University:
Purdue University
Course:
MA 15300 | College Algebra
Academic year:

2024
Views:

196

Pages:

3
Author:

Delphinixxc3

Question 1 What is a midpoint Riemann sum? Answer 1 A midpoint Riemann sum estimates the area under a curve by dividing the interval into equal subintervals and using the midpoints of these subintervals to determine the heights of rectangles. Example: For the interval [1,3] and 𝑛 = 4 n=4, we have: Δ 𝑥 = 3 − 1 4 = 1 2 Δx= 4 3−1 = 2 1 Subintervals: [ 1 , 3 2 ] , [ 3 2 , 2 ] , [ 2 , 5 2 ] , [ 5 2 , 3 ] [1, 2 3 ],[ 2 3 ,2],[2, 2 5 ],[ 2 5 ,3] The midpoints are: 𝑚 1 = 1 + 3 2 2 , 𝑚 2 = 3 2 + 2 2 , 𝑚 3 = 2 + 5 2 2 , 𝑚 4 = 5 2 + 3 2 m 1 = 2 1+ 2 3 , m 2 = 2 2 3 +2 , m 3 = 2 2+ 2 5 , m 4 = 2 2 5 +3 The sum is: Δ 𝑥 [ 𝑓 ( 𝑚 1 ) + 𝑓 ( 𝑚 2 ) + 𝑓 ( 𝑚 3 ) + 𝑓 ( 𝑚 4 ) ] Δx[f(m 1 )+f(m 2 )+f(m 3 )+f(m 4 )] Question 2 How do you write 1 6 6 1 as a percent? Answer 1 To write 1 6 6 1 as a percent: 1 6 × 100 = 16.67 % 6 1 ×100=16.67% Therefore, 1 6 6 1 is approximately 16.67%. Question 3 What is 3 2 2 3 as a fraction? Answer 1 3 2 2 3 is an improper fraction. It can be written as the mixed number: 1 1 2 1 2 1 Question 4 How do you convert 7 15 15 7 into a decimal and percent? Answer 1 To convert 7 15 15 7 to a decimal: 7 ÷ 15 = 0.4667 7÷15=0.4667 To convert it to a percent, multiply by 100: 0.4667 × 100 = 46.67 % 0.4667×100=46.67% Thus, 7 15 = 0.4667 15 7 =0.4667 or 46.67%. Question 5 How do you change 0.2 into a fraction? Answer 1 Explanation: Think of 0.2 as 2 10 10 2 , then simplify: 2 10 = 1 5 10 2 = 5 1 Thus, 0.2 = 1 5 0.2= 5 1 . Answer 2 Since 0.2 means "two-tenths," it can be directly written as 2 10 10 2 , which simplifies to 1 5 5 1 .