Answer:
The correct answer is (edit: b).
Step-by-step explanation:
The equation r = 6t gives the number of albums released, r, by a record label over time in years, t. If you graph this relations
2 answers:
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Answer:
See Below.
Step-by-step explanation:
We have:
First, we can subtract within the parentheses:
By the properties of exponents:
Approximate. Use a calculator:
Notes:
0.993 is only an approximation, hence the approximately equal sign.
I'm not given the context of the problem, but it's simpler to just simplify in the exponent like so (the fractions cancel):
Full Problem:
The value of Sara's car decreases at a rate of 8% per year.
We will use the exponential decay formula with a set time, given by:
Where a is the initial value, r is the rate, x is the time that has passed (dependent on d), and d is the amount of time for one decrease.
For this problem, we can ignore the initial value.
And since the value decreases at a rate of 8% per year, r = 0.92 (we acquire this from 1 - 0.08).
Part 1) Per Month:
Since it decreases per month, d = 12.
Approximate:
In this case, x is measured in months.
Part 2) Per Week:
Since it decreases per week, d = 52.
Approximate:
In this case, x is measured in weeks.
Part 3) Per Day:
So, d = 365.
Simplify:
In this case, x is measured in days.
Part 4)
So, as d increases, our r increases as well.
Therefore, the smaller the time interval (from months to weeks to days), the higher our rate of decrease is.
Please note that dilation does not affect angles. Thus, if an image is dilated the angle remains the same and does not change.
Therefore, even if is dilated to
by a factor of 1.5 (or by any factor for that matter), the linear dimensions of the original triangle
will either get stretched or get shrunk by a factor of 1.5 but the angles of the original triangle will not be affected in any case.
Please note that this is true for all two dimensional geometric shapes.