Answer:
∫ xe³ˣ dx
Step-by-step explanation:
The first integral can be solved with u substitution (u = ln x).
The third integral can be solved with a Pythagorean identity (cot²x = csc²x − 1).
The fourth integral can be solved with a power reduction formula (cos²x = ½ + ½ cos(2x)).
Only the second integral requires integration by parts.
The formula for exponential growth is y=a(1+r)

. Where a is the initial value when time is 0 (100 in this case). r is the growth rate, we can see that the growth is 10%. And x is how much time has passed, we want to find out how many trucks after 9 years.
So we would plug the values in to get y=100(1+.1)

. Solving this gives us 235.79, so we would round up to 236, and our answer would be 236 trucks registered in the city in year 9.
Edit: The x and the 9 are exponents, the formatting made them look a bit weird.
The number that is its own opposite is zero. Zero is both a positive and a negative number at the same time.
Answer:
33/24 or 11/8, or 1 9/24 or 1 3/8
Step-by-step explanation:
you have to find a common denominator between the two fractions. The least common denominator for 9 and 8 is 24. Since you multiply 9 by 3 to get 24, you multiply 5 by 3 and get 15. You now have the fraction 15/24. Since you multiply 8 by 3 to get 24, you also multiply 6 by 3, which is 18. You now have the fraction 18/24. You add 15/24 and 18/24, and you get 33/24, which can be simplified to 11/8. It can be shown as 1 9/24 as a mixed number, and simplified to 1 3/8.
We will have the following:
*First: We determine the translation rule:
We have that the point went from (3, -4) to (0, -5), thus the translation rule would be:

Second: We apply the translation rule to the other point to determine it's image, that is:

So, the image of the second point is (5, 6).