17th - November 12 = 87 days
= $5600 × 0.13 × 87/365
= $173.52328767123288
The next step would be to add these Interests together
$173.52328767123288 + $75.221917808
= $248.74520548
Approximately ≈ $248.75
Therefore, his investment that he has earned over this period of time is $248.75