Step-by-step explanation:
A left Riemann sum approximates a definite integral as:

Given ∫₂⁸ cos(x²) dx:
a = 2, b = 8, and f(x) = cos(x²)
Therefore, Δx = 6/n and x = 2 + (6/n) (k − 1).
Plugging into the sum:
∑₁ⁿ cos((2 + (6/n) (k − 1))²) (6/n)
Therefore, the answer is C. Notice that answer D would be a right Riemann sum rather than a left (uses k instead of k−1).
Answer:
y = (x - 3)² - 4 Vertex form
(3, -4) Vertex
Step-by-step explanation:
f(x) = x² - 6x + 5
Complete the square
y = (x - 3)² + 5 - (-3)²
y = (x - 3)² + 5 - 9
y = (x - 3)² - 4 Vertex form
(3, -4) Vertex
Hello,
As 4²+(5/2)²=22.25=89/4 (Pytagorean theorem)
Perimeter of the triangle =2*√89 /2 +5 =5+√89
Lateral area: 18*(5+√89)
Total area= 90+18√89+ 4*5/2 *2 =110+18√89 ≈279.811..(ft²)