Answer:
Refer below
Step-by-step breakdown:
The function behaves as a piecewise function defined as:
a)
We need to evaluate the limit of the function as t approaches infinity. This means determining the maximum number of fish present in the pond as time extends indefinitely.
We consider the second segment of the equation since t fits into that range, whereby t is infinite, clearly exceeding 8.
This indicates that the maximum fish population in this pond is 1600, regardless of the time.
b)
A function is considered continuous at a specific point if the limit and the function value at that point are the same.
The function value at t = 8, according to the second part of the equation, is:
We observe that a value exists, and the limit approaches this as t nears 8.
<pthus>the function maintains continuity at t = 8
c)
We seek to determine if there exists a "time" during t from 0 to 6 when the fish count in the pond reaches 250. Substituting 250 into N(t) allows us to solve for t using the first portion of the piecewise function as shown below:
The time is 4 years when the fish count in the pond becomes 250
</pthus>
The options are: • only quadrant 1 • only quadrants 1 and 4. The reasoning is that the time since the storm began is always positive, implying positive values for x in quadrants 1 and 4. It’s noteworthy that during a blizzard, temperatures can be warmer than expected; some of the coldest snowstorms have temperatures between +5 °F and +18 °F. These numbers are below zero in Celsius, hence the corresponding quadrants depend on the temperature scale used. While Alaska often experiences temperatures well below freezing in either scale, snowfall typically requires the temperature to reach the levels mentioned before occurring. US temperatures are mostly reported in Fahrenheit, while historical data often records in Celsius. I lean towards "Quadrant 1 and 4 only", but one could argue for "1 only" or "4 only" as well.
Let's denote the orbital period of planet X as T and its average distance from the sun as A. For planet Y, let its orbital period be T_1, implying that if planet Y's mean distance from the sun is twice that of planet X:
This indicates that the orbital period for planet Y increases by a factor of 
Answer:
m = - 3
Step-by-step explanation:
a³ + 27 can be recognized as a sum of cubes, which factors generally as
a³ + b³ = (a + b)(a² - ab + b²). Therefore:
a³ + 27
= a³ + 3³
= (a + 3)(a² - 3a + 9).
By comparing a² - 3a + 9 to a² + ma + 9, we find that
m = - 3.
In the case of an equilateral triangle ABC, each angle measures 60 degrees, as the total angle sum in any triangle is 180 degrees, and dividing that by 3 yields 60. Setting this equal to 3x-12, we have 60 = 3x - 12. After adding 12 to both sides, we get 72 = 3x, and dividing 72 by 3 gives us x = 24.66! I hope this clarifies things for you!
