Answer:
Gender and flavor of ice cream
Step-by-step explanation:
Hi there!

To find the indefinite integral, we must integrate by parts.
Let "u" be the expression most easily differentiated, and "dv" the remaining expression. Take the derivative of "u" and the integral of "dv":
u = 4x
du = 4
dv = cos(2 - 3x)
v = 1/3sin(2 - 3x)
Write into the format:
∫udv = uv - ∫vdu
Thus, utilize the solved for expressions above:
4x · (-1/3sin(2 - 3x)) -∫ 4(1/3sin(2 - 3x))dx
Simplify:
-4x/3 sin(2 - 3x) - ∫ 4/3sin(2 - 3x)dx
Integrate the integral:
∫4/3(sin(2 - 3x)dx
u = 2 - 3x
du = -3dx ⇒ -1/3du = dx
-1/3∫ 4/3(sin(2 - 3x)dx ⇒ -4/9cos(2 - 3x) + C
Combine:

9514 1404 393
Answer:
d = 3√10 ≈ 9.487
Step-by-step explanation:
The distance formula is appropriate.
d = √((x2 -x1)^2 +(y2 -y1)^2)
d = √((-3 -0)^2 +(2 -(-7))^2) = √(9 +81) = √90
d = 3√10
Mixed numbers are fractions with a whole number.
For example, 1 2/4, 2/8, and 7 7/8 are mixed numbers.
Hope it helps