Answer:
Part a. 1400 unit²
Part b 1240 unit²
Part c 1333.33 unit²
Step-by-step explanation:
The given function is 20·x - x²
Part a.
The dimensions of the five rectangles are;
20 × 20 + 20 × 18 + 20 × 16 + 20 × 10 + 20 × 6 = 1400 unit²
Part b.
The dimensions of the ten rectangles are;
10×20 + 10×18 + 10×16 + 10×16 + 10×14 + 10×12 + 10 × 10 + 10 × 8 + 10 × 6 + 10 ×4 = 1240 unit²
Part c.
To find the area with an infinite number of rectangles, we can use limits similar to integration;
Which gives;
![\int _{0}^{20}\left (20\cdot x - x^{2} \right )dx = \left [\dfrac{20}{2}\cdot x^{2} - \dfrac{x^{3}}{3} \right ]_{0}^{20} = \left [10\cdot x^{2} - \dfrac{x^{3}}{3} \right ]_{0}^{20}](https://tex.z-dn.net/?f=%5Cint%20_%7B0%7D%5E%7B20%7D%5Cleft%20%2820%5Ccdot%20x%20-%20x%5E%7B2%7D%20%20%5Cright%20%29dx%20%3D%20%5Cleft%20%5B%5Cdfrac%7B20%7D%7B2%7D%5Ccdot%20x%5E%7B2%7D%20-%20%5Cdfrac%7Bx%5E%7B3%7D%7D%7B3%7D%20%20%5Cright%20%5D_%7B0%7D%5E%7B20%7D%20%3D%20%5Cleft%20%5B10%5Ccdot%20x%5E%7B2%7D%20-%20%5Cdfrac%7Bx%5E%7B3%7D%7D%7B3%7D%20%20%5Cright%20%5D_%7B0%7D%5E%7B20%7D)
10×20^2 - (20^3)/3 = 4000/3 = 1333.3333
Answer:
the ratios 8/11 and 24/33 are proportional.
Step-by-step explanation:
The shaded region is a parallelogram.
The formula for the area of any parallelogram is
.
The base of the parallelogram is 2 meters long (given).
The height of the parallelogram is 9 meters (do not be fooled by the unnecessary information of 14 meters)
The height is 9 meters because the height has to be perpendicular to the base. Thus, the side length must be 9 meters.
Multiply them together.
The area of the parallelogram is 18 square meters.
Answer:
-31p
Step-by-step explanation:
........
