Given h(x) = -3x + 2, solve for x when h(x) = -4.
1 answer:
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Answer:
See below.
Step-by-step explanation:
1)
For Ben's social media post, we are told that it was initially shared to only 2 people. However, each of those shares it with 3 people. In other words, Ben's post triples every day. This means that the rate of growth is 3. Thus, Ben's post as an exponential function is:
The 2 represents the initial amount at day 0, and the 3 represents the rate at which the post grows each day.
2)
Similarly, Carter's post was originally sent to 10 people. However, each of the 10 shares it with two others. Therefore, it doubles each day. Thus, the rate is 2. So, Carter's exponential function is:
The 10 represents the initial amount while the 2 represents the rate.
3)
I've use Desmos to graph the functions. Refer to the picture attached. Red is Amber, blue is Ben, and green is Carter.
4)
To find out the number of shares each student's post will receive on day 3 and day 10, simply plug the numbers into the functions. Therefore:
For Amber:
Day 3:
Day 10:
For Ben:
Day 3:
Day 10:
And for Carter:
Day 3:
Day 10:
5)
Amber's new graph of:
will be a shifted version of her original graph. The new graph will be shifted upwards by 45 units. However, since the 45 is not affected by the x in any way, the change will be minuscule. For instance, her number of shares on day 10 of the old graph is 3,145,728. Even with the additional 45, it will just be: 3,145,773. With enough days, the additional number becomes trivial.
6)
On the 10th day, Amber's post was shared almost 3 million times, while Ben's was shared "only" 118,098 times and Carter's with 10,240. Undoubtedly, Amber's post was the fastest.
7)
If you want to most shares as possible, choose Amber with fewer friends initially but more shares. This is because the exponential potential of a number even just a bit higher is insane. For instance, 3^10 (Ben's rate at 10th day) is only 59,049 while Amber's rate will be 4^10 which is 1,048,576. Amber's number is almost 18 times higher than Ben's. Even if Ben's initial number was say 1,000 or even 1,000,000, Amber would catch up rather quickly. Therefore, the rate is the quintessential part of an exponential growth function.
Answer:
Second statement is true.
The lengths 7, 40 and 41 can not be sides of a right triangle. The lengths 12, 16, and 20 can be sides of a right triangle.
Step-by-step explanation:
for first part of statement
The lengths 7, 40 and 41 can not be sides of a right triangle.
If the square of long side is equal to the sum of square of other two sides
then the given length can be sides of a right triangle.
Check the given length by Pythagoras Theorem.
----------(1)
Let and
and
Put all the value in equation 1.
Therefore, the square of long side is not equal to the sum of square of other two sides, So given lengths 7, 40 and 41 can not be sides of a right triangle.
for second part of statement.
The lengths 12, 16, and 20 can be sides of a right triangle.
Check the given length by Pythagoras Theorem.
Let and
and
Therefore, the square of long side is equal to the sum of square of other two sides, So given the lengths 12, 16, and 20 can be sides of a right triangle.
Therefore, The lengths 7, 40 and 41 can not be sides of a right triangle. The lengths 12, 16, and 20 can be sides of a right triangle.
Answer:
Step-by-step explanation:
is in the third quadrant
To find the reference angle subtract π from it, that is
reference angle = - π =