The water level of a certain body of water is changing at a rate of W(t)=3/4cos(4-t/2) inches per hour, where t represents hours since 12 a. m. Part A: Using correct units, explain the meaning of ∫1to10 W(t)dt in terms of the context of this problem.

Part B: Write the integral that represents the number of inches that the water level changes from 7pm to midnight.

Part C: Use your calculator to evaluate your integral from Part B. Explain the meaning of the answer in terms of the context.

Part D: What is the average daily number of inches that the water level changes for this lake?

The answer is below

Step-by-step explanation:

a) The integral means the total change in level of water in inches from 1 am to 10 am. That is the water level change measured in inches between 1 am and 10 am

b) 7 pm is represented as t = 19 hours, while midnight is represented as t = 24 hours, hence the water level change between 7 pm and midnight is:

c) Using casio calculator to evaluate the integral gives:

= 2.54 inches

D) The total daily change in water level = = 0.35 inches

15 units use socratic

step-by-step explanation: 15 units

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~