Answer:
Its is a number that is consecutive duh.
Step-by-step explanation:
To find the rate of change, find the difference of people at the park at each given hour and divide that by the total number of hours in the given time frame.
Early Time interval:
Hour 1 there was 55 people.
Hour 3 there was 135 people.
The rate of change is 135 - 55 / 3-1 = 80/2 = 40 people per hour.
Late time interval:
Hour 3 had 135 people.
Hour 5 had 175 people.
The rate of change is 175 - 135 / 5-3 = 40/2 = 20 people per hour
20 is less than 40, so the late time interval had the smallest rate change.
so 15% off is 149.85 which makes it 849.85 then you add sales tax which is 79.92 and your cost is 929.07
Answer:
a. (24 ln 2 − 7) / 9
b. x tan x + ln|cos x| + C
Step-by-step explanation:
a. ∫₁² x² ln x dx
Integrate by parts.
If u = ln x, then du = 1/x dx.
If dv = x² dx, then v = ⅓ x³.
∫ u dv = uv − ∫ v du
= (ln x) (⅓ x³) − ∫ (⅓ x³) (1/x dx)
= ⅓ x³ ln x − ∫ ⅓ x² dx
= ⅓ x³ ln x − ¹/₉ x³ + C
= ¹/₉ x³ (3 ln x − 1) + C
Evaluate between x=1 and x=2.
[¹/₉ 2³ (3 ln 2 − 1) + C] − [¹/₉ 1³ (3 ln 1 − 1) + C]
⁸/₉ (3 ln 2 − 1) + C + ¹/₉ − C
⁸/₉ (3 ln 2 − 1) + ¹/₉
⁸/₃ ln 2 − ⁸/₉ + ¹/₉
⁸/₃ ln 2 − ⁷/₉
(24 ln 2 − 7) / 9
b. ∫ x sec² x dx
Integrate by parts.
If u = x, then du = dx.
If dv = sec² x dx, then v = tan x.
∫ u dv = uv − ∫ v du
= x tan x − ∫ tan x dx
= x tan x + ∫ -sin x / cos x dx
= x tan x + ln|cos x| + C
